Abstract group data - 672.729

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '24.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 84, 'aut_gen_orders': [6, 14, 4, 2, 2, 2, 2], 'aut_gens': [[1, 2, 24], [1, 2, 408], [1, 482, 360], [169, 170, 24], [349, 2, 24], [1, 14, 24], [1, 2, 372], [1, 338, 24]], 'aut_group': '5376.cw', 'aut_hash': 9208162814746553245, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 5376, 'aut_permdeg': 19, 'aut_perms': [83608870017265016, 51703565934049238, 3231441683620089, 1004449407068557, 189707034989670, 294377391273870, 106015508147670], 'aut_phi_ratio': 28.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 2, 1], [2, 4, 2, 1], [3, 7, 1, 2], [4, 2, 2, 2], [4, 4, 2, 1], [6, 7, 1, 6], [6, 14, 2, 2], [6, 28, 2, 2], [7, 3, 2, 1], [12, 14, 2, 4], [12, 28, 2, 2], [14, 3, 2, 3], [14, 6, 4, 1], [14, 12, 4, 1], [28, 6, 4, 2], [28, 12, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'F_7\\times C_2^4.C_2^3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '64.267', 'autcent_hash': 267, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': '84.7', 'autcentquo_hash': 7, 'autcentquo_nilpotent': False, 'autcentquo_order': 84, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [2, 4, 2], [3, 7, 2], [4, 2, 4], [4, 4, 2], [6, 7, 6], [6, 14, 4], [6, 28, 4], [7, 3, 2], [12, 14, 8], [12, 28, 4], [14, 3, 6], [14, 6, 4], [14, 12, 4], [28, 6, 8], [28, 12, 4]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '168.51', 'commutator_count': 1, 'commutator_label': '28.4', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '7.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 729, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['21.1', 1], ['32.28', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [2, 4, 1, 2], [3, 7, 2, 1], [4, 2, 1, 2], [4, 2, 2, 1], [4, 4, 1, 2], [6, 7, 2, 3], [6, 14, 2, 2], [6, 28, 2, 2], [7, 3, 2, 1], [12, 14, 2, 2], [12, 14, 4, 1], [12, 28, 2, 2], [14, 3, 2, 3], [14, 6, 2, 2], [14, 12, 2, 2], [28, 6, 2, 2], [28, 6, 4, 1], [28, 12, 2, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 17472, 'exponent': 84, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '168.51', 'hash': 729, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 42, 'inner_gen_orders': [2, 6, 14], 'inner_gens': [[1, 350, 360], [349, 2, 264], [337, 434, 24]], 'inner_hash': 51, 'inner_nilpotent': False, 'inner_order': 168, 'inner_split': False, 'inner_tex': 'C_2\\times C_{14}:C_6', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 24], [2, 18], [3, 16], [6, 12]], 'label': '672.729', 'linC_count': 1728, 'linC_degree': 7, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 32, 'linQ_dim': 10, 'linQ_dim_count': 32, 'linR_count': 32, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': '(D4*C14):C6', 'ngens': 7, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 36, 'number_characteristic_subgroups': 36, 'number_conjugacy_classes': 70, 'number_divisions': 39, 'number_normal_subgroups': 72, 'number_subgroup_autclasses': 120, 'number_subgroup_classes': 188, 'number_subgroups': 740, 'old_label': None, 'order': 672, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 15], [3, 14], [4, 16], [6, 210], [7, 6], [12, 224], [14, 90], [28, 96]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 504, 4], 'outer_gens': [[349, 2, 24], [337, 2, 24], [1, 2, 372], [169, 170, 24], [1, 2, 408]], 'outer_group': '32.51', 'outer_hash': 51, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 10, 'outer_perms': [362880, 5040, 120, 6, 1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [4, 5], [6, 8], [8, 1], [12, 4], [24, 1]], 'representations': {'PC': {'code': 432750340209612002826053226821748803239044006933629405, 'gens': [1, 2, 5], 'pres': [7, -2, -2, -2, -3, -2, -2, -7, 4901, 36, 58, 12604, 4631, 1908, 2650, 102, 11100, 4555, 2798, 124, 9421, 2372, 2379]}, 'GLZN': {'d': 2, 'p': 56, 'gens': [1580569, 177185, 2285373, 9748283, 178375, 176065, 4831063]}, 'Perm': {'d': 15, 'gens': [87660961920, 187297608960, 186810986880, 148, 87657292800, 87668945280, 903]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '(D_4\\times C_{14}):C_6', 'transitive_degree': 112, '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: 139964999
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 729, 'group_order': 672, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 139965010
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 729, 'group_order': 672, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 348, 'size': 1}
  • id: 139965021
    {'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 729, 'group_order': 672, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 336, 'size': 1}
  • id: 139965032
    {'aut_label': '2C', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 729, 'group_order': 672, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 12, 'size': 1}
  • id: 139965043
    {'aut_label': '2D', 'centralizer': '2.b1.a1', 'counter': 5, 'group_counter': 729, 'group_order': 672, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 523, 'size': 2}
  • id: 139965054
    {'aut_label': '2D', 'centralizer': '2.b1.a1', 'counter': 6, 'group_counter': 729, 'group_order': 672, 'label': '2E', 'order': 2, 'powers': [1, 6, 6], 'representative': 187, 'size': 2}
  • id: 139965065
    {'aut_label': '2F', 'centralizer': '4.b1.a1', 'counter': 7, 'group_counter': 729, 'group_order': 672, 'label': '2F', 'order': 2, 'powers': [1, 7, 7], 'representative': 1, 'size': 4}
  • id: 139965067
    {'aut_label': '2F', 'centralizer': '4.b1.b1', 'counter': 8, 'group_counter': 729, 'group_order': 672, 'label': '2G', 'order': 2, 'powers': [1, 8, 8], 'representative': 505, 'size': 4}
  • id: 139965068
    {'aut_label': '3A1', 'centralizer': '7.a1.a1', 'counter': 9, 'group_counter': 729, 'group_order': 672, 'label': '3A1', 'order': 3, 'powers': [10, 1, 9], 'representative': 488, 'size': 7}
  • id: 139965000
    {'aut_label': '3A-1', 'centralizer': '7.a1.a1', 'counter': 10, 'group_counter': 729, 'group_order': 672, 'label': '3A-1', 'order': 3, 'powers': [9, 1, 10], 'representative': 400, 'size': 7}
  • id: 139965001
    {'aut_label': '4A', 'centralizer': '2.b1.a1', 'counter': 11, 'group_counter': 729, 'group_order': 672, 'label': '4A', 'order': 4, 'powers': [3, 11, 11], 'representative': 168, 'size': 2}
  • id: 139965002
    {'aut_label': '4A', 'centralizer': '2.b1.a1', 'counter': 12, 'group_counter': 729, 'group_order': 672, 'label': '4B', 'order': 4, 'powers': [3, 12, 12], 'representative': 180, 'size': 2}
  • id: 139965003
    {'aut_label': '4C1', 'centralizer': '2.b1.a1', 'counter': 13, 'group_counter': 729, 'group_order': 672, 'label': '4C1', 'order': 4, 'powers': [3, 14, 14], 'representative': 355, 'size': 2}
  • id: 139965004
    {'aut_label': '4C1', 'centralizer': '2.b1.a1', 'counter': 14, 'group_counter': 729, 'group_order': 672, 'label': '4C-1', 'order': 4, 'powers': [3, 13, 13], 'representative': 19, 'size': 2}
  • id: 139965005
    {'aut_label': '4D', 'centralizer': '4.e1.a1', 'counter': 15, 'group_counter': 729, 'group_order': 672, 'label': '4D', 'order': 4, 'powers': [4, 15, 15], 'representative': 18, 'size': 4}
  • id: 139965006
    {'aut_label': '4D', 'centralizer': '4.e1.b1', 'counter': 16, 'group_counter': 729, 'group_order': 672, 'label': '4E', 'order': 4, 'powers': [4, 16, 16], 'representative': 522, 'size': 4}
  • id: 139965007
    {'aut_label': '6A1', 'centralizer': '7.a1.a1', 'counter': 17, 'group_counter': 729, 'group_order': 672, 'label': '6A1', 'order': 6, 'powers': [9, 2, 17], 'representative': 52, 'size': 7}
  • id: 139965008
    {'aut_label': '6A-1', 'centralizer': '7.a1.a1', 'counter': 18, 'group_counter': 729, 'group_order': 672, 'label': '6A-1', 'order': 6, 'powers': [10, 2, 18], 'representative': 68, 'size': 7}
  • id: 139965009
    {'aut_label': '6B1', 'centralizer': '7.a1.a1', 'counter': 19, 'group_counter': 729, 'group_order': 672, 'label': '6B1', 'order': 6, 'powers': [9, 3, 19], 'representative': 640, 'size': 7}
  • id: 139965011
    {'aut_label': '6B-1', 'centralizer': '7.a1.a1', 'counter': 20, 'group_counter': 729, 'group_order': 672, 'label': '6B-1', 'order': 6, 'powers': [10, 3, 20], 'representative': 536, 'size': 7}
  • id: 139965012
    {'aut_label': '6C1', 'centralizer': '7.a1.a1', 'counter': 21, 'group_counter': 729, 'group_order': 672, 'label': '6C1', 'order': 6, 'powers': [10, 4, 21], 'representative': 596, 'size': 7}
  • id: 139965013
    {'aut_label': '6C-1', 'centralizer': '7.a1.a1', 'counter': 22, 'group_counter': 729, 'group_order': 672, 'label': '6C-1', 'order': 6, 'powers': [9, 4, 22], 'representative': 196, 'size': 7}
  • id: 139965014
    {'aut_label': '6D1', 'centralizer': '14.b1.a1', 'counter': 23, 'group_counter': 729, 'group_order': 672, 'label': '6D1', 'order': 6, 'powers': [10, 5, 23], 'representative': 27, 'size': 14}
  • id: 139965015
    {'aut_label': '6D-1', 'centralizer': '14.b1.a1', 'counter': 24, 'group_counter': 729, 'group_order': 672, 'label': '6D-1', 'order': 6, 'powers': [9, 5, 24], 'representative': 35, 'size': 14}
  • id: 139965016
    {'aut_label': '6D1', 'centralizer': '14.b1.a1', 'counter': 25, 'group_counter': 729, 'group_order': 672, 'label': '6E1', 'order': 6, 'powers': [10, 6, 25], 'representative': 75, 'size': 14}
  • id: 139965017
    {'aut_label': '6D-1', 'centralizer': '14.b1.a1', 'counter': 26, 'group_counter': 729, 'group_order': 672, 'label': '6E-1', 'order': 6, 'powers': [9, 6, 26], 'representative': 83, 'size': 14}
  • id: 139965018
    {'aut_label': '6F1', 'centralizer': '28.b1.a1', 'counter': 27, 'group_counter': 729, 'group_order': 672, 'label': '6F1', 'order': 6, 'powers': [9, 7, 27], 'representative': 5, 'size': 28}
  • id: 139965019
    {'aut_label': '6F-1', 'centralizer': '28.b1.a1', 'counter': 28, 'group_counter': 729, 'group_order': 672, 'label': '6F-1', 'order': 6, 'powers': [10, 7, 28], 'representative': 21, 'size': 28}
  • id: 139965020
    {'aut_label': '6F1', 'centralizer': '28.b1.b1', 'counter': 29, 'group_counter': 729, 'group_order': 672, 'label': '6G1', 'order': 6, 'powers': [9, 8, 29], 'representative': 269, 'size': 28}
  • id: 139965022
    {'aut_label': '6F-1', 'centralizer': '28.b1.b1', 'counter': 30, 'group_counter': 729, 'group_order': 672, 'label': '6G-1', 'order': 6, 'powers': [10, 8, 30], 'representative': 477, 'size': 28}
  • id: 139965023
    {'aut_label': '7A1', 'centralizer': '3.a1.a1', 'counter': 31, 'group_counter': 729, 'group_order': 672, 'label': '7A1', 'order': 7, 'powers': [31, 32, 1], 'representative': 96, 'size': 3}
  • id: 139965024
    {'aut_label': '7A1', 'centralizer': '3.a1.a1', 'counter': 32, 'group_counter': 729, 'group_order': 672, 'label': '7A-1', 'order': 7, 'powers': [32, 31, 1], 'representative': 576, 'size': 3}
  • id: 139965025
    {'aut_label': '12A1', 'centralizer': '14.b1.a1', 'counter': 33, 'group_counter': 729, 'group_order': 672, 'label': '12A1', 'order': 12, 'powers': [19, 11, 33], 'representative': 32, 'size': 14}
  • id: 139965026
    {'aut_label': '12A-1', 'centralizer': '14.b1.a1', 'counter': 34, 'group_counter': 729, 'group_order': 672, 'label': '12A-1', 'order': 12, 'powers': [20, 11, 34], 'representative': 40, 'size': 14}
  • id: 139965027
    {'aut_label': '12A-1', 'centralizer': '14.b1.a1', 'counter': 35, 'group_counter': 729, 'group_order': 672, 'label': '12B1', 'order': 12, 'powers': [20, 12, 35], 'representative': 28, 'size': 14}
  • id: 139965028
    {'aut_label': '12A1', 'centralizer': '14.b1.a1', 'counter': 36, 'group_counter': 729, 'group_order': 672, 'label': '12B-1', 'order': 12, 'powers': [19, 12, 36], 'representative': 44, 'size': 14}
  • id: 139965029
    {'aut_label': '12C1', 'centralizer': '14.b1.a1', 'counter': 37, 'group_counter': 729, 'group_order': 672, 'label': '12C1', 'order': 12, 'powers': [19, 13, 40], 'representative': 3, 'size': 14}
  • id: 139965030
    {'aut_label': '12C-1', 'centralizer': '14.b1.a1', 'counter': 38, 'group_counter': 729, 'group_order': 672, 'label': '12C-1', 'order': 12, 'powers': [20, 14, 39], 'representative': 59, 'size': 14}
  • id: 139965031
    {'aut_label': '12C-1', 'centralizer': '14.b1.a1', 'counter': 39, 'group_counter': 729, 'group_order': 672, 'label': '12C5', 'order': 12, 'powers': [20, 13, 38], 'representative': 11, 'size': 14}
  • id: 139965033
    {'aut_label': '12C1', 'centralizer': '14.b1.a1', 'counter': 40, 'group_counter': 729, 'group_order': 672, 'label': '12C-5', 'order': 12, 'powers': [19, 14, 37], 'representative': 51, 'size': 14}
  • id: 139965034
    {'aut_label': '12D1', 'centralizer': '28.e1.a1', 'counter': 41, 'group_counter': 729, 'group_order': 672, 'label': '12D1', 'order': 12, 'powers': [21, 15, 41], 'representative': 202, 'size': 28}
  • id: 139965035
    {'aut_label': '12D-1', 'centralizer': '28.e1.a1', 'counter': 42, 'group_counter': 729, 'group_order': 672, 'label': '12D-1', 'order': 12, 'powers': [22, 15, 42], 'representative': 590, 'size': 28}
  • id: 139965036
    {'aut_label': '12D1', 'centralizer': '28.e1.b1', 'counter': 43, 'group_counter': 729, 'group_order': 672, 'label': '12E1', 'order': 12, 'powers': [21, 16, 43], 'representative': 94, 'size': 28}
  • id: 139965037
    {'aut_label': '12D-1', 'centralizer': '28.e1.b1', 'counter': 44, 'group_counter': 729, 'group_order': 672, 'label': '12E-1', 'order': 12, 'powers': [22, 16, 44], 'representative': 554, 'size': 28}
  • id: 139965038
    {'aut_label': '14A1', 'centralizer': '3.a1.a1', 'counter': 45, 'group_counter': 729, 'group_order': 672, 'label': '14A1', 'order': 14, 'powers': [31, 46, 2], 'representative': 60, 'size': 3}
  • id: 139965039
    {'aut_label': '14A1', 'centralizer': '3.a1.a1', 'counter': 46, 'group_counter': 729, 'group_order': 672, 'label': '14A-1', 'order': 14, 'powers': [32, 45, 2], 'representative': 156, 'size': 3}
  • id: 139965040
    {'aut_label': '14B1', 'centralizer': '3.a1.a1', 'counter': 47, 'group_counter': 729, 'group_order': 672, 'label': '14B1', 'order': 14, 'powers': [31, 48, 3], 'representative': 48, 'size': 3}
  • id: 139965041
    {'aut_label': '14B1', 'centralizer': '3.a1.a1', 'counter': 48, 'group_counter': 729, 'group_order': 672, 'label': '14B-1', 'order': 14, 'powers': [32, 47, 3], 'representative': 624, 'size': 3}
  • id: 139965042
    {'aut_label': '14C1', 'centralizer': '3.a1.a1', 'counter': 49, 'group_counter': 729, 'group_order': 672, 'label': '14C1', 'order': 14, 'powers': [31, 50, 4], 'representative': 204, 'size': 3}
  • id: 139965044
    {'aut_label': '14C1', 'centralizer': '3.a1.a1', 'counter': 50, 'group_counter': 729, 'group_order': 672, 'label': '14C-1', 'order': 14, 'powers': [32, 49, 4], 'representative': 492, 'size': 3}
  • id: 139965045
    {'aut_label': '14D1', 'centralizer': '6.b1.a1', 'counter': 51, 'group_counter': 729, 'group_order': 672, 'label': '14D1', 'order': 14, 'powers': [31, 52, 5], 'representative': 31, 'size': 6}
  • id: 139965046
    {'aut_label': '14D1', 'centralizer': '6.b1.a1', 'counter': 52, 'group_counter': 729, 'group_order': 672, 'label': '14D-1', 'order': 14, 'powers': [32, 51, 5], 'representative': 127, 'size': 6}
  • id: 139965047
    {'aut_label': '14D1', 'centralizer': '6.b1.a1', 'counter': 53, 'group_counter': 729, 'group_order': 672, 'label': '14E1', 'order': 14, 'powers': [32, 54, 6], 'representative': 79, 'size': 6}
  • id: 139965048
    {'aut_label': '14D1', 'centralizer': '6.b1.a1', 'counter': 54, 'group_counter': 729, 'group_order': 672, 'label': '14E-1', 'order': 14, 'powers': [31, 53, 6], 'representative': 271, 'size': 6}
  • id: 139965049
    {'aut_label': '14F1', 'centralizer': '12.b1.a1', 'counter': 55, 'group_counter': 729, 'group_order': 672, 'label': '14F1', 'order': 14, 'powers': [31, 56, 7], 'representative': 97, 'size': 12}
  • id: 139965050
    {'aut_label': '14F1', 'centralizer': '12.b1.a1', 'counter': 56, 'group_counter': 729, 'group_order': 672, 'label': '14F-1', 'order': 14, 'powers': [32, 55, 7], 'representative': 289, 'size': 12}
  • id: 139965051
    {'aut_label': '14F1', 'centralizer': '12.b1.b1', 'counter': 57, 'group_counter': 729, 'group_order': 672, 'label': '14G1', 'order': 14, 'powers': [31, 58, 8], 'representative': 25, 'size': 12}
  • id: 139965052
    {'aut_label': '14F1', 'centralizer': '12.b1.b1', 'counter': 58, 'group_counter': 729, 'group_order': 672, 'label': '14G-1', 'order': 14, 'powers': [32, 57, 8], 'representative': 121, 'size': 12}
  • id: 139965053
    {'aut_label': '28A1', 'centralizer': '6.b1.a1', 'counter': 59, 'group_counter': 729, 'group_order': 672, 'label': '28A1', 'order': 28, 'powers': [47, 60, 11], 'representative': 24, 'size': 6}
  • id: 139965055
    {'aut_label': '28A1', 'centralizer': '6.b1.a1', 'counter': 60, 'group_counter': 729, 'group_order': 672, 'label': '28A-1', 'order': 28, 'powers': [48, 59, 11], 'representative': 120, 'size': 6}
  • id: 139965056
    {'aut_label': '28A1', 'centralizer': '6.b1.a1', 'counter': 61, 'group_counter': 729, 'group_order': 672, 'label': '28B1', 'order': 28, 'powers': [47, 62, 12], 'representative': 36, 'size': 6}
  • id: 139965057
    {'aut_label': '28A1', 'centralizer': '6.b1.a1', 'counter': 62, 'group_counter': 729, 'group_order': 672, 'label': '28B-1', 'order': 28, 'powers': [48, 61, 12], 'representative': 132, 'size': 6}
  • id: 139965058
    {'aut_label': '28C1', 'centralizer': '6.b1.a1', 'counter': 63, 'group_counter': 729, 'group_order': 672, 'label': '28C1', 'order': 28, 'powers': [47, 64, 14], 'representative': 103, 'size': 6}
  • id: 139965059
    {'aut_label': '28C1', 'centralizer': '6.b1.a1', 'counter': 64, 'group_counter': 729, 'group_order': 672, 'label': '28C-1', 'order': 28, 'powers': [48, 63, 13], 'representative': 307, 'size': 6}
  • id: 139965060
    {'aut_label': '28C1', 'centralizer': '6.b1.a1', 'counter': 65, 'group_counter': 729, 'group_order': 672, 'label': '28C5', 'order': 28, 'powers': [48, 66, 14], 'representative': 295, 'size': 6}
  • id: 139965061
    {'aut_label': '28C1', 'centralizer': '6.b1.a1', 'counter': 66, 'group_counter': 729, 'group_order': 672, 'label': '28C-5', 'order': 28, 'powers': [47, 65, 13], 'representative': 55, 'size': 6}
  • id: 139965062
    {'aut_label': '28D1', 'centralizer': '12.e1.a1', 'counter': 67, 'group_counter': 729, 'group_order': 672, 'label': '28D1', 'order': 28, 'powers': [49, 68, 15], 'representative': 102, 'size': 12}
  • id: 139965063
    {'aut_label': '28D1', 'centralizer': '12.e1.a1', 'counter': 68, 'group_counter': 729, 'group_order': 672, 'label': '28D-1', 'order': 28, 'powers': [50, 67, 15], 'representative': 294, 'size': 12}
  • id: 139965064
    {'aut_label': '28D1', 'centralizer': '12.e1.b1', 'counter': 69, 'group_counter': 729, 'group_order': 672, 'label': '28E1', 'order': 28, 'powers': [49, 70, 16], 'representative': 30, 'size': 12}
  • id: 139965066
    {'aut_label': '28D1', 'centralizer': '12.e1.b1', 'counter': 70, 'group_counter': 729, 'group_order': 672, 'label': '28E-1', 'order': 28, 'powers': [50, 69, 16], 'representative': 126, 'size': 12}
• 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: 12824307
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.1a', '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], 'schur_index': 1}
  • id: 12824318
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.1b', '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], 'schur_index': 1}
  • id: 12824329
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.1c', '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], 'schur_index': 1}
  • id: 12824340
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.1d', '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], 'schur_index': 1}
  • id: 12824341
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.1e', '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], 'schur_index': 1}
  • id: 12824342
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.1f', '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], 'schur_index': 1}
  • id: 12824343
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.1g', '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], 'schur_index': 1}
  • id: 12824344
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.1h', '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], 'schur_index': 1}
  • id: 12824345
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.1i', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'schur_index': 1}
  • id: 12824308
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.1j', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -2, -1, -1, 2, 2, -2, -2, 2, 2, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, -2, 2, -2, -2, -2, 2, 2, 2, 2], 'schur_index': 1}
  • id: 12824309
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.1k', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, 2, -1, -1, -2, -2, 2, 2, -2, 2, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 2, 2, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, -2, -2, -2, -2, -2, 2, -2, 2, 2, 2, 2, 2, -2, -2], 'schur_index': 1}
  • id: 12824310
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.1l', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, -2, -1, -1, -2, -2, 2, 2, 2, -2, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 2, 2, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 2, 2, -2, -2, -2, 2, -2, 2, 2, 2, -2, -2, 2, 2], 'schur_index': 1}
  • id: 12824311
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.1m', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, 2, -1, -1, 2, 2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 2, 2, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, -2, 2, -2, -2, -2, -2, -2, -2, -2], 'schur_index': 1}
  • id: 12824312
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.1n', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -2, -2, -1, -1, 2, 2, 2, 2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2], 'schur_index': 1}
  • id: 12824313
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.1o', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -2, 2, -1, -1, -2, -2, -2, -2, 2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2], 'schur_index': 1}
  • id: 12824314
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.1p', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, -2, -1, -1, -2, -2, -2, -2, -2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, -2, -2], 'schur_index': 1}
  • id: 12824315
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.2a', '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, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, -2, 2, 0, 0, 0, -2, 2, 0, 0, 0, 0, -2, -2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12824316
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.2b', '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, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, -2, 0, 0, 0, 2, -2, 0, 0, 0, 0, -2, -2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12824317
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 2, 2, 2, -2, -2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -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], 'schur_index': 1}
  • id: 12824319
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 2, 2, -2, 2, 2, -2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -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], 'schur_index': 1}
  • id: 12824320
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.2e', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 4, 4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12824321
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.2f', 'multiplicity': 2, 'nt': [12, 14], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, -2, -2, -4, 4, 0, 0, 0, 0, 2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 2, -2, 0, 0, 0, 2, -2, 0, 0, 0, 0, -4, -4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12824322
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.2g', 'multiplicity': 2, 'nt': [12, 14], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, -2, -2, 4, -4, 0, 0, 0, 0, 2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, -2, 2, 0, 0, 0, -2, 2, 0, 0, 0, 0, -4, -4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12824323
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.2h', 'multiplicity': 2, 'nt': [12, 14], 'qdim': 4, 'qvalues': [4, 4, -4, -4, -4, 4, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, -2, 2, 2, -2, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 4, 4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12824324
    {'cdim': 2, 'counter': 25, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.2i', 'multiplicity': 2, 'nt': [12, 14], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, 2, -2, -2, 2, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 4, 4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12824326
    {'cdim': 3, 'counter': 27, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.3a', 'multiplicity': 2, 'nt': [7, 3], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12824327
    {'cdim': 3, 'counter': 28, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.3b', 'multiplicity': 2, 'nt': [14, 5], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -6, -6, -6, -6, 0, 0, 6, 6, -6, -6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12824328
    {'cdim': 3, 'counter': 29, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.3c', 'multiplicity': 2, 'nt': [14, 5], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -6, -6, -6, 6, 0, 0, -6, -6, 6, 6, -6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 12824330
    {'cdim': 3, 'counter': 30, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.3d', 'multiplicity': 2, 'nt': [14, 5], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -6, -6, 6, -6, 0, 0, -6, -6, 6, 6, 6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 12824331
    {'cdim': 3, 'counter': 31, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.3e', 'multiplicity': 2, 'nt': [14, 5], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -6, -6, 6, 6, 0, 0, 6, 6, -6, -6, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12824332
    {'cdim': 3, 'counter': 32, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.3f', 'multiplicity': 2, 'nt': [14, 5], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, 6, -6, -6, 0, 0, 6, 6, 6, 6, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12824333
    {'cdim': 3, 'counter': 33, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.3g', 'multiplicity': 2, 'nt': [14, 5], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, 6, -6, 6, 0, 0, -6, -6, -6, -6, 6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 12824334
    {'cdim': 3, 'counter': 34, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.3h', 'multiplicity': 2, 'nt': [14, 5], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, 6, 6, -6, 0, 0, -6, -6, -6, -6, -6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 12824325
    {'cdim': 2, 'counter': 26, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.2j', 'multiplicity': 4, 'nt': [24, 17], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, -4, -4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, -8, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12824335
    {'cdim': 6, 'counter': 35, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.6a', 'multiplicity': 2, 'nt': [28, 22], 'qdim': 12, 'qvalues': [12, -12, -12, 12, 0, 0, 0, 0, 0, 0, -12, 12, 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, 0, 0, 0, 0, 2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12824336
    {'cdim': 6, 'counter': 36, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.6b', 'multiplicity': 2, 'nt': [28, 22], 'qdim': 12, 'qvalues': [12, -12, -12, 12, 0, 0, 0, 0, 0, 0, 12, -12, 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, 0, 0, 0, 0, 2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12824337
    {'cdim': 6, 'counter': 37, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.6c', 'multiplicity': 2, 'nt': [28, 22], 'qdim': 12, 'qvalues': [12, 12, -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, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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], 'schur_index': 1}
  • id: 12824338
    {'cdim': 6, 'counter': 38, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.6d', 'multiplicity': 2, 'nt': [28, 22], 'qdim': 12, 'qvalues': [12, 12, -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, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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], 'schur_index': 1}
  • id: 12824339
    {'cdim': 6, 'counter': 39, 'faithful': False, 'group': '672.729', 'group_order': 672, 'image': None, 'label': '672.729.6e', 'multiplicity': 4, 'nt': [56, 0], 'qdim': 24, 'qvalues': [24, -24, 24, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 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, 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: 29680003
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 672, 'label': '672.729.1a', '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]]]}
  • id: 29680014
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 336, 'label': '672.729.1b', '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]]]}
  • id: 29680025
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.b1', 'kernel_order': 336, 'label': '672.729.1c', '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]]]}
  • id: 29680036
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 336, 'label': '672.729.1d', '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]]]}
  • id: 29680047
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 336, 'label': '672.729.1e', '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]]]}
  • id: 29680058
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 336, 'label': '672.729.1f', '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]]]}
  • id: 29680069
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.b1', 'kernel_order': 336, 'label': '672.729.1g', '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]]]}
  • id: 29680071
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 336, 'label': '672.729.1h', '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]]]}
  • id: 29680072
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 9, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 224, 'label': '672.729.1i1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 29680004
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 10, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 224, 'label': '672.729.1i2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 29680005
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 11, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1.a1', 'kernel_order': 112, 'label': '672.729.1j1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[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: 29680006
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 12, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1.a1', 'kernel_order': 112, 'label': '672.729.1j2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[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: 29680007
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 13, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.b1', 'kernel_order': 112, 'label': '672.729.1k1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 29680008
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 14, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.b1', 'kernel_order': 112, 'label': '672.729.1k2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, 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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 29680009
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 15, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.a1', 'kernel_order': 112, 'label': '672.729.1l1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, 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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-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: 29680010
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 16, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.a1', 'kernel_order': 112, 'label': '672.729.1l2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, 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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-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: 29680011
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 17, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1.a1', 'kernel_order': 112, 'label': '672.729.1m1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 29680012
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 18, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1.a1', 'kernel_order': 112, 'label': '672.729.1m2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 29680013
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 19, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.a1', 'kernel_order': 112, 'label': '672.729.1n1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[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: 29680015
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 20, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.a1', 'kernel_order': 112, 'label': '672.729.1n2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[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: 29680016
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 21, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.b1', 'kernel_order': 112, 'label': '672.729.1o1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 29680017
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 22, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.b1', 'kernel_order': 112, 'label': '672.729.1o2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, 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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 29680018
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 23, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 112, 'label': '672.729.1p1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, 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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-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: 29680019
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 24, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 112, 'label': '672.729.1p2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, 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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-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: 29680020
    {'center': '4.c1.a1', 'center_index': 4, 'center_order': 168, 'counter': 25, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.b1', 'kernel_order': 84, 'label': '672.729.2a', '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]], [[2, 0]], [[2, 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]], [[0, 0]], [[-2, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29680021
    {'center': '4.c1.a1', 'center_index': 4, 'center_order': 168, 'counter': 26, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.a1', 'kernel_order': 84, 'label': '672.729.2b', '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]], [[2, 0]], [[2, 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]], [[0, 0]], [[2, 0]], [[-2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29680022
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 168, 'counter': 27, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.c1.b1', 'kernel_order': 84, 'label': '672.729.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 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]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 29680023
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 168, 'counter': 28, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.c1.a1', 'kernel_order': 84, 'label': '672.729.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 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]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 29680024
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 168, 'counter': 29, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 42, 'label': '672.729.2e1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[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]], [[2, 0]], [[2, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[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]], [[-2, 1]], [[0, 0]], [[2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29680026
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 168, 'counter': 30, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 42, 'label': '672.729.2e2', 'nt': [8, 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]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[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]], [[2, 0]], [[2, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[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]], [[2, 1]], [[0, 0]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29680027
    {'center': '4.c1.a1', 'center_index': 4, 'center_order': 168, 'counter': 31, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1.b1', 'kernel_order': 28, 'label': '672.729.2f1', 'nt': [12, 14], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[2, -1]], [[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]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29680028
    {'center': '4.c1.a1', 'center_index': 4, 'center_order': 168, 'counter': 32, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1.b1', 'kernel_order': 28, 'label': '672.729.2f2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, -1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[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]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29680029
    {'center': '4.c1.a1', 'center_index': 4, 'center_order': 168, 'counter': 33, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1.a1', 'kernel_order': 28, 'label': '672.729.2g1', 'nt': [12, 14], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[-2, -1]], [[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]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29680030
    {'center': '4.c1.a1', 'center_index': 4, 'center_order': 168, 'counter': 34, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1.a1', 'kernel_order': 28, 'label': '672.729.2g2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, -1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[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]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29680031
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 168, 'counter': 35, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1.b1', 'kernel_order': 28, 'label': '672.729.2h1', 'nt': [12, 14], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[2, -1]], [[2, 1]], [[2, -1]], [[-2, -1]], [[-2, 1]], [[2, 1]], [[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]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 29680032
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 168, 'counter': 36, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1.b1', 'kernel_order': 28, 'label': '672.729.2h2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[2, 1]], [[2, -1]], [[2, 1]], [[-2, 1]], [[-2, -1]], [[2, -1]], [[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]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 29680033
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 168, 'counter': 37, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1.a1', 'kernel_order': 28, 'label': '672.729.2i1', 'nt': [12, 14], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[2, -1]], [[2, 1]], [[-2, -1]], [[2, -1]], [[2, 1]], [[-2, 1]], [[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]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 29680034
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 168, 'counter': 38, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1.a1', 'kernel_order': 28, 'label': '672.729.2i2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[2, 1]], [[2, -1]], [[-2, 1]], [[2, 1]], [[2, -1]], [[-2, -1]], [[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]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 29680035
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 168, 'counter': 39, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '48.47', 'image_order': 48, 'indicator': 0, 'kernel': '48.a1.a1', 'kernel_order': 14, 'label': '672.729.2j1', 'nt': [24, 17], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 4]], [[0, 0]], [[0, 0]], [[-2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 2]], [[-2, 4]], [[2, 2]], [[2, 2]], [[-2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 5]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 5]], [[-2, 1]], [[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]], [[-2, 3]], [[0, 0]], [[2, 3]], [[2, 3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29680037
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 168, 'counter': 40, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '48.47', 'image_order': 48, 'indicator': 0, 'kernel': '48.a1.a1', 'kernel_order': 14, 'label': '672.729.2j2', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 2]], [[0, 0]], [[0, 0]], [[2, 3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 4]], [[2, 2]], [[-2, 4]], [[-2, 4]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[-2, 5]], [[2, 1]], [[2, 5]], [[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]], [[2, 3]], [[0, 0]], [[-2, 3]], [[-2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29680038
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 168, 'counter': 41, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '48.47', 'image_order': 48, 'indicator': 0, 'kernel': '48.a1.a1', 'kernel_order': 14, 'label': '672.729.2j3', 'nt': [24, 17], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 4]], [[0, 0]], [[0, 0]], [[2, 3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 2]], [[-2, 4]], [[2, 2]], [[2, 2]], [[-2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 5]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 5]], [[2, 1]], [[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]], [[2, 3]], [[0, 0]], [[-2, 3]], [[-2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29680039
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 168, 'counter': 42, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '48.47', 'image_order': 48, 'indicator': 0, 'kernel': '48.a1.a1', 'kernel_order': 14, 'label': '672.729.2j4', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 2]], [[0, 0]], [[0, 0]], [[-2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 4]], [[2, 2]], [[-2, 4]], [[-2, 4]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[2, 5]], [[-2, 1]], [[-2, 5]], [[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]], [[-2, 3]], [[0, 0]], [[2, 3]], [[2, 3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29680040
    {'center': '21.a1.a1', 'center_index': 21, 'center_order': 32, 'counter': 43, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '21.1', 'image_order': 21, 'indicator': 0, 'kernel': '21.a1.a1', 'kernel_order': 32, 'label': '672.729.3a1', 'nt': [7, 3], 'q_character': None, 'values': [[[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]], [[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]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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, 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, 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, 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: 29680041
    {'center': '21.a1.a1', 'center_index': 21, 'center_order': 32, 'counter': 44, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '21.1', 'image_order': 21, 'indicator': 0, 'kernel': '21.a1.a1', 'kernel_order': 32, 'label': '672.729.3a2', 'nt': [7, 2], 'q_character': None, 'values': [[[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]], [[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]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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, 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, 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, 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: 29680042
    {'center': '21.a1.a1', 'center_index': 21, 'center_order': 32, 'counter': 45, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.e1.a1', 'kernel_order': 16, 'label': '672.729.3b1', 'nt': [14, 5], 'q_character': None, 'values': [[[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]], [[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]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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, 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, 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, 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: 29680043
    {'center': '21.a1.a1', 'center_index': 21, 'center_order': 32, 'counter': 46, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.e1.a1', 'kernel_order': 16, 'label': '672.729.3b2', 'nt': [14, 2], 'q_character': None, 'values': [[[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]], [[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]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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, 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, 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, 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: 29680044
    {'center': '21.a1.a1', 'center_index': 21, 'center_order': 32, 'counter': 47, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.c1.b1', 'kernel_order': 16, 'label': '672.729.3c1', 'nt': [14, 5], 'q_character': None, 'values': [[[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]], [[-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]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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, 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, 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, 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: 29680045
    {'center': '21.a1.a1', 'center_index': 21, 'center_order': 32, 'counter': 48, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.c1.b1', 'kernel_order': 16, 'label': '672.729.3c2', 'nt': [14, 2], 'q_character': None, 'values': [[[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]], [[-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]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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, 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, 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, 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: 29680046
    {'center': '21.a1.a1', 'center_index': 21, 'center_order': 32, 'counter': 49, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.c1.a1', 'kernel_order': 16, 'label': '672.729.3d1', 'nt': [14, 5], 'q_character': None, 'values': [[[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]], [[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]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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, 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, 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, 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: 29680048
    {'center': '21.a1.a1', 'center_index': 21, 'center_order': 32, 'counter': 50, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.c1.a1', 'kernel_order': 16, 'label': '672.729.3d2', 'nt': [14, 2], 'q_character': None, 'values': [[[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]], [[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]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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, 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, 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, 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: 29680049
    {'center': '21.a1.a1', 'center_index': 21, 'center_order': 32, 'counter': 51, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.d1.a1', 'kernel_order': 16, 'label': '672.729.3e1', 'nt': [14, 5], 'q_character': None, 'values': [[[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]], [[-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]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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, 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, 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, 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: 29680050
    {'center': '21.a1.a1', 'center_index': 21, 'center_order': 32, 'counter': 52, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.d1.a1', 'kernel_order': 16, 'label': '672.729.3e2', 'nt': [14, 2], 'q_character': None, 'values': [[[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]], [[-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]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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, 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, 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, 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: 29680051
    {'center': '21.a1.a1', 'center_index': 21, 'center_order': 32, 'counter': 53, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.b1.a1', 'kernel_order': 16, 'label': '672.729.3f1', 'nt': [14, 5], 'q_character': None, 'values': [[[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]], [[-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]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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, 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, 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, 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: 29680052
    {'center': '21.a1.a1', 'center_index': 21, 'center_order': 32, 'counter': 54, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.b1.a1', 'kernel_order': 16, 'label': '672.729.3f2', 'nt': [14, 2], 'q_character': None, 'values': [[[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]], [[-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]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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, 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, 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, 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: 29680053
    {'center': '21.a1.a1', 'center_index': 21, 'center_order': 32, 'counter': 55, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.a1.b1', 'kernel_order': 16, 'label': '672.729.3g1', 'nt': [14, 5], 'q_character': None, 'values': [[[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]], [[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]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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, 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, 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, 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: 29680054
    {'center': '21.a1.a1', 'center_index': 21, 'center_order': 32, 'counter': 56, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.a1.b1', 'kernel_order': 16, 'label': '672.729.3g2', 'nt': [14, 2], 'q_character': None, 'values': [[[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]], [[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]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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, 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, 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, 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: 29680055
    {'center': '21.a1.a1', 'center_index': 21, 'center_order': 32, 'counter': 57, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.a1.a1', 'kernel_order': 16, 'label': '672.729.3h1', 'nt': [14, 5], 'q_character': None, 'values': [[[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]], [[-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]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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, 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, 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, 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: 29680056
    {'center': '21.a1.a1', 'center_index': 21, 'center_order': 32, 'counter': 58, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.a1.a1', 'kernel_order': 16, 'label': '672.729.3h2', 'nt': [14, 2], 'q_character': None, 'values': [[[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]], [[-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]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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, 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, 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, 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: 29680057
    {'center': '84.c1.a1', 'center_index': 84, 'center_order': 8, 'counter': 59, 'cyclotomic_n': 7, 'dim': 6, 'faithful': False, 'field': [2, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '168.20', 'image_order': 168, 'indicator': 0, 'kernel': '168.b1.b1', 'kernel_order': 4, 'label': '672.729.6a1', 'nt': [28, 22], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [2, 1], [2, 2], [2, -3]], [[-2, 1], [-2, 2], [-2, -3]], [[-2, 0], [-2, 1], [-2, 2], [-2, -3]], [[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]], [[2, 0], [2, 1], [2, 2], [2, -3]], [[2, 1], [2, 2], [2, -3]], [[-2, 1], [-2, 2], [-2, -3]], [[0, 0]], [[-2, 0], [-2, 1], [-2, 2], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29680059
    {'center': '84.c1.a1', 'center_index': 84, 'center_order': 8, 'counter': 60, 'cyclotomic_n': 7, 'dim': 6, 'faithful': False, 'field': [2, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '168.20', 'image_order': 168, 'indicator': 0, 'kernel': '168.b1.b1', 'kernel_order': 4, 'label': '672.729.6a2', 'nt': [28, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 2], [-2, -3]], [[2, 0], [2, 1], [2, 2], [2, -3]], [[2, 1], [2, 2], [2, -3]], [[-2, 0], [-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]], [[-2, 1], [-2, 2], [-2, -3]], [[-2, 0], [-2, 1], [-2, 2], [-2, -3]], [[2, 0], [2, 1], [2, 2], [2, -3]], [[0, 0]], [[2, 1], [2, 2], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29680060
    {'center': '84.c1.a1', 'center_index': 84, 'center_order': 8, 'counter': 61, 'cyclotomic_n': 7, 'dim': 6, 'faithful': False, 'field': [2, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '168.20', 'image_order': 168, 'indicator': 0, 'kernel': '168.b1.a1', 'kernel_order': 4, 'label': '672.729.6b1', 'nt': [28, 22], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [2, 1], [2, 2], [2, -3]], [[-2, 1], [-2, 2], [-2, -3]], [[-2, 0], [-2, 1], [-2, 2], [-2, -3]], [[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]], [[-2, 0], [-2, 1], [-2, 2], [-2, -3]], [[-2, 1], [-2, 2], [-2, -3]], [[2, 1], [2, 2], [2, -3]], [[0, 0]], [[2, 0], [2, 1], [2, 2], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29680061
    {'center': '84.c1.a1', 'center_index': 84, 'center_order': 8, 'counter': 62, 'cyclotomic_n': 7, 'dim': 6, 'faithful': False, 'field': [2, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '168.20', 'image_order': 168, 'indicator': 0, 'kernel': '168.b1.a1', 'kernel_order': 4, 'label': '672.729.6b2', 'nt': [28, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 2], [-2, -3]], [[2, 0], [2, 1], [2, 2], [2, -3]], [[2, 1], [2, 2], [2, -3]], [[-2, 0], [-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]], [[2, 1], [2, 2], [2, -3]], [[2, 0], [2, 1], [2, 2], [2, -3]], [[-2, 0], [-2, 1], [-2, 2], [-2, -3]], [[0, 0]], [[-2, 1], [-2, 2], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29680062
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 8, 'counter': 63, 'cyclotomic_n': 7, 'dim': 6, 'faithful': False, 'field': [2, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '168.20', 'image_order': 168, 'indicator': 0, 'kernel': '168.c1.b1', 'kernel_order': 4, 'label': '672.729.6c1', 'nt': [28, 22], 'q_character': None, 'values': [[[6, 0]], [[6, 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]], [[-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]], [[2, 0], [2, 1], [2, 2], [2, -3]], [[-2, 1], [-2, 2], [-2, -3]], [[2, 0], [2, 1], [2, 2], [2, -3]], [[-2, 1], [-2, 2], [-2, -3]], [[-2, 0], [-2, 1], [-2, 2], [-2, -3]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29680063
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 8, 'counter': 64, 'cyclotomic_n': 7, 'dim': 6, 'faithful': False, 'field': [2, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '168.20', 'image_order': 168, 'indicator': 0, 'kernel': '168.c1.b1', 'kernel_order': 4, 'label': '672.729.6c2', 'nt': [28, 2], 'q_character': None, 'values': [[[6, 0]], [[6, 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]], [[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]], [[-2, 1], [-2, 2], [-2, -3]], [[2, 0], [2, 1], [2, 2], [2, -3]], [[-2, 1], [-2, 2], [-2, -3]], [[2, 0], [2, 1], [2, 2], [2, -3]], [[2, 1], [2, 2], [2, -3]], [[-2, 0], [-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29680064
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 8, 'counter': 65, 'cyclotomic_n': 7, 'dim': 6, 'faithful': False, 'field': [2, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '168.20', 'image_order': 168, 'indicator': 0, 'kernel': '168.c1.a1', 'kernel_order': 4, 'label': '672.729.6d1', 'nt': [28, 22], 'q_character': None, 'values': [[[6, 0]], [[6, 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]], [[-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]], [[2, 0], [2, 1], [2, 2], [2, -3]], [[-2, 1], [-2, 2], [-2, -3]], [[2, 0], [2, 1], [2, 2], [2, -3]], [[-2, 1], [-2, 2], [-2, -3]], [[-2, 0], [-2, 1], [-2, 2], [-2, -3]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29680065
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 8, 'counter': 66, 'cyclotomic_n': 7, 'dim': 6, 'faithful': False, 'field': [2, -1, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '168.20', 'image_order': 168, 'indicator': 0, 'kernel': '168.c1.a1', 'kernel_order': 4, 'label': '672.729.6d2', 'nt': [28, 2], 'q_character': None, 'values': [[[6, 0]], [[6, 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]], [[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]], [[-2, 1], [-2, 2], [-2, -3]], [[2, 0], [2, 1], [2, 2], [2, -3]], [[-2, 1], [-2, 2], [-2, -3]], [[2, 0], [2, 1], [2, 2], [2, -3]], [[2, 1], [2, 2], [2, -3]], [[-2, 0], [-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29680066
    {'center': '84.d1.a1', 'center_index': 84, 'center_order': 8, 'counter': 67, 'cyclotomic_n': 28, 'dim': 6, 'faithful': False, 'field': [4, 0, -3, 0, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '336.167', 'image_order': 336, 'indicator': 0, 'kernel': '336.a1.a1', 'kernel_order': 2, 'label': '672.729.6e1', 'nt': [56, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 7]], [[6, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 2], [-2, 4], [-2, 8]], [[-2, 2], [2, 4], [2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [2, 2], [-2, 4], [-2, 8]], [[-2, 2], [2, 4], [2, 8]], [[2, 0], [-2, 2], [2, 4], [2, 8]], [[2, 2], [-2, 4], [-2, 8]], [[2, 0], [-2, 2], [2, 4], [2, 8]], [[2, 2], [-2, 4], [-2, 8]], [[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, 9], [-2, 11]], [[0, 0]], [[2, 1], [-2, 7], [2, 9], [-2, 11]], [[-2, 1], [-2, 9], [2, 11]], [[-2, 1], [2, 7], [-2, 9], [2, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29680067
    {'center': '84.d1.a1', 'center_index': 84, 'center_order': 8, 'counter': 68, 'cyclotomic_n': 28, 'dim': 6, 'faithful': False, 'field': [4, 0, -3, 0, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '336.167', 'image_order': 336, 'indicator': 0, 'kernel': '336.a1.a1', 'kernel_order': 2, 'label': '672.729.6e2', 'nt': [56, 4], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 7]], [[-6, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [2, 4], [2, 8]], [[-2, 0], [2, 2], [-2, 4], [-2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [2, 4], [2, 8]], [[-2, 0], [2, 2], [-2, 4], [-2, 8]], [[2, 2], [-2, 4], [-2, 8]], [[2, 0], [-2, 2], [2, 4], [2, 8]], [[2, 2], [-2, 4], [-2, 8]], [[2, 0], [-2, 2], [2, 4], [2, 8]], [[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, 7], [2, 9], [-2, 11]], [[0, 0]], [[2, 1], [2, 9], [-2, 11]], [[-2, 1], [2, 7], [-2, 9], [2, 11]], [[-2, 1], [-2, 9], [2, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29680068
    {'center': '84.d1.a1', 'center_index': 84, 'center_order': 8, 'counter': 69, 'cyclotomic_n': 28, 'dim': 6, 'faithful': False, 'field': [4, 0, -3, 0, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '336.167', 'image_order': 336, 'indicator': 0, 'kernel': '336.a1.a1', 'kernel_order': 2, 'label': '672.729.6e3', 'nt': [56, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 7]], [[6, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [2, 4], [2, 8]], [[-2, 0], [2, 2], [-2, 4], [-2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [2, 4], [2, 8]], [[-2, 0], [2, 2], [-2, 4], [-2, 8]], [[2, 2], [-2, 4], [-2, 8]], [[2, 0], [-2, 2], [2, 4], [2, 8]], [[2, 2], [-2, 4], [-2, 8]], [[2, 0], [-2, 2], [2, 4], [2, 8]], [[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, 7], [-2, 9], [2, 11]], [[0, 0]], [[-2, 1], [-2, 9], [2, 11]], [[2, 1], [-2, 7], [2, 9], [-2, 11]], [[2, 1], [2, 9], [-2, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29680070
    {'center': '84.d1.a1', 'center_index': 84, 'center_order': 8, 'counter': 70, 'cyclotomic_n': 28, 'dim': 6, 'faithful': False, 'field': [4, 0, -3, 0, 1], 'group': '672.729', 'group_counter': 729, 'group_order': 672, 'image': None, 'image_isoclass': '336.167', 'image_order': 336, 'indicator': 0, 'kernel': '336.a1.a1', 'kernel_order': 2, 'label': '672.729.6e4', 'nt': [56, 4], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 7]], [[-6, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 2], [-2, 4], [-2, 8]], [[-2, 2], [2, 4], [2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [2, 2], [-2, 4], [-2, 8]], [[-2, 2], [2, 4], [2, 8]], [[2, 0], [-2, 2], [2, 4], [2, 8]], [[2, 2], [-2, 4], [-2, 8]], [[2, 0], [-2, 2], [2, 4], [2, 8]], [[2, 2], [-2, 4], [-2, 8]], [[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, 9], [2, 11]], [[0, 0]], [[-2, 1], [2, 7], [-2, 9], [2, 11]], [[2, 1], [2, 9], [-2, 11]], [[2, 1], [-2, 7], [2, 9], [-2, 11]], [[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: 110520915
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 672, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 42, 'label': '672.729.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.729', 'subgroup_hash': 729, 'subgroup_order': 672, 'subgroup_tex': '(D_4\\times C_{14}):C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110521015
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 336, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.165', 'subgroup_hash': 165, 'subgroup_order': 336, 'subgroup_tex': 'C_2\\times C_{28}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110521026
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 336, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.2.a1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.165', 'subgroup_hash': 165, 'subgroup_order': 336, 'subgroup_tex': 'C_2\\times C_{28}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110521037
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 336, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.164', 'subgroup_hash': 164, 'subgroup_order': 336, 'subgroup_tex': 'C_2\\times C_{14}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110521048
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 336, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.49', 'subgroup_hash': 49, 'subgroup_order': 336, 'subgroup_tex': '(C_2\\times C_{14}):C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110521059
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 336, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.2.c1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.49', 'subgroup_hash': 49, 'subgroup_order': 336, 'subgroup_tex': '(C_2\\times C_{14}):C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110521070
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 336, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, '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: 110521081
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 336, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.50', 'subgroup_hash': 50, 'subgroup_order': 336, 'subgroup_tex': 'C_{28}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110521092
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': True, 'core_order': 224, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 14, 'label': '672.729.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '3.a1.a1', 'outer_equivalence': False, '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': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '224.156', 'subgroup_hash': 156, 'subgroup_order': 224, 'subgroup_tex': 'C_{28}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110520916
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 168, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.51', 'subgroup_hash': 51, 'subgroup_order': 168, 'subgroup_tex': 'C_2\\times C_{14}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110520927
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 168, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.51', 'subgroup_hash': 51, 'subgroup_order': 168, 'subgroup_tex': 'C_2\\times C_{14}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110520938
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 168, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.4.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.51', 'subgroup_hash': 51, 'subgroup_order': 168, 'subgroup_tex': 'C_2\\times C_{14}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110520949
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 168, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, '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: 110520960
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 168, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.19', 'subgroup_hash': 19, 'subgroup_order': 168, 'subgroup_tex': 'C_{14}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110520971
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 168, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.19', 'subgroup_hash': 19, 'subgroup_order': 168, 'subgroup_tex': 'C_{14}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110520982
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 168, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.4.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.19', 'subgroup_hash': 19, 'subgroup_order': 168, 'subgroup_tex': 'C_{14}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110520993
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 84, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '168.19', 'subgroup_hash': 19, 'subgroup_order': 168, 'subgroup_tex': 'C_{14}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110521004
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 84, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.4.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '168.19', 'subgroup_hash': 19, 'subgroup_order': 168, 'subgroup_tex': 'C_{14}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110521014
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '168.20', 'subgroup_hash': 20, 'subgroup_order': 168, 'subgroup_tex': 'C_{28}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110521016
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.4.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '168.20', 'subgroup_hash': 20, 'subgroup_order': 168, 'subgroup_tex': 'C_{28}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110521017
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.20', 'subgroup_hash': 20, 'subgroup_order': 168, 'subgroup_tex': 'C_{28}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110521018
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.4.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.20', 'subgroup_hash': 20, 'subgroup_order': 168, 'subgroup_tex': 'C_{28}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110521019
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.4.h1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.h1.c1', 'outer_equivalence': False, 'perfect': False, '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': '168.20', 'subgroup_hash': 20, 'subgroup_order': 168, 'subgroup_tex': 'C_{28}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110521020
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.4.h1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.h1.d1', 'outer_equivalence': False, 'perfect': False, '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': '168.20', 'subgroup_hash': 20, 'subgroup_order': 168, 'subgroup_tex': 'C_{28}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110521021
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 112, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, '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': '112.38', 'subgroup_hash': 38, 'subgroup_order': 112, 'subgroup_tex': 'D_4\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110521022
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 112, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.6.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.b1', 'outer_equivalence': False, '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': '112.38', 'subgroup_hash': 38, 'subgroup_order': 112, 'subgroup_tex': 'D_4\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110521023
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 112, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.b1.a1', 'outer_equivalence': False, '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': '112.37', 'subgroup_hash': 37, 'subgroup_order': 112, 'subgroup_tex': 'C_2^2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 110521024
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 112, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.c1.a1', 'outer_equivalence': False, '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': '112.20', 'subgroup_hash': 20, 'subgroup_order': 112, 'subgroup_tex': 'C_2^2:C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 110521025
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 112, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.6.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.c1.b1', 'outer_equivalence': False, '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': '112.20', 'subgroup_hash': 20, 'subgroup_order': 112, 'subgroup_tex': 'C_2^2:C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 110521027
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': True, 'core_order': 112, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.d1.a1', 'outer_equivalence': False, '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': '112.38', 'subgroup_hash': 38, 'subgroup_order': 112, 'subgroup_tex': 'D_4\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110521028
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': True, 'core_order': 112, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.e1.a1', 'outer_equivalence': False, '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': '112.21', 'subgroup_hash': 21, 'subgroup_order': 112, 'subgroup_tex': 'C_4:C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 110521029
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 32, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '672.729.7.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.168', 'subgroup_hash': 168, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110521030
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': True, 'centralizer_order': 32, 'characteristic': True, 'core_order': 84, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 110521031
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 84, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': True, '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: 110521032
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 84, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.8.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 110521033
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 84, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 110521034
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 84, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.8.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 110521035
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 42, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '84.9', 'subgroup_hash': 9, 'subgroup_order': 84, 'subgroup_tex': 'C_{14}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110521036
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 42, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '84.9', 'subgroup_hash': 9, 'subgroup_order': 84, 'subgroup_tex': 'C_{14}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110521038
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 42, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.8.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '84.9', 'subgroup_hash': 9, 'subgroup_order': 84, 'subgroup_tex': 'C_{14}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110521039
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 42, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '84.9', 'subgroup_hash': 9, 'subgroup_order': 84, 'subgroup_tex': 'C_{14}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110521040
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 42, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.9', 'subgroup_hash': 9, 'subgroup_order': 84, 'subgroup_tex': 'C_{14}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110521041
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 42, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.8.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '84.9', 'subgroup_hash': 9, 'subgroup_order': 84, 'subgroup_tex': 'C_{14}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110521042
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 42, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.2', 'subgroup_hash': 2, 'subgroup_order': 84, 'subgroup_tex': 'C_7:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110521043
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 42, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.9', 'subgroup_hash': 9, 'subgroup_order': 84, 'subgroup_tex': 'C_{14}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110521044
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 42, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.8.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '84.9', 'subgroup_hash': 9, 'subgroup_order': 84, 'subgroup_tex': 'C_{14}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110521045
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 42, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.2', 'subgroup_hash': 2, 'subgroup_order': 84, 'subgroup_tex': 'C_7:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110521046
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 42, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.8.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '84.2', 'subgroup_hash': 2, 'subgroup_order': 84, 'subgroup_tex': 'C_7:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110521047
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 56, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, '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': '56.13', 'subgroup_hash': 13, 'subgroup_order': 56, 'subgroup_tex': 'C_2^2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110521049
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 56, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, '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': '56.13', 'subgroup_hash': 13, 'subgroup_order': 56, 'subgroup_tex': 'C_2^2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110521050
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 56, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.12.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1.b1', 'outer_equivalence': False, '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': '56.13', 'subgroup_hash': 13, 'subgroup_order': 56, 'subgroup_tex': 'C_2^2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110521051
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 56, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.c1.a1', 'outer_equivalence': False, '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': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 110521052
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 56, 'counter': 53, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.d1.a1', 'outer_equivalence': False, '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': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 110521053
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 56, 'counter': 54, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.e1.a1', 'outer_equivalence': False, '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': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 110521054
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 56, 'counter': 55, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.12.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.e1.b1', 'outer_equivalence': False, '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': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 110521055
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 28, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 110521056
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 28, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.12.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 110521057
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 28, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.9', 'subgroup_hash': 9, 'subgroup_order': 56, 'subgroup_tex': 'C_7\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110521058
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 28, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.12.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '56.9', 'subgroup_hash': 9, 'subgroup_order': 56, 'subgroup_tex': 'C_7\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110521060
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 28, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.9', 'subgroup_hash': 9, 'subgroup_order': 56, 'subgroup_tex': 'C_7\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110521061
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 28, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.12.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '56.9', 'subgroup_hash': 9, 'subgroup_order': 56, 'subgroup_tex': 'C_7\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110521062
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 28, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.12.h1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.h1.c1', 'outer_equivalence': False, 'perfect': False, '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': '56.9', 'subgroup_hash': 9, 'subgroup_order': 56, 'subgroup_tex': 'C_7\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110521063
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 28, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.12.h1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.h1.d1', 'outer_equivalence': False, 'perfect': False, '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': '56.9', 'subgroup_hash': 9, 'subgroup_order': 56, 'subgroup_tex': 'C_7\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110521064
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 16, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.14.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110521065
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 16, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.14.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110521066
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 16, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.14.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110521067
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 16, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.14.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110521068
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 16, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.14.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110521069
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 16, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.14.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110521071
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 16, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.14.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110521072
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': True, 'centralizer_order': 32, 'characteristic': True, 'core_order': 42, 'counter': 71, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 110521073
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': True, 'centralizer_order': 32, 'characteristic': True, 'core_order': 42, 'counter': 72, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '42.2', 'subgroup_hash': 2, 'subgroup_order': 42, 'subgroup_tex': 'C_7:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110521074
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': True, 'centralizer_order': 32, 'characteristic': True, 'core_order': 42, 'counter': 73, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '42.2', 'subgroup_hash': 2, 'subgroup_order': 42, 'subgroup_tex': 'C_7:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110521075
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 21, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.2', 'subgroup_hash': 2, 'subgroup_order': 42, 'subgroup_tex': 'C_7:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110521076
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 21, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.16.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '42.2', 'subgroup_hash': 2, 'subgroup_order': 42, 'subgroup_tex': 'C_7:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110521077
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 21, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.2', 'subgroup_hash': 2, 'subgroup_order': 42, 'subgroup_tex': 'C_7:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110521078
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 21, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.16.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '42.2', 'subgroup_hash': 2, 'subgroup_order': 42, 'subgroup_tex': 'C_7:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110521079
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': True, 'centralizer_order': 84, 'characteristic': True, 'core_order': 32, 'counter': 78, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '672.729.21.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '21.a1.a1', 'outer_equivalence': False, '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': ['U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 2}
  • id: 110521080
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': True, 'core_order': 28, 'counter': 79, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.15', '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', 'S', 'L1', 'D1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110521082
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 28, 'counter': 80, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '672.729.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, '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': ['C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 110521083
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 28, 'counter': 81, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '672.729.24.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.b1', 'outer_equivalence': False, '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': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 110521084
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 28, 'counter': 82, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.c1.a1', 'outer_equivalence': False, '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': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110521085
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 28, 'counter': 83, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.24.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.c1.b1', 'outer_equivalence': False, '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': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110521086
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 14, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110521087
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 14, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110521088
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 14, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.24.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110521089
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 14, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110521090
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 14, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110521091
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 14, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.24.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110521093
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 14, 'counter': 90, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.729.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 110521094
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 14, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.24.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110521095
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 14, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.24.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110521096
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 14, 'counter': 93, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.729.24.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 110521097
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 14, 'counter': 94, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.729.24.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 110521098
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.28.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110521099
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.28.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110521100
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.28.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110521101
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.28.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110521102
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.28.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110520917
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.28.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110520918
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.28.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110520919
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.28.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110520920
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.28.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110520921
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.28.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110520922
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.28.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110520923
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.28.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110520924
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.28.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110520925
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.28.h1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.h1.c1', 'outer_equivalence': False, 'perfect': False, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110520926
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.28.h1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.h1.d1', 'outer_equivalence': False, 'perfect': False, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110520928
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': True, 'centralizer_order': 32, 'characteristic': True, 'core_order': 21, 'counter': 110, 'cyclic': False, 'direct': True, 'hall': 21, 'label': '672.729.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.28', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 28, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 110520929
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': False, 'core_order': 16, 'counter': 111, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.42.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '42.a1.a1', 'outer_equivalence': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110520930
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': False, 'core_order': 16, 'counter': 112, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.42.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '42.a1.b1', 'outer_equivalence': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110520931
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 16, 'counter': 113, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.42.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '42.b1.a1', 'outer_equivalence': False, '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110520932
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': False, 'core_order': 16, 'counter': 114, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.42.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '42.c1.a1', 'outer_equivalence': False, '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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110520933
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': False, 'core_order': 16, 'counter': 115, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.42.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '42.c1.b1', 'outer_equivalence': False, '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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110520934
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': True, 'core_order': 16, 'counter': 116, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.42.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '42.d1.a1', 'outer_equivalence': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110520935
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': True, 'core_order': 16, 'counter': 117, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.42.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '42.e1.a1', 'outer_equivalence': False, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110520936
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': True, 'core_order': 14, 'counter': 118, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '672.729.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.47', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 47, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110520937
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': True, 'core_order': 14, 'counter': 119, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '672.729.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.45', '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': ['C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110520939
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': True, 'core_order': 14, 'counter': 120, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '672.729.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.45', '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110520940
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 7, 'counter': 121, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.729.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110520941
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 7, 'counter': 122, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.729.48.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110520942
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 7, 'counter': 123, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.729.48.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110520943
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 7, 'counter': 124, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.729.48.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110520944
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 4, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.56.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110520945
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.56.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110520946
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.56.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110520947
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.56.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110520948
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.56.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110520950
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.56.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110520951
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.56.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110520952
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 132, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.729.56.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110520953
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 133, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.729.56.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110520954
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 134, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.729.56.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110520955
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.56.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110520956
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.56.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110520957
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.56.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110520958
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.56.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110520959
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 139, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.729.56.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110520961
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 140, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.729.56.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110520962
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 8, 'counter': 141, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.84.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '84.a1.a1', 'outer_equivalence': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 110520963
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 8, 'counter': 142, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.84.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '84.b1.a1', 'outer_equivalence': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 110520964
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 8, 'counter': 143, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.84.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '84.b1.b1', 'outer_equivalence': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 110520965
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 8, 'counter': 144, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.84.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '84.c1.a1', 'outer_equivalence': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110520966
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 8, 'counter': 145, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.84.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '84.d1.a1', 'outer_equivalence': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110520967
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 8, 'counter': 146, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.84.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '84.e1.a1', 'outer_equivalence': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110520968
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 8, 'counter': 147, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.84.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '84.e1.b1', 'outer_equivalence': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110520969
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 4, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.84.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110520970
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 4, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.84.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110520972
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': False, 'core_order': 4, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.84.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110520973
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': False, 'core_order': 4, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.84.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110520974
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': False, 'core_order': 4, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.84.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110520975
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': False, 'core_order': 4, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.84.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110520976
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': False, 'core_order': 4, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.84.h1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.h1.c1', 'outer_equivalence': False, 'perfect': False, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110520977
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': False, 'core_order': 4, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.84.h1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.h1.d1', 'outer_equivalence': False, 'perfect': False, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110520978
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': True, 'core_order': 7, 'counter': 156, 'cyclic': True, 'direct': False, 'hall': 7, 'label': '672.729.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '96.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.168', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 168, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}:D_4', 'simple': True, 'solvable': True, 'special_labels': ['L2', 'C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 7}
  • id: 110520979
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 157, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.729.112.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110520980
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 158, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.729.112.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110520981
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 159, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.729.112.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110520983
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 160, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.729.112.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110520984
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 161, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.729.112.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110520985
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 162, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.729.112.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110520986
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 163, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.729.112.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110520987
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': True, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 4, 'counter': 164, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.168.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '168.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '168.51', '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': ['Z', 'Phi', 'U1'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 110520988
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 4, 'counter': 165, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '672.729.168.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '168.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '168.20', '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110520989
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 4, 'counter': 166, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '672.729.168.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '168.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '168.20', '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110520990
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 4, 'counter': 167, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.168.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '168.c1.a1', 'outer_equivalence': False, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 110520991
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 4, 'counter': 168, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.729.168.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '168.c1.b1', 'outer_equivalence': False, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 110520992
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 2, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.168.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 110520994
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 2, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.168.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 110520995
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 2, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.168.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 110520996
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 2, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.168.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 110520997
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 2, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.168.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 110520998
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 2, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.168.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 110520999
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 2, 'counter': 175, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.729.168.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110521000
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 2, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.168.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 110521001
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 2, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.729.168.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 110521002
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 2, 'counter': 178, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.729.168.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110521003
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 2, 'counter': 179, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.729.168.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110521005
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 180, 'cyclic': True, 'direct': None, 'hall': 3, 'label': '672.729.224.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 224, '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: 110521006
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': True, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 2, 'counter': 181, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '672.729.336.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '336.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '336.167', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 167, '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': True, 'solvable': True, 'special_labels': [], '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: 110521007
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': True, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 2, 'counter': 182, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '672.729.336.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '336.b1.a1', 'outer_equivalence': False, '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': True, 'solvable': True, 'special_labels': [], '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: 110521008
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': True, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 2, 'counter': 183, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '672.729.336.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '336.c1.a1', 'outer_equivalence': False, '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': True, 'solvable': True, 'special_labels': [], '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: 110521009
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 1, 'counter': 184, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.729.336.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 110521010
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 1, 'counter': 185, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.729.336.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, '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: 110521011
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 1, 'counter': 186, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.729.336.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 110521012
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 1, 'counter': 187, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.729.336.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, '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: 110521013
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.729', 'ambient_counter': 729, 'ambient_order': 672, 'ambient_tex': '(D_4\\times C_{14}):C_6', 'central': True, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 1, 'counter': 188, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '672.729.672.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '672.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '672.729', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 729, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 672, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '(D_4\\times C_{14}):C_6', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'D2', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 110520915
    {'ambient': '672.729', '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': '168.a1.a1', 'complements': ['672.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1', '2.c1.a1', '2.c1.b1', '2.d1.a1', '2.e1.a1', '3.a1.a1', '7.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6604, 3082, 4241, 6239, 5430, 6176, 4914, 3197], 'generators': [1, 336, 168, 8, 6, 96, 348], 'label': '672.729.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1', '2.c1.a1', '2.c1.b1', '2.d1.a1', '2.e1.a1', '3.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '168.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '168.51'}
  • id: 110520916
    {'ambient': '672.729', 'aut_centralizer_order': 32, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '168.47', 'aut_weyl_index': 32, 'centralizer': '42.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'contains': ['8.a1.a1', '8.c1.a1', '8.c1.b1', '8.d1.a1', '8.f1.a1', '12.a1.a1', '28.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4614, 5544, 6952, 1155, 4794, 9629, 6524, 260], 'generators': [187, 336, 8, 348, 96], 'label': '672.729.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'normal_contains': ['8.a1.a1', '8.c1.a1', '8.c1.b1', '12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '168.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '42.2'}
  • id: 110520917
    {'ambient': '672.729', 'aut_centralizer_order': 96, 'aut_label': '28.e1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1344, 'centralizer': '28.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '14.a1.b1', '14.c1.a1', '14.e1.a1'], 'contains': ['56.a1.a1', '56.j1.a1', '84.e1.a1'], 'core': '84.e1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [4827, -1, 5862, -1, 2497, -1, 7091, -1], 'generators': [6, 336, 8, 12], 'label': '672.729.28.e1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.e1.a1', 'projective_image': '168.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110520918
    {'ambient': '672.729', 'aut_centralizer_order': 96, 'aut_label': '28.e1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1344, 'centralizer': '28.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '14.a1.a1', '14.c1.b1', '14.e1.a1'], 'contains': ['56.a1.a1', '56.j1.b1', '84.e1.b1'], 'core': '84.e1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [4827, -1, 6210, -1, 2497, -1, 5970, -1], 'generators': [522, 336, 8, 12], 'label': '672.729.28.e1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.e1.b1', 'projective_image': '168.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.e1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110520919
    {'ambient': '672.729', 'aut_centralizer_order': 48, 'aut_label': '28.f1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1344, 'centralizer': '14.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '14.b1.a1'], 'contains': ['56.d1.a1', '56.f1.a1', '56.g1.a1', '84.f1.a1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [8606, -1, 394, -1, 9854, -1, 280, -1], 'generators': [355, 168, 8, 336], 'label': '672.729.28.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '28.f1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110520920
    {'ambient': '672.729', 'aut_centralizer_order': 48, 'aut_label': '28.f1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1344, 'centralizer': '14.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '14.b1.a1'], 'contains': ['56.d1.a1', '56.f1.b1', '56.g1.a1', '84.f1.b1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 14, 'diagramx': [8606, -1, 631, -1, 9854, -1, 1066, -1], 'generators': [355, 516, 8, 336], 'label': '672.729.28.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '28.f1.b1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110520921
    {'ambient': '672.729', 'aut_centralizer_order': 24, 'aut_label': '28.g1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '8.3', 'aut_weyl_index': 672, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '14.d1.a1'], 'contains': ['56.e1.a1', '56.e1.b1', '56.f1.a1', '84.g1.a1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [9828, -1, 2260, -1, 7255, -1, 1831, -1], 'generators': [1, 168, 8, 336], 'label': '672.729.28.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '28.g1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110520922
    {'ambient': '672.729', 'aut_centralizer_order': 24, 'aut_label': '28.g1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '8.3', 'aut_weyl_index': 672, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.b1', '14.d1.a1'], 'contains': ['56.e1.a1', '56.e1.b1', '56.f1.b1', '84.g1.b1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 14, 'diagramx': [9828, -1, 1950, -1, 7255, -1, 2382, -1], 'generators': [1, 516, 8, 336], 'label': '672.729.28.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '28.g1.b1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.g1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110520923
    {'ambient': '672.729', 'aut_centralizer_order': 24, 'aut_label': '28.h1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1344, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '14.a1.a1'], 'contains': ['56.h1.a1', '56.i1.a1', '56.j1.b1', '84.h1.a1'], 'core': '168.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [1232, -1, 9434, -1, 732, -1, 8207, -1], 'generators': [1, 522, 8, 12], 'label': '672.729.28.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1.a1', 'old_label': '28.h1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110520924
    {'ambient': '672.729', 'aut_centralizer_order': 24, 'aut_label': '28.h1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1344, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.b1', '14.a1.b1'], 'contains': ['56.h1.a1', '56.i1.b1', '56.j1.a1', '84.h1.b1'], 'core': '168.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [1232, -1, 7960, -1, 732, -1, 9929, -1], 'generators': [169, 6, 8, 12], 'label': '672.729.28.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1.b1', 'old_label': '28.h1.b1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.h1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110520925
    {'ambient': '672.729', 'aut_centralizer_order': 24, 'aut_label': '28.h1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1344, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.c1', '14.a1.a1'], 'contains': ['56.h1.b1', '56.i1.a1', '56.j1.b1', '84.h1.c1'], 'core': '168.c1.b1', 'coset_action_label': None, 'count': 14, 'diagramx': [1232, -1, 9637, -1, 732, -1, 8044, -1], 'generators': [337, 522, 8, 12], 'label': '672.729.28.h1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1.a1', 'old_label': '28.h1.c1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.h1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110520926
    {'ambient': '672.729', 'aut_centralizer_order': 24, 'aut_label': '28.h1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1344, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.d1', '14.a1.b1'], 'contains': ['56.h1.b1', '56.i1.b1', '56.j1.a1', '84.h1.d1'], 'core': '168.c1.b1', 'coset_action_label': None, 'count': 14, 'diagramx': [1232, -1, 8299, -1, 732, -1, 9567, -1], 'generators': [505, 6, 8, 12], 'label': '672.729.28.h1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1.b1', 'old_label': '28.h1.d1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.h1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110520927
    {'ambient': '672.729', 'aut_centralizer_order': 16, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '168.47', 'aut_weyl_index': 32, 'centralizer': '84.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.c1.a1', '2.d1.a1'], 'contains': ['8.a1.a1', '8.e1.a1', '8.g1.a1', '8.i1.a1', '12.b1.a1', '28.b1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3654, 2457, 3576, 1950, 3661, 6695, 4001, 2891], 'generators': [1, 336, 8, 348, 96], 'label': '672.729.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.c1.a1', '2.d1.a1'], 'normal_contains': ['8.a1.a1', '12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '168.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '84.9'}
  • id: 110520928
    {'ambient': '672.729', 'aut_centralizer_order': 128, 'aut_label': '32.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '42.1', 'aut_weyl_index': 128, 'centralizer': '21.a1.a1', 'complements': ['21.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.d1.a1', '16.d1.b1', '16.e1.a1', '16.e1.b1'], 'contains': ['96.a1.a1', '224.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2574, 8978, 5812, 2119, 2989, 6538, 5666, 3102], 'generators': [8, 96], 'label': '672.729.32.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.b1.a1', '16.c1.a1', '16.a1.a1'], 'normal_contains': ['96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '672.729', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.28', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 110520929
    {'ambient': '672.729', 'aut_centralizer_order': 168, 'aut_label': '42.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 336, 'centralizer': '8.a1.a1', 'complements': ['16.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '14.a1.a1', '21.a1.a1'], 'contains': ['84.a1.a1', '84.b1.a1', '84.e1.b1', '84.h1.a1', '84.h1.c1'], 'core': '42.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4505, 1073, 6613, 4920, 2798, 1757, 6148, 9116], 'generators': [1, 522, 336], 'label': '672.729.42.a1.a1', 'mobius_quo': 0, 'mobius_sub': -7, 'normal_closure': '42.a1.a1', 'normal_contained_in': ['6.a1.a1', '21.a1.a1'], 'normal_contains': ['84.a1.a1', '84.b1.a1', '84.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '42.a1.a1', 'projective_image': '168.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '21.1', 'quotient_action_kernel_order': 21, 'quotient_fusion': None, 'short_label': '42.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 110520930
    {'ambient': '672.729', 'aut_centralizer_order': 168, 'aut_label': '42.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 336, 'centralizer': '8.a1.a1', 'complements': ['16.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.b1', '14.a1.b1', '21.a1.a1'], 'contains': ['84.a1.a1', '84.b1.b1', '84.e1.a1', '84.h1.b1', '84.h1.d1'], 'core': '42.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4505, 1073, 6303, 8473, 2798, 1757, 6912, 7525], 'generators': [505, 6, 336], 'label': '672.729.42.a1.b1', 'mobius_quo': 0, 'mobius_sub': -7, 'normal_closure': '42.a1.b1', 'normal_contained_in': ['6.a1.b1', '21.a1.a1'], 'normal_contains': ['84.a1.a1', '84.b1.b1', '84.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '42.a1.b1', 'projective_image': '168.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '21.1', 'quotient_action_kernel_order': 21, 'quotient_fusion': None, 'short_label': '42.a1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 110520931
    {'ambient': '672.729', 'aut_centralizer_order': 336, 'aut_label': '42.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '16.14', 'aut_weyl_index': 336, 'centralizer': '2.b1.a1', 'complements': ['16.e1.a1', '16.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '14.b1.a1', '21.a1.a1'], 'contains': ['84.a1.a1', '84.c1.a1', '84.d1.a1', '84.f1.a1', '84.f1.b1'], 'core': '42.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8140, 4069, 1854, 6814, 8534, 2399, 2782, 8321], 'generators': [355, 348, 168], 'label': '672.729.42.b1.a1', 'mobius_quo': 0, 'mobius_sub': -7, 'normal_closure': '42.b1.a1', 'normal_contained_in': ['6.b1.a1', '21.a1.a1'], 'normal_contains': ['84.a1.a1', '84.c1.a1', '84.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '42.b1.a1', 'projective_image': '168.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '21.1', 'quotient_action_kernel_order': 21, 'quotient_fusion': None, 'short_label': '42.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110520932
    {'ambient': '672.729', 'aut_centralizer_order': 168, 'aut_label': '42.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 336, 'centralizer': '8.a1.a1', 'complements': ['16.e1.b1', '16.d1.a1', '16.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '14.c1.a1', '21.a1.a1'], 'contains': ['84.b1.a1', '84.d1.a1', '84.e1.a1'], 'core': '42.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5570, 1782, 4012, 6079, 4495, 1212, 4512, 7908], 'generators': [1, 6], 'label': '672.729.42.c1.a1', 'mobius_quo': 0, 'mobius_sub': -7, 'normal_closure': '42.c1.a1', 'normal_contained_in': ['6.c1.a1', '21.a1.a1'], 'normal_contains': ['84.b1.a1', '84.d1.a1', '84.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '42.c1.a1', 'projective_image': '168.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '21.1', 'quotient_action_kernel_order': 21, 'quotient_fusion': None, 'short_label': '42.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 110520933
    {'ambient': '672.729', 'aut_centralizer_order': 168, 'aut_label': '42.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 336, 'centralizer': '8.a1.a1', 'complements': ['16.e1.a1', '16.d1.a1', '16.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['6.c1.b1', '14.c1.b1', '21.a1.a1'], 'contains': ['84.b1.b1', '84.d1.a1', '84.e1.b1'], 'core': '42.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5570, 1782, 4232, 7550, 4495, 1212, 4646, 8734], 'generators': [505, 522], 'label': '672.729.42.c1.b1', 'mobius_quo': 0, 'mobius_sub': -7, 'normal_closure': '42.c1.b1', 'normal_contained_in': ['6.c1.b1', '21.a1.a1'], 'normal_contains': ['84.b1.b1', '84.d1.a1', '84.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '42.c1.b1', 'projective_image': '168.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '21.1', 'quotient_action_kernel_order': 21, 'quotient_fusion': None, 'short_label': '42.c1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 110520934
    {'ambient': '672.729', 'aut_centralizer_order': 168, 'aut_label': '42.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 168, 'centralizer': '8.a1.a1', 'complements': ['16.d1.a1', '16.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '14.d1.a1', '21.a1.a1'], 'contains': ['84.b1.a1', '84.b1.b1', '84.c1.a1', '84.g1.a1', '84.g1.b1'], 'core': '42.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9218, 2491, 3004, 9052, 6377, 260, 3539, 9535], 'generators': [1, 348, 168], 'label': '672.729.42.d1.a1', 'mobius_quo': 0, 'mobius_sub': -7, 'normal_closure': '42.d1.a1', 'normal_contained_in': ['6.d1.a1', '21.a1.a1'], 'normal_contains': ['84.b1.a1', '84.b1.b1', '84.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '42.d1.a1', 'projective_image': '168.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '21.1', 'quotient_action_kernel_order': 21, 'quotient_fusion': None, 'short_label': '42.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 110520935
    {'ambient': '672.729', 'aut_centralizer_order': 168, 'aut_label': '42.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 168, 'centralizer': '8.a1.a1', 'complements': ['16.e1.a1', '16.e1.b1', '16.d1.a1', '16.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '14.e1.a1', '21.a1.a1'], 'contains': ['84.c1.a1', '84.e1.a1', '84.e1.b1'], 'core': '42.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6918, 3360, 4712, 7986, 6145, 762, 5624, 9887], 'generators': [6, 168], 'label': '672.729.42.e1.a1', 'mobius_quo': 0, 'mobius_sub': -7, 'normal_closure': '42.e1.a1', 'normal_contained_in': ['6.e1.a1', '21.a1.a1'], 'normal_contains': ['84.c1.a1', '84.e1.b1', '84.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '42.e1.a1', 'projective_image': '168.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '21.1', 'quotient_action_kernel_order': 21, 'quotient_fusion': None, 'short_label': '42.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 110520936
    {'ambient': '672.729', 'aut_centralizer_order': 896, 'aut_label': '48.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 896, 'centralizer': '3.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.d1.a1', '24.e1.a1', '24.e1.b1'], 'contains': ['96.a1.a1', '336.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3326, 6765, 5094, 2466, 3512, 4962, 5246, 5473], 'generators': [348, 96], 'label': '672.729.48.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1'], 'normal_contains': ['96.a1.a1', '336.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '336.167', 'quotient_action_image': '3.1', 'quotient_action_kernel': '16.13', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110520937
    {'ambient': '672.729', 'aut_centralizer_order': 896, 'aut_label': '48.b1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 896, 'centralizer': '3.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.a1.a1', '24.b1.a1', '24.b1.b1', '24.f1.a1', '24.g1.a1', '24.g1.b1', '24.h1.a1'], 'contains': ['96.a1.a1', '336.b1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6491, 8132, 1134, 3583, 6099, 4578, 2230, 5834], 'generators': [336, 96], 'label': '672.729.48.b1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': ['16.b1.a1', '24.a1.a1', '24.b1.b1', '24.b1.a1'], 'normal_contains': ['96.a1.a1', '336.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '336.165', 'quotient_action_image': '3.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110520938
    {'ambient': '672.729', 'aut_centralizer_order': 16, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '168.47', 'aut_weyl_index': 32, 'centralizer': '84.b1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.c1.b1', '2.d1.a1'], 'contains': ['8.a1.a1', '8.e1.b1', '8.g1.b1', '8.i1.b1', '12.b1.b1', '28.b1.b1'], 'core': '4.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3654, 2457, 4898, 7643, 3661, 6695, 5256, 2316], 'generators': [505, 336, 8, 348, 96], 'label': '672.729.4.b1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.b1', 'normal_contained_in': ['2.a1.b1', '2.c1.b1', '2.d1.a1'], 'normal_contains': ['8.a1.a1', '12.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.b1', 'projective_image': '168.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.b1', 'subgroup_fusion': None, 'weyl_group': '84.9'}
  • id: 110520939
    {'ambient': '672.729', 'aut_centralizer_order': 896, 'aut_label': '48.c1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 896, 'centralizer': '3.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.a1.a1', '24.c1.a1', '24.c1.b1', '24.i1.a1', '24.i1.b1', '24.j1.a1', '24.j1.b1'], 'contains': ['96.a1.a1', '336.c1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [571, 7270, 8859, 1497, 1570, 5346, 7757, 4946], 'generators': [12, 96], 'label': '672.729.48.c1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '48.c1.a1', 'normal_contained_in': ['16.c1.a1', '24.a1.a1', '24.c1.a1', '24.c1.b1'], 'normal_contains': ['96.a1.a1', '336.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.c1.a1', 'projective_image': '336.165', 'quotient_action_image': '3.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110520940
    {'ambient': '672.729', 'aut_centralizer_order': 224, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '6.2', 'aut_weyl_index': 896, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.c1.a1', '24.d1.a1', '24.f1.a1'], 'contains': ['96.a1.a1', '336.d1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2714, -1, 6962, -1, 3335, -1, 6330, -1], 'generators': [523, 96], 'label': '672.729.48.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.d1.a1', 'projective_image': '672.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110520941
    {'ambient': '672.729', 'aut_centralizer_order': 224, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '6.2', 'aut_weyl_index': 896, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.b1', '24.c1.b1', '24.d1.a1', '24.f1.a1'], 'contains': ['96.a1.a1', '336.d1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2714, -1, 7310, -1, 3335, -1, 6226, -1], 'generators': [187, 96], 'label': '672.729.48.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.d1.b1', 'projective_image': '672.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110520942
    {'ambient': '672.729', 'aut_centralizer_order': 112, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.2', 'aut_weyl_index': 896, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '24.e1.a1', '24.g1.a1', '24.i1.a1'], 'contains': ['96.a1.a1', '336.e1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1936, -1, 3683, -1, 2593, -1, 4250, -1], 'generators': [1, 96], 'label': '672.729.48.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '48.e1.a1', 'projective_image': '672.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110520943
    {'ambient': '672.729', 'aut_centralizer_order': 112, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.2', 'aut_weyl_index': 896, 'centralizer': '12.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.b1', '24.e1.b1', '24.g1.b1', '24.i1.b1'], 'contains': ['96.a1.a1', '336.e1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1936, -1, 5482, -1, 2593, -1, 5474, -1], 'generators': [505, 96], 'label': '672.729.48.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '48.e1.b1', 'projective_image': '672.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110520944
    {'ambient': '672.729', 'aut_centralizer_order': 768, 'aut_label': '56.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5376, 'centralizer': '7.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '28.a1.a1', '28.b1.a1', '28.b1.b1', '28.c1.a1', '28.d1.a1', '28.e1.a1', '28.e1.b1'], 'contains': ['112.a1.a1', '112.b1.a1', '112.c1.a1', '168.a1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5572, -1, 4708, -1, 5142, -1, 4949, -1], 'generators': [348, 336, 8], 'label': '672.729.56.a1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.a1.a1', 'projective_image': '168.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110520945
    {'ambient': '672.729', 'aut_centralizer_order': 192, 'aut_label': '56.b1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2688, 'centralizer': '14.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '28.a1.a1'], 'contains': ['112.a1.a1', '112.d1.a1', '112.d1.b1', '168.d1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [3826, -1, 7217, -1, 4539, -1, 6681, -1], 'generators': [187, 348, 8], 'label': '672.729.56.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.b1.a1', 'projective_image': '336.167', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110520946
    {'ambient': '672.729', 'aut_centralizer_order': 96, 'aut_label': '56.c1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2688, 'centralizer': '28.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '28.b1.a1'], 'contains': ['112.a1.a1', '112.e1.a1', '168.e1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [3125, -1, 3775, -1, 2824, -1, 4387, -1], 'generators': [1, 348, 8], 'label': '672.729.56.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '56.c1.a1', 'projective_image': '336.167', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110520947
    {'ambient': '672.729', 'aut_centralizer_order': 96, 'aut_label': '56.c1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2688, 'centralizer': '28.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.b1', '28.b1.b1'], 'contains': ['112.a1.a1', '112.e1.b1', '168.e1.b1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [3125, -1, 5149, -1, 2824, -1, 5306, -1], 'generators': [505, 348, 8], 'label': '672.729.56.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.b1', 'old_label': '56.c1.b1', 'projective_image': '336.167', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110520948
    {'ambient': '672.729', 'aut_centralizer_order': 192, 'aut_label': '56.d1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2688, 'centralizer': '14.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '28.a1.a1', '28.f1.a1', '28.f1.b1'], 'contains': ['112.b1.a1', '112.d1.a1', '112.d1.b1', '168.f1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [6085, -1, 1387, -1, 6849, -1, 1895, -1], 'generators': [187, 336, 8], 'label': '672.729.56.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.d1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110520949
    {'ambient': '672.729', 'aut_centralizer_order': 32, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '168.47', 'aut_weyl_index': 32, 'centralizer': '42.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '12.c1.a1', '28.c1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9114, 8139, 1432, 6251, 7068, 5756, 3098, 4289], 'generators': [348, 8, 336, 168, 96], 'label': '672.729.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.b1', '8.b1.a1', '12.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '168.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '42.2'}
  • id: 110520950
    {'ambient': '672.729', 'aut_centralizer_order': 96, 'aut_label': '56.e1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2688, 'centralizer': '28.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '28.b1.a1', '28.g1.a1', '28.g1.b1'], 'contains': ['112.b1.a1', '112.e1.a1', '168.g1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [6505, -1, 2272, -1, 5910, -1, 2746, -1], 'generators': [1, 336, 8], 'label': '672.729.56.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '56.e1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110520951
    {'ambient': '672.729', 'aut_centralizer_order': 96, 'aut_label': '56.e1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2688, 'centralizer': '28.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.b1', '28.b1.b1', '28.g1.a1', '28.g1.b1'], 'contains': ['112.b1.a1', '112.e1.b1', '168.g1.b1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [6505, -1, 2523, -1, 5910, -1, 3189, -1], 'generators': [505, 336, 8], 'label': '672.729.56.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '56.e1.b1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.e1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110520952
    {'ambient': '672.729', 'aut_centralizer_order': 192, 'aut_label': '56.f1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2688, 'centralizer': '14.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '28.c1.a1', '28.f1.a1', '28.g1.a1'], 'contains': ['112.b1.a1', '168.b1.a1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [9433, -1, 1115, -1, 7943, -1, 1405, -1], 'generators': [168, 8, 336], 'label': '672.729.56.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.f1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110520953
    {'ambient': '672.729', 'aut_centralizer_order': 192, 'aut_label': '56.f1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2688, 'centralizer': '14.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '28.c1.a1', '28.f1.b1', '28.g1.b1'], 'contains': ['112.b1.a1', '168.b1.b1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [9433, -1, 1604, -1, 7943, -1, 2332, -1], 'generators': [516, 8, 336], 'label': '672.729.56.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.f1.b1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.f1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110520954
    {'ambient': '672.729', 'aut_centralizer_order': 192, 'aut_label': '56.g1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2688, 'centralizer': '14.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '28.d1.a1', '28.f1.a1', '28.f1.b1'], 'contains': ['112.b1.a1', '168.h1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [8026, -1, 428, -1, 8296, -1, 1195, -1], 'generators': [355, 8, 336], 'label': '672.729.56.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.g1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110520955
    {'ambient': '672.729', 'aut_centralizer_order': 192, 'aut_label': '56.h1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2688, 'centralizer': '14.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '28.a1.a1', '28.h1.a1', '28.h1.b1'], 'contains': ['112.c1.a1', '112.d1.a1', '168.c1.a1'], 'core': '168.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [1783, -1, 8289, -1, 1886, -1, 8531, -1], 'generators': [523, 12, 8], 'label': '672.729.56.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.h1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110520956
    {'ambient': '672.729', 'aut_centralizer_order': 192, 'aut_label': '56.h1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2688, 'centralizer': '14.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.b1', '28.a1.a1', '28.h1.c1', '28.h1.d1'], 'contains': ['112.c1.a1', '112.d1.b1', '168.c1.b1'], 'core': '168.c1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [1783, -1, 8761, -1, 1886, -1, 8169, -1], 'generators': [187, 12, 8], 'label': '672.729.56.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.h1.b1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.h1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110520957
    {'ambient': '672.729', 'aut_centralizer_order': 96, 'aut_label': '56.i1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2688, 'centralizer': '28.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '28.b1.a1', '28.h1.a1', '28.h1.c1'], 'contains': ['112.c1.a1', '112.e1.a1', '168.i1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [1454, -1, 9508, -1, 947, -1, 7237, -1], 'generators': [1, 12, 8], 'label': '672.729.56.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1.a1', 'old_label': '56.i1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110520958
    {'ambient': '672.729', 'aut_centralizer_order': 96, 'aut_label': '56.i1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2688, 'centralizer': '28.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.b1', '28.b1.b1', '28.h1.b1', '28.h1.d1'], 'contains': ['112.c1.a1', '112.e1.b1', '168.i1.b1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [1454, -1, 7799, -1, 947, -1, 8888, -1], 'generators': [505, 12, 8], 'label': '672.729.56.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1.b1', 'old_label': '56.i1.b1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.i1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110520959
    {'ambient': '672.729', 'aut_centralizer_order': 96, 'aut_label': '56.j1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2688, 'centralizer': '28.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '28.e1.a1', '28.h1.b1', '28.h1.d1'], 'contains': ['112.c1.a1', '168.j1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [1092, -1, 8126, -1, 247, -1, 9439, -1], 'generators': [6, 8, 12], 'label': '672.729.56.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1.b1', 'old_label': '56.j1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110520960
    {'ambient': '672.729', 'aut_centralizer_order': 32, 'aut_label': '4.d1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '168.47', 'aut_weyl_index': 32, 'centralizer': '42.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.c1.a1', '2.c1.b1'], 'contains': ['8.a1.a1', '8.h1.a1', '12.d1.a1', '28.d1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6655, 6765, 3132, 3020, 7554, 8690, 3581, 1658], 'generators': [355, 8, 336, 348, 96], 'label': '672.729.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.b1.a1', '2.c1.a1', '2.c1.b1'], 'normal_contains': ['8.a1.a1', '12.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '168.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '42.2'}
  • id: 110520961
    {'ambient': '672.729', 'aut_centralizer_order': 96, 'aut_label': '56.j1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2688, 'centralizer': '28.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.b1', '28.e1.b1', '28.h1.a1', '28.h1.c1'], 'contains': ['112.c1.a1', '168.j1.b1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [1092, -1, 9692, -1, 247, -1, 7647, -1], 'generators': [522, 8, 12], 'label': '672.729.56.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1.a1', 'old_label': '56.j1.b1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.j1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110520962
    {'ambient': '672.729', 'aut_centralizer_order': 1344, 'aut_label': '84.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1344, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '28.a1.a1', '42.a1.a1', '42.a1.b1', '42.b1.a1'], 'contains': ['168.a1.a1', '168.c1.a1', '168.c1.b1', '168.d1.a1', '168.f1.a1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4549, 4648, 6706, 4310, 5361, 3613, 5996, 6574], 'generators': [187, 348, 336], 'label': '672.729.84.a1.a1', 'mobius_quo': 0, 'mobius_sub': 14, 'normal_closure': '84.a1.a1', 'normal_contained_in': ['12.a1.a1', '42.a1.a1', '42.a1.b1', '42.b1.a1'], 'normal_contains': ['168.a1.a1', '168.c1.a1', '168.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '84.a1.a1', 'projective_image': '168.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '42.2', 'quotient_action_kernel_order': 42, 'quotient_fusion': None, 'short_label': '84.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110520963
    {'ambient': '672.729', 'aut_centralizer_order': 672, 'aut_label': '84.b1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1344, 'centralizer': '4.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '28.b1.a1', '42.a1.a1', '42.c1.a1', '42.d1.a1'], 'contains': ['168.a1.a1', '168.e1.a1', '168.g1.a1', '168.i1.a1'], 'core': '84.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4351, 1629, 3608, 4818, 3990, 1805, 4517, 7908], 'generators': [1, 348, 336], 'label': '672.729.84.b1.a1', 'mobius_quo': 0, 'mobius_sub': 14, 'normal_closure': '84.b1.a1', 'normal_contained_in': ['12.b1.a1', '42.a1.a1', '42.c1.a1', '42.d1.a1'], 'normal_contains': ['168.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '84.b1.a1', 'projective_image': '168.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '21.1', 'quotient_action_kernel_order': 21, 'quotient_fusion': None, 'short_label': '84.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110520964
    {'ambient': '672.729', 'aut_centralizer_order': 672, 'aut_label': '84.b1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1344, 'centralizer': '4.b1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '28.b1.b1', '42.a1.b1', '42.c1.b1', '42.d1.a1'], 'contains': ['168.a1.a1', '168.e1.b1', '168.g1.b1', '168.i1.b1'], 'core': '84.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4351, 1629, 4342, 8473, 3990, 1805, 4819, 7657], 'generators': [505, 348, 336], 'label': '672.729.84.b1.b1', 'mobius_quo': 0, 'mobius_sub': 14, 'normal_closure': '84.b1.b1', 'normal_contained_in': ['12.b1.b1', '42.a1.b1', '42.c1.b1', '42.d1.a1'], 'normal_contains': ['168.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '84.b1.b1', 'projective_image': '168.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '21.1', 'quotient_action_kernel_order': 21, 'quotient_fusion': None, 'short_label': '84.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110520965
    {'ambient': '672.729', 'aut_centralizer_order': 1344, 'aut_label': '84.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1344, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '28.c1.a1', '42.b1.a1', '42.d1.a1', '42.e1.a1'], 'contains': ['168.a1.a1', '168.b1.a1', '168.b1.b1'], 'core': '84.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8822, 5266, 2027, 7541, 7267, 1329, 3355, 8657], 'generators': [348, 168], 'label': '672.729.84.c1.a1', 'mobius_quo': 0, 'mobius_sub': 14, 'normal_closure': '84.c1.a1', 'normal_contained_in': ['12.c1.a1', '42.b1.a1', '42.d1.a1', '42.e1.a1'], 'normal_contains': ['168.a1.a1', '168.b1.b1', '168.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '84.c1.a1', 'projective_image': '168.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '42.2', 'quotient_action_kernel_order': 42, 'quotient_fusion': None, 'short_label': '84.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110520966
    {'ambient': '672.729', 'aut_centralizer_order': 1344, 'aut_label': '84.d1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1344, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '28.d1.a1', '42.b1.a1', '42.c1.a1', '42.c1.b1'], 'contains': ['168.a1.a1', '168.h1.a1'], 'core': '84.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7192, 4030, 3057, 6095, 7540, 3050, 3717, 7323], 'generators': [355, 348], 'label': '672.729.84.d1.a1', 'mobius_quo': 0, 'mobius_sub': 14, 'normal_closure': '84.d1.a1', 'normal_contained_in': ['12.d1.a1', '42.b1.a1', '42.c1.a1', '42.c1.b1'], 'normal_contains': ['168.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '84.d1.a1', 'projective_image': '168.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '42.2', 'quotient_action_kernel_order': 42, 'quotient_fusion': None, 'short_label': '84.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110520967
    {'ambient': '672.729', 'aut_centralizer_order': 672, 'aut_label': '84.e1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1344, 'centralizer': '4.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '28.e1.a1', '42.a1.b1', '42.c1.a1', '42.e1.a1'], 'contains': ['168.a1.a1', '168.j1.a1'], 'core': '84.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4812, 2991, 5880, 6738, 3771, 2281, 6126, 6907], 'generators': [6, 336], 'label': '672.729.84.e1.a1', 'mobius_quo': 0, 'mobius_sub': 14, 'normal_closure': '84.e1.a1', 'normal_contained_in': ['12.e1.a1', '42.a1.b1', '42.c1.a1', '42.e1.a1'], 'normal_contains': ['168.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '84.e1.a1', 'projective_image': '168.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '21.1', 'quotient_action_kernel_order': 21, 'quotient_fusion': None, 'short_label': '84.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110520968
    {'ambient': '672.729', 'aut_centralizer_order': 672, 'aut_label': '84.e1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1344, 'centralizer': '4.e1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.e1.b1', '28.e1.b1', '42.a1.a1', '42.c1.b1', '42.e1.a1'], 'contains': ['168.a1.a1', '168.j1.b1'], 'core': '84.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4812, 2991, 6100, 5291, 3771, 2281, 5866, 8241], 'generators': [522, 336], 'label': '672.729.84.e1.b1', 'mobius_quo': 0, 'mobius_sub': 14, 'normal_closure': '84.e1.b1', 'normal_contained_in': ['12.e1.b1', '42.a1.a1', '42.c1.b1', '42.e1.a1'], 'normal_contains': ['168.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '84.e1.b1', 'projective_image': '168.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '21.1', 'quotient_action_kernel_order': 21, 'quotient_fusion': None, 'short_label': '84.e1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110520969
    {'ambient': '672.729', 'aut_centralizer_order': 336, 'aut_label': '84.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1344, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '28.f1.a1', '42.b1.a1'], 'contains': ['168.b1.a1', '168.f1.a1', '168.h1.a1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8423, -1, 645, -1, 8530, -1, 957, -1], 'generators': [355, 168], 'label': '672.729.84.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '84.f1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110520970
    {'ambient': '672.729', 'aut_centralizer_order': 336, 'aut_label': '84.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1344, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.b1', '28.f1.b1', '42.b1.a1'], 'contains': ['168.b1.b1', '168.f1.a1', '168.h1.a1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8423, -1, 898, -1, 8530, -1, 1538, -1], 'generators': [355, 516], 'label': '672.729.84.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '84.f1.b1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110520971
    {'ambient': '672.729', 'aut_centralizer_order': 16, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '168.47', 'aut_weyl_index': 32, 'centralizer': '84.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.c1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.j1.a1', '12.e1.a1', '28.e1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2618, 3894, 5770, 5228, 2621, 7634, 6975, 918], 'generators': [6, 8, 12, 336, 96], 'label': '672.729.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.a1.b1', '2.c1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '12.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '168.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '84.9'}
  • id: 110520972
    {'ambient': '672.729', 'aut_centralizer_order': 168, 'aut_label': '84.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 672, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '28.g1.a1', '42.d1.a1'], 'contains': ['168.b1.a1', '168.g1.a1', '168.g1.b1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9782, -1, 2712, -1, 7058, -1, 2427, -1], 'generators': [1, 168], 'label': '672.729.84.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '84.g1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110520973
    {'ambient': '672.729', 'aut_centralizer_order': 168, 'aut_label': '84.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 672, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.b1', '28.g1.b1', '42.d1.a1'], 'contains': ['168.b1.b1', '168.g1.a1', '168.g1.b1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9782, -1, 2184, -1, 7058, -1, 2870, -1], 'generators': [1, 516], 'label': '672.729.84.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '84.g1.b1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.g1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110520974
    {'ambient': '672.729', 'aut_centralizer_order': 168, 'aut_label': '84.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1344, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '28.h1.a1', '42.a1.a1'], 'contains': ['168.c1.a1', '168.i1.a1', '168.j1.b1'], 'core': '168.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [755, -1, 9176, -1, 408, -1, 7447, -1], 'generators': [1, 522], 'label': '672.729.84.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '84.h1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110520975
    {'ambient': '672.729', 'aut_centralizer_order': 168, 'aut_label': '84.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1344, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.b1', '28.h1.b1', '42.a1.b1'], 'contains': ['168.c1.a1', '168.i1.b1', '168.j1.a1'], 'core': '168.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [755, -1, 7508, -1, 408, -1, 9202, -1], 'generators': [169, 6], 'label': '672.729.84.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '84.h1.b1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.h1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110520976
    {'ambient': '672.729', 'aut_centralizer_order': 168, 'aut_label': '84.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1344, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.c1', '28.h1.c1', '42.a1.a1'], 'contains': ['168.c1.b1', '168.i1.a1', '168.j1.b1'], 'core': '168.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [755, -1, 9715, -1, 408, -1, 7361, -1], 'generators': [337, 522], 'label': '672.729.84.h1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '84.h1.c1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.h1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110520977
    {'ambient': '672.729', 'aut_centralizer_order': 168, 'aut_label': '84.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1344, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.d1', '28.h1.d1', '42.a1.b1'], 'contains': ['168.c1.b1', '168.i1.b1', '168.j1.a1'], 'core': '168.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [755, -1, 8184, -1, 408, -1, 9011, -1], 'generators': [505, 6], 'label': '672.729.84.h1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '84.h1.d1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.h1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110520978
    {'ambient': '672.729', 'aut_centralizer_order': 896, 'aut_label': '96.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 896, 'centralizer': '3.a1.a1', 'complements': ['7.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.a1.a1', '48.b1.a1', '48.c1.a1', '48.d1.a1', '48.d1.b1', '48.e1.a1', '48.e1.b1'], 'contains': ['672.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2501, 8190, 5559, 2131, 3335, 4962, 5559, 5473], 'generators': [96], 'label': '672.729.96.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': ['32.a1.a1', '48.b1.a1', '48.c1.a1', '48.a1.a1'], 'normal_contains': ['672.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '672.729', 'quotient_action_image': '3.1', 'quotient_action_kernel': '32.28', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110520979
    {'ambient': '672.729', 'aut_centralizer_order': 768, 'aut_label': '112.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5376, 'centralizer': '7.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '56.a1.a1', '56.b1.a1', '56.c1.a1', '56.c1.b1'], 'contains': ['224.a1.a1', '336.a1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [3499, -1, 5162, -1, 3817, -1, 5341, -1], 'generators': [348, 8], 'label': '672.729.112.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '112.a1.a1', 'projective_image': '336.167', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110520980
    {'ambient': '672.729', 'aut_centralizer_order': 768, 'aut_label': '112.b1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5376, 'centralizer': '7.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '56.a1.a1', '56.d1.a1', '56.e1.a1', '56.e1.b1', '56.f1.a1', '56.f1.b1', '56.g1.a1'], 'contains': ['224.a1.a1', '336.b1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6486, -1, 1629, -1, 6260, -1, 2327, -1], 'generators': [336, 8], 'label': '672.729.112.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '112.b1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110520981
    {'ambient': '672.729', 'aut_centralizer_order': 768, 'aut_label': '112.c1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5376, 'centralizer': '7.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '56.a1.a1', '56.h1.a1', '56.h1.b1', '56.i1.a1', '56.i1.b1', '56.j1.a1', '56.j1.b1'], 'contains': ['224.a1.a1', '336.c1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [1404, -1, 8581, -1, 1731, -1, 8040, -1], 'generators': [12, 8], 'label': '672.729.112.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '112.c1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110520982
    {'ambient': '672.729', 'aut_centralizer_order': 16, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '168.47', 'aut_weyl_index': 32, 'centralizer': '84.e1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.c1.b1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.j1.b1', '12.e1.b1', '28.e1.b1'], 'core': '4.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2618, 3894, 6121, 4043, 2621, 7634, 5909, 3548], 'generators': [522, 8, 12, 336, 96], 'label': '672.729.4.e1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.b1', 'normal_contained_in': ['2.a1.a1', '2.c1.b1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '12.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.b1', 'projective_image': '168.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.b1', 'subgroup_fusion': None, 'weyl_group': '84.9'}
  • id: 110520983
    {'ambient': '672.729', 'aut_centralizer_order': 192, 'aut_label': '112.d1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5376, 'centralizer': '14.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '56.b1.a1', '56.d1.a1', '56.h1.a1'], 'contains': ['224.a1.a1', '336.d1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2634, -1, 7061, -1, 3673, -1, 6609, -1], 'generators': [523, 8], 'label': '672.729.112.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '112.d1.a1', 'projective_image': '672.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110520984
    {'ambient': '672.729', 'aut_centralizer_order': 192, 'aut_label': '112.d1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5376, 'centralizer': '14.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.b1', '56.b1.a1', '56.d1.a1', '56.h1.b1'], 'contains': ['224.a1.a1', '336.d1.b1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2634, -1, 8303, -1, 3673, -1, 6451, -1], 'generators': [187, 8], 'label': '672.729.112.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '112.d1.b1', 'projective_image': '672.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110520985
    {'ambient': '672.729', 'aut_centralizer_order': 96, 'aut_label': '112.e1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5376, 'centralizer': '28.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '56.c1.a1', '56.e1.a1', '56.i1.a1'], 'contains': ['224.a1.a1', '336.e1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [2124, -1, 3775, -1, 2824, -1, 4387, -1], 'generators': [1, 8], 'label': '672.729.112.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.b1.a1', 'old_label': '112.e1.a1', 'projective_image': '672.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110520986
    {'ambient': '672.729', 'aut_centralizer_order': 96, 'aut_label': '112.e1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5376, 'centralizer': '28.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.b1', '56.c1.b1', '56.e1.b1', '56.i1.b1'], 'contains': ['224.a1.a1', '336.e1.b1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [2124, -1, 5573, -1, 2824, -1, 5569, -1], 'generators': [505, 8], 'label': '672.729.112.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.b1.b1', 'old_label': '112.e1.b1', 'projective_image': '672.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110520987
    {'ambient': '672.729', 'aut_centralizer_order': 5376, 'aut_label': '168.a1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5376, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '56.a1.a1', '84.a1.a1', '84.b1.a1', '84.b1.b1', '84.c1.a1', '84.d1.a1', '84.e1.a1', '84.e1.b1'], 'contains': ['336.a1.a1', '336.b1.a1', '336.c1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4943, 5266, 4569, 4547, 4991, 3613, 4883, 6647], 'generators': [348, 336], 'label': '672.729.168.a1.a1', 'mobius_quo': 2, 'mobius_sub': -56, 'normal_closure': '168.a1.a1', 'normal_contained_in': ['24.a1.a1', '84.a1.a1', '84.b1.a1', '84.b1.b1', '84.c1.a1', '84.d1.a1', '84.e1.b1', '84.e1.a1'], 'normal_contains': ['336.b1.a1', '336.c1.a1', '336.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '168.a1.a1', 'projective_image': '168.51', 'quotient_action_image': '1.1', 'quotient_action_kernel': '168.51', 'quotient_action_kernel_order': 168, 'quotient_fusion': None, 'short_label': '168.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110520988
    {'ambient': '672.729', 'aut_centralizer_order': 1344, 'aut_label': '168.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2688, 'centralizer': '2.b1.a1', 'complements': ['4.h1.d1', '4.h1.b1', '4.h1.a1', '4.h1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '56.f1.a1', '84.c1.a1', '84.f1.a1', '84.g1.a1'], 'contains': ['336.b1.a1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9380, 7560, 1231, 5512, 7516, 3277, 1730, 6883], 'generators': [168], 'label': '672.729.168.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '168.b1.a1', 'normal_contained_in': ['24.b1.a1', '84.c1.a1'], 'normal_contains': ['336.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '168.b1.a1', 'projective_image': '336.165', 'quotient_action_image': '2.1', 'quotient_action_kernel': '84.9', 'quotient_action_kernel_order': 84, 'quotient_fusion': None, 'short_label': '168.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110520989
    {'ambient': '672.729', 'aut_centralizer_order': 1344, 'aut_label': '168.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2688, 'centralizer': '2.b1.a1', 'complements': ['4.h1.d1', '4.h1.b1', '4.h1.a1', '4.h1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['24.b1.b1', '56.f1.b1', '84.c1.a1', '84.f1.b1', '84.g1.b1'], 'contains': ['336.b1.a1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9380, 7560, 1837, 4019, 7516, 3277, 2413, 7103], 'generators': [516], 'label': '672.729.168.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '168.b1.b1', 'normal_contained_in': ['24.b1.b1', '84.c1.a1'], 'normal_contains': ['336.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '168.b1.b1', 'projective_image': '336.165', 'quotient_action_image': '2.1', 'quotient_action_kernel': '84.9', 'quotient_action_kernel_order': 84, 'quotient_fusion': None, 'short_label': '168.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110520990
    {'ambient': '672.729', 'aut_centralizer_order': 1344, 'aut_label': '168.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2688, 'centralizer': '2.b1.a1', 'complements': ['4.g1.a1', '4.g1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '56.h1.a1', '84.a1.a1', '84.h1.a1', '84.h1.b1'], 'contains': ['336.c1.a1', '336.d1.a1'], 'core': '168.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1222, 6407, 7508, 2986, 1886, 4207, 7858, 6127], 'generators': [523, 12], 'label': '672.729.168.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '168.c1.a1', 'normal_contained_in': ['24.c1.a1', '84.a1.a1'], 'normal_contains': ['336.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '168.c1.a1', 'projective_image': '336.165', 'quotient_action_image': '2.1', 'quotient_action_kernel': '84.2', 'quotient_action_kernel_order': 84, 'quotient_fusion': None, 'short_label': '168.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110520991
    {'ambient': '672.729', 'aut_centralizer_order': 1344, 'aut_label': '168.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2688, 'centralizer': '2.b1.a1', 'complements': ['4.g1.a1', '4.g1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['24.c1.b1', '56.h1.b1', '84.a1.a1', '84.h1.c1', '84.h1.d1'], 'contains': ['336.c1.a1', '336.d1.b1'], 'core': '168.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1222, 6407, 8641, 2639, 1886, 4207, 7656, 6378], 'generators': [187, 12], 'label': '672.729.168.c1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '168.c1.b1', 'normal_contained_in': ['24.c1.b1', '84.a1.a1'], 'normal_contains': ['336.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '168.c1.b1', 'projective_image': '336.165', 'quotient_action_image': '2.1', 'quotient_action_kernel': '84.2', 'quotient_action_kernel_order': 84, 'quotient_fusion': None, 'short_label': '168.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110520992
    {'ambient': '672.729', 'aut_centralizer_order': 1344, 'aut_label': '168.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2688, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '56.b1.a1', '84.a1.a1'], 'contains': ['336.a1.a1', '336.d1.a1', '336.d1.b1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3887, -1, 6822, -1, 4238, -1, 6124, -1], 'generators': [187, 348], 'label': '672.729.168.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '168.d1.a1', 'projective_image': '336.167', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110520993
    {'ambient': '672.729', 'aut_centralizer_order': 8, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '168.47', 'aut_weyl_index': 32, 'centralizer': '42.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.b1.a1', '8.f1.a1', '8.h1.a1', '12.f1.a1', '28.f1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7838, -1, 336, -1, 9026, -1, 575, -1], 'generators': [355, 8, 336, 168, 96], 'label': '672.729.4.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.f1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 110520994
    {'ambient': '672.729', 'aut_centralizer_order': 672, 'aut_label': '168.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2688, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '56.c1.a1', '84.b1.a1'], 'contains': ['336.a1.a1', '336.e1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3357, -1, 3665, -1, 3164, -1, 4479, -1], 'generators': [1, 348], 'label': '672.729.168.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '168.e1.a1', 'projective_image': '336.167', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110520995
    {'ambient': '672.729', 'aut_centralizer_order': 672, 'aut_label': '168.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2688, 'centralizer': '4.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.b1', '56.c1.b1', '84.b1.b1'], 'contains': ['336.a1.a1', '336.e1.b1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3357, -1, 4975, -1, 3164, -1, 5145, -1], 'generators': [505, 348], 'label': '672.729.168.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '168.e1.b1', 'projective_image': '336.167', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.e1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110520996
    {'ambient': '672.729', 'aut_centralizer_order': 1344, 'aut_label': '168.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2688, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '56.d1.a1', '84.a1.a1', '84.f1.a1', '84.f1.b1'], 'contains': ['336.b1.a1', '336.d1.a1', '336.d1.b1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5905, -1, 1037, -1, 6459, -1, 2026, -1], 'generators': [187, 336], 'label': '672.729.168.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '168.f1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110520997
    {'ambient': '672.729', 'aut_centralizer_order': 672, 'aut_label': '168.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2688, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '56.e1.a1', '84.b1.a1', '84.g1.a1', '84.g1.b1'], 'contains': ['336.b1.a1', '336.e1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6196, -1, 2412, -1, 5792, -1, 2746, -1], 'generators': [1, 336], 'label': '672.729.168.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '168.g1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110520998
    {'ambient': '672.729', 'aut_centralizer_order': 672, 'aut_label': '168.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2688, 'centralizer': '4.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.b1', '56.e1.b1', '84.b1.b1', '84.g1.a1', '84.g1.b1'], 'contains': ['336.b1.a1', '336.e1.b1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6196, -1, 2633, -1, 5792, -1, 3010, -1], 'generators': [505, 336], 'label': '672.729.168.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '168.g1.b1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.g1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110520999
    {'ambient': '672.729', 'aut_centralizer_order': 1344, 'aut_label': '168.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2688, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '56.g1.a1', '84.d1.a1', '84.f1.a1', '84.f1.b1'], 'contains': ['336.b1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8026, -1, 607, -1, 8119, -1, 1367, -1], 'generators': [355], 'label': '672.729.168.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '168.h1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110521000
    {'ambient': '672.729', 'aut_centralizer_order': 672, 'aut_label': '168.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2688, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '56.i1.a1', '84.b1.a1', '84.h1.a1', '84.h1.c1'], 'contains': ['336.c1.a1', '336.e1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [733, -1, 9398, -1, 1174, -1, 7237, -1], 'generators': [1, 12], 'label': '672.729.168.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '168.i1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110521001
    {'ambient': '672.729', 'aut_centralizer_order': 672, 'aut_label': '168.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2688, 'centralizer': '4.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.b1', '56.i1.b1', '84.b1.b1', '84.h1.b1', '84.h1.d1'], 'contains': ['336.c1.a1', '336.e1.b1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [733, -1, 8058, -1, 1174, -1, 8710, -1], 'generators': [505, 12], 'label': '672.729.168.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '168.i1.b1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.i1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110521002
    {'ambient': '672.729', 'aut_centralizer_order': 672, 'aut_label': '168.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2688, 'centralizer': '4.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '56.j1.a1', '84.e1.a1', '84.h1.b1', '84.h1.d1'], 'contains': ['336.c1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1036, -1, 7756, -1, 408, -1, 9059, -1], 'generators': [6], 'label': '672.729.168.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '168.j1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110521003
    {'ambient': '672.729', 'aut_centralizer_order': 672, 'aut_label': '168.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2688, 'centralizer': '4.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.b1', '56.j1.b1', '84.e1.b1', '84.h1.a1', '84.h1.c1'], 'contains': ['336.c1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1036, -1, 9674, -1, 408, -1, 7486, -1], 'generators': [522], 'label': '672.729.168.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '168.j1.b1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.j1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110521004
    {'ambient': '672.729', 'aut_centralizer_order': 8, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '168.47', 'aut_weyl_index': 32, 'centralizer': '42.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.b1.b1', '8.f1.a1', '8.h1.a1', '12.f1.b1', '28.f1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7838, -1, 825, -1, 9026, -1, 1170, -1], 'generators': [355, 8, 336, 516, 96], 'label': '672.729.4.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.f1.b1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.b1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 110521005
    {'ambient': '672.729', 'aut_centralizer_order': 768, 'aut_label': '224.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5376, 'centralizer': '7.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '112.a1.a1', '112.b1.a1', '112.c1.a1', '112.d1.a1', '112.d1.b1', '112.e1.a1', '112.e1.b1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [2368, -1, 5788, -1, 3504, -1, 5645, -1], 'generators': [8], 'label': '672.729.224.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '224.a1.a1', 'projective_image': '672.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110521006
    {'ambient': '672.729', 'aut_centralizer_order': 5376, 'aut_label': '336.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5376, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '112.a1.a1', '168.a1.a1', '168.d1.a1', '168.e1.a1', '168.e1.b1'], 'contains': ['672.a1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3587, 6742, 4975, 3279, 3817, 3927, 5246, 6396], 'generators': [348], 'label': '672.729.336.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '336.a1.a1', 'normal_contained_in': ['48.a1.a1', '168.a1.a1'], 'normal_contains': ['672.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '336.a1.a1', 'projective_image': '336.167', 'quotient_action_image': '1.1', 'quotient_action_kernel': '336.167', 'quotient_action_kernel_order': 336, 'quotient_fusion': None, 'short_label': '336.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110521007
    {'ambient': '672.729', 'aut_centralizer_order': 5376, 'aut_label': '336.b1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5376, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '112.b1.a1', '168.a1.a1', '168.b1.a1', '168.b1.b1', '168.f1.a1', '168.g1.a1', '168.g1.b1', '168.h1.a1'], 'contains': ['672.a1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6361, 7560, 1737, 4019, 6179, 3613, 2370, 6647], 'generators': [336], 'label': '672.729.336.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '336.b1.a1', 'normal_contained_in': ['48.b1.a1', '168.a1.a1', '168.b1.b1', '168.b1.a1'], 'normal_contains': ['672.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '336.b1.a1', 'projective_image': '336.165', 'quotient_action_image': '1.1', 'quotient_action_kernel': '336.165', 'quotient_action_kernel_order': 336, 'quotient_fusion': None, 'short_label': '336.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110521008
    {'ambient': '672.729', 'aut_centralizer_order': 5376, 'aut_label': '336.c1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5376, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '112.c1.a1', '168.a1.a1', '168.c1.a1', '168.c1.b1', '168.i1.a1', '168.i1.b1', '168.j1.a1', '168.j1.b1'], 'contains': ['672.a1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1222, 7151, 8499, 2974, 1731, 4241, 7706, 6176], 'generators': [12], 'label': '672.729.336.c1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '336.c1.a1', 'normal_contained_in': ['48.c1.a1', '168.a1.a1', '168.c1.a1', '168.c1.b1'], 'normal_contains': ['672.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '336.c1.a1', 'projective_image': '336.165', 'quotient_action_image': '1.1', 'quotient_action_kernel': '336.165', 'quotient_action_kernel_order': 336, 'quotient_fusion': None, 'short_label': '336.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110521009
    {'ambient': '672.729', 'aut_centralizer_order': 1344, 'aut_label': '336.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5376, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '112.d1.a1', '168.c1.a1', '168.d1.a1', '168.f1.a1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2852, -1, 6870, -1, 3661, -1, 6271, -1], 'generators': [523], 'label': '672.729.336.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '168.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '336.d1.a1', 'projective_image': '672.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110521010
    {'ambient': '672.729', 'aut_centralizer_order': 1344, 'aut_label': '336.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5376, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.b1', '112.d1.b1', '168.c1.b1', '168.d1.a1', '168.f1.a1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2852, -1, 7623, -1, 3661, -1, 6154, -1], 'generators': [187], 'label': '672.729.336.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '168.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '336.d1.b1', 'projective_image': '672.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110521011
    {'ambient': '672.729', 'aut_centralizer_order': 672, 'aut_label': '336.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5376, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '112.e1.a1', '168.e1.a1', '168.g1.a1', '168.i1.a1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2160, -1, 3719, -1, 2995, -1, 4433, -1], 'generators': [1], 'label': '672.729.336.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '336.e1.a1', 'projective_image': '672.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110521012
    {'ambient': '672.729', 'aut_centralizer_order': 672, 'aut_label': '336.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5376, 'centralizer': '4.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.b1', '112.e1.b1', '168.e1.b1', '168.g1.b1', '168.i1.b1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2160, -1, 5523, -1, 2995, -1, 5474, -1], 'generators': [505], 'label': '672.729.336.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '336.e1.b1', 'projective_image': '672.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110521013
    {'ambient': '672.729', 'aut_centralizer_order': None, 'aut_label': '672.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '224.a1.a1', '336.a1.a1', '336.b1.a1', '336.c1.a1', '336.d1.a1', '336.d1.b1', '336.e1.a1', '336.e1.b1'], 'contains': [], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2501, 7355, 5708, 3126, 3504, 4084, 5559, 6286], 'generators': [], 'label': '672.729.672.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '672.a1.a1', 'normal_contained_in': ['96.a1.a1', '336.b1.a1', '336.c1.a1', '336.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '672.a1.a1', 'projective_image': '672.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110521014
    {'ambient': '672.729', 'aut_centralizer_order': 4, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '336.125', 'aut_weyl_index': 16, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.b1.a1', '8.g1.a1', '8.g1.b1', '12.g1.a1', '28.g1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9666, -1, 2390, -1, 6658, -1, 1928, -1], 'generators': [1, 8, 336, 168, 96], 'label': '672.729.4.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.g1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '84.9'}
  • id: 110521015
    {'ambient': '672.729', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '672.1266', 'aut_weyl_index': 8, 'centralizer': '168.a1.a1', 'complements': ['336.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.e1.b1', '4.h1.a1', '4.h1.c1', '6.a1.a1', '14.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2956, 1124, 6851, 2428, 3333, 7634, 6241, 3548], 'generators': [1, 96, 336, 8, 522, 12], 'label': '672.729.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.e1.b1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '168.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '168.51'}
  • id: 110521016
    {'ambient': '672.729', 'aut_centralizer_order': 4, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '336.125', 'aut_weyl_index': 16, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.b1.b1', '8.g1.a1', '8.g1.b1', '12.g1.b1', '28.g1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9666, -1, 1927, -1, 6658, -1, 2301, -1], 'generators': [1, 8, 336, 516, 96], 'label': '672.729.4.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.g1.b1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1.b1', 'subgroup_fusion': None, 'weyl_group': '84.9'}
  • id: 110521017
    {'ambient': '672.729', 'aut_centralizer_order': 4, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '168.47', 'aut_weyl_index': 32, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.c1.a1', '8.i1.a1', '8.j1.b1', '12.h1.a1', '28.h1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [473, -1, 9169, -1, 897, -1, 8062, -1], 'generators': [1, 8, 12, 522, 96], 'label': '672.729.4.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.h1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1.a1', 'subgroup_fusion': None, 'weyl_group': '84.9'}
  • id: 110521018
    {'ambient': '672.729', 'aut_centralizer_order': 4, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '168.47', 'aut_weyl_index': 32, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1'], 'contains': ['8.c1.a1', '8.i1.b1', '8.j1.a1', '12.h1.b1', '28.h1.b1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [473, -1, 8244, -1, 897, -1, 9363, -1], 'generators': [169, 8, 12, 6, 96], 'label': '672.729.4.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '4.h1.b1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1.b1', 'subgroup_fusion': None, 'weyl_group': '84.9'}
  • id: 110521019
    {'ambient': '672.729', 'aut_centralizer_order': 4, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '168.47', 'aut_weyl_index': 32, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.c1.b1', '8.i1.a1', '8.j1.b1', '12.h1.c1', '28.h1.c1'], 'core': '8.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [473, -1, 9536, -1, 897, -1, 7791, -1], 'generators': [337, 8, 12, 522, 96], 'label': '672.729.4.h1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.h1.c1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1.c1', 'subgroup_fusion': None, 'weyl_group': '84.9'}
  • id: 110521020
    {'ambient': '672.729', 'aut_centralizer_order': 4, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '168.47', 'aut_weyl_index': 32, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1'], 'contains': ['8.c1.b1', '8.i1.b1', '8.j1.a1', '12.h1.d1', '28.h1.d1'], 'core': '8.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [473, -1, 8710, -1, 897, -1, 9087, -1], 'generators': [505, 8, 12, 6, 96], 'label': '672.729.4.h1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '4.h1.d1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1.d1', 'subgroup_fusion': None, 'weyl_group': '84.9'}
  • id: 110521021
    {'ambient': '672.729', 'aut_centralizer_order': 28, 'aut_label': '6.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '96.231', 'aut_weyl_index': 56, 'centralizer': '24.a1.a1', 'complements': ['112.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.e1.b1', '12.h1.a1', '12.h1.c1', '42.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2833, 482, 6762, 3346, 3030, 4067, 6151, 7124], 'generators': [1, 336, 96, 522, 12], 'label': '672.729.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1', '3.a1.a1'], 'normal_contains': ['12.a1.a1', '12.b1.a1', '12.e1.b1', '42.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '168.51', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.15'}
  • id: 110521022
    {'ambient': '672.729', 'aut_centralizer_order': 28, 'aut_label': '6.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '96.231', 'aut_weyl_index': 56, 'centralizer': '24.a1.a1', 'complements': ['112.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.b1.b1', '12.e1.a1', '12.h1.b1', '12.h1.d1', '42.a1.b1'], 'core': '6.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2833, 482, 6525, 8946, 3030, 4067, 6734, 4910], 'generators': [505, 336, 96, 6, 12], 'label': '672.729.6.a1.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.a1.b1', 'normal_contained_in': ['2.a1.b1', '3.a1.a1'], 'normal_contains': ['12.a1.a1', '12.b1.b1', '12.e1.a1', '42.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.b1', 'projective_image': '168.51', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1.b1', 'subgroup_fusion': None, 'weyl_group': '24.15'}
  • id: 110521023
    {'ambient': '672.729', 'aut_centralizer_order': 56, 'aut_label': '6.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '96.231', 'aut_weyl_index': 56, 'centralizer': '6.b1.a1', 'complements': ['112.e1.a1', '112.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.c1.a1', '12.d1.a1', '12.f1.a1', '12.f1.b1', '42.b1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7446, 4846, 1601, 6387, 7983, 4826, 2626, 6017], 'generators': [355, 168, 96, 348, 336], 'label': '672.729.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.b1.a1', '3.a1.a1'], 'normal_contains': ['12.a1.a1', '12.c1.a1', '12.d1.a1', '42.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '168.51', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 110521024
    {'ambient': '672.729', 'aut_centralizer_order': 28, 'aut_label': '6.c1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '96.231', 'aut_weyl_index': 56, 'centralizer': '24.a1.a1', 'complements': ['112.e1.b1', '112.d1.a1', '112.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.d1.a1', '12.e1.a1', '42.c1.a1'], 'core': '6.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4112, 1481, 3940, 5439, 4039, 3298, 4225, 5448], 'generators': [1, 96, 348, 6, 336], 'label': '672.729.6.c1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.c1.a1', 'normal_contained_in': ['2.c1.a1', '3.a1.a1'], 'normal_contains': ['12.b1.a1', '12.d1.a1', '12.e1.a1', '42.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '168.51', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.15'}
  • id: 110521025
    {'ambient': '672.729', 'aut_centralizer_order': 28, 'aut_label': '6.c1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '96.231', 'aut_weyl_index': 56, 'centralizer': '24.a1.a1', 'complements': ['112.e1.a1', '112.d1.a1', '112.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.b1', '3.a1.a1'], 'contains': ['12.b1.b1', '12.d1.a1', '12.e1.b1', '42.c1.b1'], 'core': '6.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4112, 1481, 4405, 7334, 4039, 3298, 4673, 6586], 'generators': [505, 96, 348, 522, 336], 'label': '672.729.6.c1.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.c1.b1', 'normal_contained_in': ['2.c1.b1', '3.a1.a1'], 'normal_contains': ['12.b1.b1', '12.d1.a1', '12.e1.b1', '42.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.c1.b1', 'projective_image': '168.51', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.c1.b1', 'subgroup_fusion': None, 'weyl_group': '24.15'}
  • id: 110521026
    {'ambient': '672.729', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '672.1266', 'aut_weyl_index': 8, 'centralizer': '168.a1.a1', 'complements': ['336.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.b1', '4.e1.a1', '4.h1.b1', '4.h1.d1', '6.a1.b1', '14.a1.b1'], 'core': '2.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2956, 1124, 6380, 7609, 3333, 7634, 6854, 667], 'generators': [505, 96, 336, 8, 6, 12], 'label': '672.729.2.a1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.b1', '4.e1.a1', '6.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.b1', 'projective_image': '168.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.b1', 'subgroup_fusion': None, 'weyl_group': '168.51'}
  • id: 110521027
    {'ambient': '672.729', 'aut_centralizer_order': 28, 'aut_label': '6.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '192.1410', 'aut_weyl_index': 28, 'centralizer': '24.a1.a1', 'complements': ['112.d1.a1', '112.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.b1.b1', '12.c1.a1', '12.g1.a1', '12.g1.b1', '42.d1.a1'], 'core': '6.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8660, 2695, 2875, 9640, 6049, 1797, 3340, 7626], 'generators': [1, 168, 96, 348, 336], 'label': '672.729.6.d1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.d1.a1', 'normal_contained_in': ['2.d1.a1', '3.a1.a1'], 'normal_contains': ['12.b1.a1', '12.b1.b1', '12.c1.a1', '42.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '168.51', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.15'}
  • id: 110521045
    {'ambient': '672.729', 'aut_centralizer_order': 16, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '84.7', 'aut_weyl_index': 64, 'centralizer': '84.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.h1.b1', '4.h1.d1'], 'contains': ['16.c1.a1', '24.j1.a1', '56.j1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [180, -1, 8795, -1, 151, -1, 9748, -1], 'generators': [6, 12, 96, 8], 'label': '672.729.8.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '8.j1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1.a1', 'subgroup_fusion': None, 'weyl_group': '42.2'}
  • id: 110521028
    {'ambient': '672.729', 'aut_centralizer_order': 28, 'aut_label': '6.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '192.1410', 'aut_weyl_index': 28, 'centralizer': '24.a1.a1', 'complements': ['112.e1.a1', '112.e1.b1', '112.d1.a1', '112.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.e1.a1', '12.e1.b1', '42.e1.a1'], 'core': '6.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6104, 3848, 5211, 8088, 5152, 2521, 5468, 8134], 'generators': [6, 96, 12, 168, 336], 'label': '672.729.6.e1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.e1.a1', 'normal_contained_in': ['2.e1.a1', '3.a1.a1'], 'normal_contains': ['12.c1.a1', '12.e1.b1', '12.e1.a1', '42.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.e1.a1', 'projective_image': '168.51', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '24.15'}
  • id: 110521029
    {'ambient': '672.729', 'aut_centralizer_order': 6, 'aut_label': '7.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 42, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['14.a1.a1', '14.a1.b1', '14.b1.a1', '14.c1.a1', '14.c1.b1', '14.d1.a1', '14.e1.a1', '21.a1.a1'], 'core': '21.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7654, -1, 4295, -1, 5808, -1, 5156, -1], 'generators': [1, 336, 348, 6, 168, 8], 'label': '672.729.7.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '7.a1.a1', 'projective_image': '168.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 110521030
    {'ambient': '672.729', 'aut_centralizer_order': 128, 'aut_label': '8.a1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '42.1', 'aut_weyl_index': 128, 'centralizer': '21.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.e1.b1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '24.a1.a1', '56.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4660, 8122, 5154, 2272, 4191, 7634, 5045, 2316], 'generators': [348, 8, 96, 336], 'label': '672.729.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '4.c1.a1', '4.d1.a1', '4.e1.b1', '4.e1.a1'], 'normal_contains': ['16.b1.a1', '16.c1.a1', '16.a1.a1', '24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '168.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 110521031
    {'ambient': '672.729', 'aut_centralizer_order': 32, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '84.7', 'aut_weyl_index': 64, 'centralizer': '42.b1.a1', 'complements': ['84.h1.d1', '84.h1.b1', '84.h1.a1', '84.h1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['16.b1.a1', '24.b1.a1', '56.f1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9334, 9131, 593, 4370, 8859, 6857, 675, 2860], 'generators': [168, 336, 96, 8], 'label': '672.729.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.c1.a1'], 'normal_contains': ['16.b1.a1', '24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '336.165', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '42.2'}
  • id: 110521032
    {'ambient': '672.729', 'aut_centralizer_order': 32, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '84.7', 'aut_weyl_index': 64, 'centralizer': '42.b1.a1', 'complements': ['84.h1.d1', '84.h1.b1', '84.h1.a1', '84.h1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.f1.b1', '4.g1.b1'], 'contains': ['16.b1.a1', '24.b1.b1', '56.f1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9334, 9131, 1272, 3663, 8859, 6857, 1487, 3371], 'generators': [516, 336, 96, 8], 'label': '672.729.8.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': ['4.c1.a1'], 'normal_contains': ['16.b1.a1', '24.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.b1', 'projective_image': '336.165', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.b1.b1', 'subgroup_fusion': None, 'weyl_group': '42.2'}
  • id: 110521033
    {'ambient': '672.729', 'aut_centralizer_order': 32, 'aut_label': '8.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '84.7', 'aut_weyl_index': 64, 'centralizer': '42.b1.a1', 'complements': ['84.g1.a1', '84.g1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.h1.a1', '4.h1.b1'], 'contains': ['16.c1.a1', '16.d1.a1', '24.c1.a1', '56.h1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2105, 7054, 8155, 1155, 1437, 8455, 8824, 1165], 'generators': [523, 8, 96, 12], 'label': '672.729.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.c1.a1', '24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '336.165', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '42.2'}
  • id: 110521034
    {'ambient': '672.729', 'aut_centralizer_order': 32, 'aut_label': '8.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '84.7', 'aut_weyl_index': 64, 'centralizer': '42.b1.a1', 'complements': ['84.g1.a1', '84.g1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.h1.c1', '4.h1.d1'], 'contains': ['16.c1.a1', '16.d1.b1', '24.c1.b1', '56.h1.b1'], 'core': '8.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2105, 7054, 9311, 360, 1437, 8455, 8600, 1741], 'generators': [187, 8, 96, 12], 'label': '672.729.8.c1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.b1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.c1.a1', '24.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.b1', 'projective_image': '336.165', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.c1.b1', 'subgroup_fusion': None, 'weyl_group': '42.2'}
  • id: 110521035
    {'ambient': '672.729', 'aut_centralizer_order': 32, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '84.7', 'aut_weyl_index': 64, 'centralizer': '42.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.a1.a1', '16.d1.a1', '16.d1.b1', '24.d1.a1', '56.b1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3591, -1, 7019, -1, 3813, -1, 7300, -1], 'generators': [187, 8, 96, 348], 'label': '672.729.8.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.d1.a1', 'projective_image': '336.167', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 110521036
    {'ambient': '672.729', 'aut_centralizer_order': 16, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '84.7', 'aut_weyl_index': 64, 'centralizer': '84.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.a1.a1', '16.e1.a1', '24.e1.a1', '56.c1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2559, -1, 3802, -1, 1815, -1, 3926, -1], 'generators': [1, 8, 96, 348], 'label': '672.729.8.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.e1.a1', 'projective_image': '336.167', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '42.2'}
  • id: 110521037
    {'ambient': '672.729', 'aut_centralizer_order': 8, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '672.1266', 'aut_weyl_index': 8, 'centralizer': '42.b1.a1', 'complements': ['336.e1.a1', '336.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '4.d1.a1', '4.f1.a1', '4.f1.b1', '6.b1.a1', '14.b1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7446, 6288, 1571, 4779, 7554, 8739, 2972, 2108], 'generators': [355, 96, 168, 8, 348, 336], 'label': '672.729.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.c1.a1', '4.d1.a1', '6.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '168.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '42.2'}
  • id: 110521038
    {'ambient': '672.729', 'aut_centralizer_order': 16, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '84.7', 'aut_weyl_index': 64, 'centralizer': '84.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1'], 'contains': ['16.a1.a1', '16.e1.b1', '24.e1.b1', '56.c1.b1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2559, -1, 5592, -1, 1815, -1, 5457, -1], 'generators': [505, 8, 96, 348], 'label': '672.729.8.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '8.e1.b1', 'projective_image': '336.167', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.b1', 'subgroup_fusion': None, 'weyl_group': '42.2'}
  • id: 110521039
    {'ambient': '672.729', 'aut_centralizer_order': 32, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '84.7', 'aut_weyl_index': 64, 'centralizer': '42.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.f1.a1', '4.f1.b1'], 'contains': ['16.b1.a1', '16.d1.a1', '16.d1.b1', '24.f1.a1', '56.d1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5531, -1, 1014, -1, 5864, -1, 1275, -1], 'generators': [187, 8, 96, 336], 'label': '672.729.8.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.f1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 110521040
    {'ambient': '672.729', 'aut_centralizer_order': 16, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '84.7', 'aut_weyl_index': 64, 'centralizer': '84.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.g1.a1', '4.g1.b1'], 'contains': ['16.b1.a1', '16.e1.a1', '24.g1.a1', '56.e1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6353, -1, 2035, -1, 5486, -1, 2025, -1], 'generators': [1, 8, 96, 336], 'label': '672.729.8.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.g1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1.a1', 'subgroup_fusion': None, 'weyl_group': '42.2'}
  • id: 110521041
    {'ambient': '672.729', 'aut_centralizer_order': 16, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '84.7', 'aut_weyl_index': 64, 'centralizer': '84.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '4.g1.a1', '4.g1.b1'], 'contains': ['16.b1.a1', '16.e1.b1', '24.g1.b1', '56.e1.b1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6353, -1, 2473, -1, 5486, -1, 2576, -1], 'generators': [505, 8, 96, 336], 'label': '672.729.8.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.g1.b1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1.b1', 'subgroup_fusion': None, 'weyl_group': '42.2'}
  • id: 110521042
    {'ambient': '672.729', 'aut_centralizer_order': 32, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '84.7', 'aut_weyl_index': 64, 'centralizer': '42.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.f1.a1', '4.f1.b1'], 'contains': ['16.b1.a1', '24.h1.a1', '56.g1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7240, -1, 289, -1, 9195, -1, 477, -1], 'generators': [355, 336, 96, 8], 'label': '672.729.8.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.h1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.a1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 110521043
    {'ambient': '672.729', 'aut_centralizer_order': 16, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '84.7', 'aut_weyl_index': 64, 'centralizer': '84.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.h1.a1', '4.h1.c1'], 'contains': ['16.c1.a1', '16.e1.a1', '24.i1.a1', '56.i1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [884, -1, 9583, -1, 1059, -1, 7524, -1], 'generators': [1, 8, 96, 12], 'label': '672.729.8.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.i1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1.a1', 'subgroup_fusion': None, 'weyl_group': '42.2'}
  • id: 110521044
    {'ambient': '672.729', 'aut_centralizer_order': 16, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '84.7', 'aut_weyl_index': 64, 'centralizer': '84.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '4.h1.b1', '4.h1.d1'], 'contains': ['16.c1.a1', '16.e1.b1', '24.i1.b1', '56.i1.b1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [884, -1, 8483, -1, 1059, -1, 9047, -1], 'generators': [505, 8, 96, 12], 'label': '672.729.8.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '8.i1.b1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1.b1', 'subgroup_fusion': None, 'weyl_group': '42.2'}
  • id: 110521046
    {'ambient': '672.729', 'aut_centralizer_order': 16, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '84.7', 'aut_weyl_index': 64, 'centralizer': '84.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '4.h1.a1', '4.h1.c1'], 'contains': ['16.c1.a1', '24.j1.b1', '56.j1.b1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [180, -1, 9895, -1, 151, -1, 8388, -1], 'generators': [522, 12, 96, 8], 'label': '672.729.8.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.j1.b1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1.b1', 'subgroup_fusion': None, 'weyl_group': '42.2'}
  • id: 110521047
    {'ambient': '672.729', 'aut_centralizer_order': 224, 'aut_label': '12.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '24.15', 'aut_weyl_index': 224, 'centralizer': '6.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.a1.b1', '6.b1.a1'], 'contains': ['24.a1.a1', '24.c1.a1', '24.c1.b1', '24.d1.a1', '24.f1.a1', '84.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4399, 5414, 6649, 2323, 4794, 6088, 6340, 3909], 'generators': [187, 336, 96, 348], 'label': '672.729.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1', '6.a1.b1', '6.b1.a1'], 'normal_contains': ['24.a1.a1', '24.c1.a1', '24.c1.b1', '84.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '168.51', 'quotient_action_image': '6.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 110521048
    {'ambient': '672.729', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '672.1266', 'aut_weyl_index': 8, 'centralizer': '168.a1.a1', 'complements': ['336.e1.b1', '336.d1.a1', '336.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.d1.a1', '4.e1.a1', '6.c1.a1', '14.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4718, 2429, 3857, 3760, 4228, 6630, 4328, 1370], 'generators': [1, 96, 8, 348, 6, 336], 'label': '672.729.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.d1.a1', '4.e1.a1', '6.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '168.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '168.51'}
  • id: 110521049
    {'ambient': '672.729', 'aut_centralizer_order': 112, 'aut_label': '12.b1', 'aut_quo_index': 12, 'aut_stab_index': 2, 'aut_weyl_group': '24.15', 'aut_weyl_index': 224, 'centralizer': '12.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1', '6.c1.a1', '6.d1.a1'], 'contains': ['24.a1.a1', '24.e1.a1', '24.g1.a1', '24.i1.a1', '84.b1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2953, 1856, 3530, 3904, 3122, 3857, 4148, 6036], 'generators': [1, 336, 96, 348], 'label': '672.729.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.b1.a1', '6.a1.a1', '6.c1.a1', '6.d1.a1'], 'normal_contains': ['24.a1.a1', '84.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '168.51', 'quotient_action_image': '12.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 110521050
    {'ambient': '672.729', 'aut_centralizer_order': 112, 'aut_label': '12.b1', 'aut_quo_index': 12, 'aut_stab_index': 2, 'aut_weyl_group': '24.15', 'aut_weyl_index': 224, 'centralizer': '12.b1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.a1.b1', '6.c1.b1', '6.d1.a1'], 'contains': ['24.a1.a1', '24.e1.b1', '24.g1.b1', '24.i1.b1', '84.b1.b1'], 'core': '12.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2953, 1856, 4610, 8641, 3122, 3857, 4824, 5473], 'generators': [505, 336, 96, 348], 'label': '672.729.12.b1.b1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.b1.b1', 'normal_contained_in': ['4.b1.b1', '6.a1.b1', '6.c1.b1', '6.d1.a1'], 'normal_contains': ['24.a1.a1', '84.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.b1', 'projective_image': '168.51', 'quotient_action_image': '12.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.b1.b1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 110521051
    {'ambient': '672.729', 'aut_centralizer_order': 224, 'aut_label': '12.c1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '24.15', 'aut_weyl_index': 224, 'centralizer': '6.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.b1.a1', '6.d1.a1', '6.e1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.b1.b1', '84.c1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8568, 6402, 1644, 7360, 6954, 3098, 2972, 7066], 'generators': [348, 96, 336, 168], 'label': '672.729.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.c1.a1', '6.b1.a1', '6.d1.a1', '6.e1.a1'], 'normal_contains': ['24.a1.a1', '24.b1.b1', '24.b1.a1', '84.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '168.51', 'quotient_action_image': '6.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 110521052
    {'ambient': '672.729', 'aut_centralizer_order': 224, 'aut_label': '12.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '24.15', 'aut_weyl_index': 224, 'centralizer': '6.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.b1.a1', '6.c1.a1', '6.c1.b1'], 'contains': ['24.a1.a1', '24.h1.a1', '84.d1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6015, 4427, 3113, 5651, 7884, 5328, 3166, 4940], 'generators': [355, 96, 336, 348], 'label': '672.729.12.d1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.d1.a1', 'normal_contained_in': ['4.d1.a1', '6.b1.a1', '6.c1.a1', '6.c1.b1'], 'normal_contains': ['24.a1.a1', '84.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '168.51', 'quotient_action_image': '6.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 110521053
    {'ambient': '672.729', 'aut_centralizer_order': 112, 'aut_label': '12.e1', 'aut_quo_index': 12, 'aut_stab_index': 2, 'aut_weyl_group': '24.15', 'aut_weyl_index': 224, 'centralizer': '12.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.a1.b1', '6.c1.a1', '6.e1.a1'], 'contains': ['24.a1.a1', '24.j1.a1', '84.e1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1496, 3065, 5830, 6505, 2169, 4617, 6734, 4442], 'generators': [6, 96, 12, 336], 'label': '672.729.12.e1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.e1.a1', 'normal_contained_in': ['4.e1.a1', '6.a1.b1', '6.c1.a1', '6.e1.a1'], 'normal_contains': ['24.a1.a1', '84.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '168.51', 'quotient_action_image': '12.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 110521054
    {'ambient': '672.729', 'aut_centralizer_order': 112, 'aut_label': '12.e1', 'aut_quo_index': 12, 'aut_stab_index': 2, 'aut_weyl_group': '24.15', 'aut_weyl_index': 224, 'centralizer': '12.e1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '6.a1.a1', '6.c1.b1', '6.e1.a1'], 'contains': ['24.a1.a1', '24.j1.b1', '84.e1.b1'], 'core': '12.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1496, 3065, 6122, 4962, 2169, 4617, 5776, 6568], 'generators': [522, 96, 12, 336], 'label': '672.729.12.e1.b1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.e1.b1', 'normal_contained_in': ['4.e1.b1', '6.a1.a1', '6.c1.b1', '6.e1.a1'], 'normal_contains': ['24.a1.a1', '84.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.e1.b1', 'projective_image': '168.51', 'quotient_action_image': '12.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.e1.b1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 110521055
    {'ambient': '672.729', 'aut_centralizer_order': 56, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.15', 'aut_weyl_index': 224, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.b1.a1'], 'contains': ['24.b1.a1', '24.f1.a1', '24.h1.a1', '84.f1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8079, -1, 105, -1, 9527, -1, 86, -1], 'generators': [355, 96, 336, 168], 'label': '672.729.12.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.f1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110521056
    {'ambient': '672.729', 'aut_centralizer_order': 56, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.15', 'aut_weyl_index': 224, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '6.b1.a1'], 'contains': ['24.b1.b1', '24.f1.a1', '24.h1.a1', '84.f1.b1'], 'core': '24.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8079, -1, 341, -1, 9527, -1, 872, -1], 'generators': [355, 96, 336, 516], 'label': '672.729.12.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.f1.b1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110521057
    {'ambient': '672.729', 'aut_centralizer_order': 28, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.45', 'aut_weyl_index': 112, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.d1.a1'], 'contains': ['24.b1.a1', '24.g1.a1', '24.g1.b1', '84.g1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9392, -1, 2509, -1, 6652, -1, 1668, -1], 'generators': [1, 96, 336, 168], 'label': '672.729.12.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '12.g1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 110521058
    {'ambient': '672.729', 'aut_centralizer_order': 28, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.45', 'aut_weyl_index': 112, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.b1', '6.d1.a1'], 'contains': ['24.b1.b1', '24.g1.a1', '24.g1.b1', '84.g1.b1'], 'core': '24.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9392, -1, 2011, -1, 6652, -1, 2219, -1], 'generators': [1, 96, 336, 516], 'label': '672.729.12.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '12.g1.b1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.b1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 110521059
    {'ambient': '672.729', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '672.1266', 'aut_weyl_index': 8, 'centralizer': '168.a1.a1', 'complements': ['336.e1.a1', '336.d1.a1', '336.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.b1', '4.d1.a1', '4.e1.b1', '6.c1.b1', '14.c1.b1'], 'core': '2.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4718, 2429, 4498, 5799, 4228, 6630, 4914, 2845], 'generators': [505, 96, 8, 348, 522, 336], 'label': '672.729.2.c1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.b1', '4.d1.a1', '4.e1.b1', '6.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.b1', 'projective_image': '168.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.b1', 'subgroup_fusion': None, 'weyl_group': '168.51'}
  • id: 110521060
    {'ambient': '672.729', 'aut_centralizer_order': 28, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.15', 'aut_weyl_index': 224, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.a1.a1'], 'contains': ['24.c1.a1', '24.i1.a1', '24.j1.b1', '84.h1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [356, -1, 8868, -1, 456, -1, 7881, -1], 'generators': [1, 96, 12, 522], 'label': '672.729.12.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.h1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 110521061
    {'ambient': '672.729', 'aut_centralizer_order': 28, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.15', 'aut_weyl_index': 224, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.b1', '6.a1.b1'], 'contains': ['24.c1.a1', '24.i1.b1', '24.j1.a1', '84.h1.b1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [356, -1, 7934, -1, 456, -1, 9405, -1], 'generators': [169, 96, 12, 6], 'label': '672.729.12.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '12.h1.b1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.b1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 110521062
    {'ambient': '672.729', 'aut_centralizer_order': 28, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.15', 'aut_weyl_index': 224, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.c1', '6.a1.a1'], 'contains': ['24.c1.b1', '24.i1.a1', '24.j1.b1', '84.h1.c1'], 'core': '24.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [356, -1, 9078, -1, 456, -1, 7718, -1], 'generators': [337, 96, 12, 522], 'label': '672.729.12.h1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.h1.c1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.c1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 110521063
    {'ambient': '672.729', 'aut_centralizer_order': 28, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.15', 'aut_weyl_index': 224, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.d1', '6.a1.b1'], 'contains': ['24.c1.b1', '24.i1.b1', '24.j1.a1', '84.h1.d1'], 'core': '24.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [356, -1, 8319, -1, 456, -1, 9241, -1], 'generators': [505, 96, 12, 6], 'label': '672.729.12.h1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '12.h1.d1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.d1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 110521064
    {'ambient': '672.729', 'aut_centralizer_order': 24, 'aut_label': '14.a1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '16.14', 'aut_weyl_index': 336, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '7.a1.a1'], 'contains': ['28.a1.a1', '28.b1.a1', '28.e1.b1', '28.h1.a1', '28.h1.c1', '42.a1.a1'], 'core': '42.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [4261, -1, 7271, -1, 3333, -1, 6330, -1], 'generators': [1, 12, 522, 336, 8], 'label': '672.729.14.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.a1.a1', 'projective_image': '168.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 110521065
    {'ambient': '672.729', 'aut_centralizer_order': 24, 'aut_label': '14.a1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '16.14', 'aut_weyl_index': 336, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '7.a1.a1'], 'contains': ['28.a1.a1', '28.b1.b1', '28.e1.a1', '28.h1.b1', '28.h1.d1', '42.a1.b1'], 'core': '42.a1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [4261, -1, 6407, -1, 3333, -1, 7202, -1], 'generators': [505, 12, 6, 336, 8], 'label': '672.729.14.a1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.a1.b1', 'projective_image': '168.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.a1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 110521066
    {'ambient': '672.729', 'aut_centralizer_order': 48, 'aut_label': '14.b1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '16.14', 'aut_weyl_index': 336, 'centralizer': '14.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '7.a1.a1'], 'contains': ['28.a1.a1', '28.c1.a1', '28.d1.a1', '28.f1.a1', '28.f1.b1', '42.b1.a1'], 'core': '42.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8447, -1, 1693, -1, 8353, -1, 2845, -1], 'generators': [355, 336, 348, 168, 8], 'label': '672.729.14.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.b1.a1', 'projective_image': '168.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110521067
    {'ambient': '672.729', 'aut_centralizer_order': 24, 'aut_label': '14.c1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '16.14', 'aut_weyl_index': 336, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '7.a1.a1'], 'contains': ['28.b1.a1', '28.d1.a1', '28.e1.a1', '42.c1.a1'], 'core': '42.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5482, -1, 3857, -1, 4417, -1, 4449, -1], 'generators': [1, 336, 6, 8, 348], 'label': '672.729.14.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.c1.a1', 'projective_image': '168.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 110521068
    {'ambient': '672.729', 'aut_centralizer_order': 24, 'aut_label': '14.c1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '16.14', 'aut_weyl_index': 336, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.b1', '7.a1.a1'], 'contains': ['28.b1.b1', '28.d1.a1', '28.e1.b1', '42.c1.b1'], 'core': '42.c1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [5482, -1, 4405, -1, 4417, -1, 5032, -1], 'generators': [505, 336, 522, 8, 348], 'label': '672.729.14.c1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.c1.b1', 'projective_image': '168.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.c1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 110521069
    {'ambient': '672.729', 'aut_centralizer_order': 24, 'aut_label': '14.d1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '32.27', 'aut_weyl_index': 168, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '7.a1.a1'], 'contains': ['28.b1.a1', '28.b1.b1', '28.c1.a1', '28.g1.a1', '28.g1.b1', '42.d1.a1'], 'core': '42.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [9479, -1, 2874, -1, 6352, -1, 3808, -1], 'generators': [1, 336, 348, 168, 8], 'label': '672.729.14.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.d1.a1', 'projective_image': '168.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 110521070
    {'ambient': '672.729', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1344.6612', 'aut_weyl_index': 4, 'centralizer': '168.a1.a1', 'complements': ['336.d1.a1', '336.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.b1.b1', '4.c1.a1', '4.g1.a1', '4.g1.b1', '6.d1.a1', '14.d1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8899, 3734, 2738, 8633, 6314, 4761, 3604, 4289], 'generators': [1, 96, 168, 8, 348, 336], 'label': '672.729.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.b1.b1', '4.c1.a1', '6.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '168.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': '168.51'}
  • id: 110521071
    {'ambient': '672.729', 'aut_centralizer_order': 24, 'aut_label': '14.e1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '32.27', 'aut_weyl_index': 168, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '7.a1.a1'], 'contains': ['28.c1.a1', '28.e1.a1', '28.e1.b1', '42.e1.a1'], 'core': '42.e1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7196, -1, 5211, -1, 5488, -1, 5666, -1], 'generators': [6, 336, 168, 8, 12], 'label': '672.729.14.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.e1.a1', 'projective_image': '168.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 110521072
    {'ambient': '672.729', 'aut_centralizer_order': 128, 'aut_label': '16.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '42.1', 'aut_weyl_index': 128, 'centralizer': '21.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.d1.a1', '8.e1.a1', '8.e1.b1'], 'contains': ['32.a1.a1', '48.a1.a1', '112.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3125, 7412, 5377, 2115, 3466, 6905, 5487, 2845], 'generators': [348, 96, 8], 'label': '672.729.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.a1.a1', '48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '336.167', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 110521073
    {'ambient': '672.729', 'aut_centralizer_order': 128, 'aut_label': '16.b1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '42.1', 'aut_weyl_index': 128, 'centralizer': '21.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '8.f1.a1', '8.g1.a1', '8.g1.b1', '8.h1.a1'], 'contains': ['32.a1.a1', '48.b1.a1', '112.b1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6519, 9518, 945, 3299, 6216, 6176, 2076, 3356], 'generators': [336, 96, 8], 'label': '672.729.16.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.b1', '8.b1.a1'], 'normal_contains': ['32.a1.a1', '48.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 110521074
    {'ambient': '672.729', 'aut_centralizer_order': 128, 'aut_label': '16.c1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '42.1', 'aut_weyl_index': 128, 'centralizer': '21.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.c1.a1', '8.c1.b1', '8.i1.a1', '8.i1.b1', '8.j1.a1', '8.j1.b1'], 'contains': ['32.a1.a1', '48.c1.a1', '112.c1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1000, 8360, 9436, 930, 1252, 7634, 8350, 2316], 'generators': [12, 96, 8], 'label': '672.729.16.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.a1.a1', '8.c1.a1', '8.c1.b1'], 'normal_contains': ['32.a1.a1', '48.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 110521075
    {'ambient': '672.729', 'aut_centralizer_order': 32, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '42.1', 'aut_weyl_index': 128, 'centralizer': '42.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.d1.a1', '8.f1.a1'], 'contains': ['32.a1.a1', '48.d1.a1', '112.d1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2721, -1, 7013, -1, 3130, -1, 6862, -1], 'generators': [523, 96, 8], 'label': '672.729.16.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.d1.a1', 'projective_image': '672.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 110521076
    {'ambient': '672.729', 'aut_centralizer_order': 32, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '42.1', 'aut_weyl_index': 128, 'centralizer': '42.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.b1', '8.d1.a1', '8.f1.a1'], 'contains': ['32.a1.a1', '48.d1.b1', '112.d1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2721, -1, 7418, -1, 3130, -1, 6501, -1], 'generators': [187, 96, 8], 'label': '672.729.16.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.d1.b1', 'projective_image': '672.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.b1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 110521077
    {'ambient': '672.729', 'aut_centralizer_order': 16, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '42.1', 'aut_weyl_index': 128, 'centralizer': '84.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.g1.a1', '8.i1.a1'], 'contains': ['32.a1.a1', '48.e1.a1', '112.e1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1952, -1, 3810, -1, 2191, -1, 4012, -1], 'generators': [1, 96, 8], 'label': '672.729.16.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.e1.a1', 'projective_image': '672.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1.a1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 110521078
    {'ambient': '672.729', 'aut_centralizer_order': 16, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '42.1', 'aut_weyl_index': 128, 'centralizer': '84.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.b1', '8.g1.b1', '8.i1.b1'], 'contains': ['32.a1.a1', '48.e1.b1', '112.e1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1952, -1, 5782, -1, 2191, -1, 5685, -1], 'generators': [505, 96, 8], 'label': '672.729.16.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '16.e1.b1', 'projective_image': '672.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1.b1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 110521079
    {'ambient': '672.729', 'aut_centralizer_order': 42, 'aut_label': '21.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 42, 'centralizer': '8.a1.a1', 'complements': ['32.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '7.a1.a1'], 'contains': ['42.a1.a1', '42.a1.b1', '42.b1.a1', '42.c1.a1', '42.c1.b1', '42.d1.a1', '42.e1.a1'], 'core': '21.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7107, 1953, 4171, 7872, 5769, 1190, 4852, 8648], 'generators': [1, 6, 168], 'label': '672.729.21.a1.a1', 'mobius_quo': 0, 'mobius_sub': 7, 'normal_closure': '21.a1.a1', 'normal_contained_in': ['3.a1.a1'], 'normal_contains': ['42.a1.a1', '42.a1.b1', '42.b1.a1', '42.c1.a1', '42.c1.b1', '42.d1.a1', '42.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '21.a1.a1', 'projective_image': '168.51', 'quotient_action_image': '1.1', 'quotient_action_kernel': '21.1', 'quotient_action_kernel_order': 21, 'quotient_fusion': None, 'short_label': '21.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 110521080
    {'ambient': '672.729', 'aut_centralizer_order': 896, 'aut_label': '24.a1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 896, 'centralizer': '3.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.b1.b1', '12.c1.a1', '12.d1.a1', '12.e1.a1', '12.e1.b1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.c1.a1', '168.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4505, 5544, 4813, 3688, 4841, 4648, 4673, 5473], 'generators': [348, 96, 336], 'label': '672.729.24.a1.a1', 'mobius_quo': -2, 'mobius_sub': 8, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.b1.b1', '12.c1.a1', '12.d1.a1', '12.e1.b1', '12.e1.a1'], 'normal_contains': ['48.b1.a1', '48.c1.a1', '48.a1.a1', '168.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '168.51', 'quotient_action_image': '3.1', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110521081
    {'ambient': '672.729', 'aut_centralizer_order': 4, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1344.6612', 'aut_weyl_index': 4, 'centralizer': '168.a1.a1', 'complements': ['336.e1.a1', '336.e1.b1', '336.d1.a1', '336.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.e1.a1', '4.e1.b1', '6.e1.a1', '14.e1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6604, 4982, 5317, 6679, 5042, 5721, 5566, 4962], 'generators': [6, 96, 8, 12, 168, 336], 'label': '672.729.2.e1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.e1.b1', '4.e1.a1', '6.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '168.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1.a1', 'subgroup_fusion': None, 'weyl_group': '168.51'}
  • id: 110521082
    {'ambient': '672.729', 'aut_centralizer_order': 224, 'aut_label': '24.b1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '12.5', 'aut_weyl_index': 448, 'centralizer': '6.b1.a1', 'complements': ['28.h1.d1', '28.h1.b1', '28.h1.a1', '28.h1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.c1.a1', '12.f1.a1', '12.g1.a1'], 'contains': ['48.b1.a1', '168.b1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9235, 7991, 522, 4593, 7766, 4032, 1300, 5907], 'generators': [168, 336, 96], 'label': '672.729.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.b1.a1', '12.c1.a1'], 'normal_contains': ['48.b1.a1', '168.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '336.165', 'quotient_action_image': '6.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 110521083
    {'ambient': '672.729', 'aut_centralizer_order': 224, 'aut_label': '24.b1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '12.5', 'aut_weyl_index': 448, 'centralizer': '6.b1.a1', 'complements': ['28.h1.d1', '28.h1.b1', '28.h1.a1', '28.h1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '12.c1.a1', '12.f1.b1', '12.g1.b1'], 'contains': ['48.b1.a1', '168.b1.b1'], 'core': '24.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9235, 7991, 1236, 4222, 7766, 4032, 2227, 6268], 'generators': [516, 336, 96], 'label': '672.729.24.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.b1.b1', 'normal_contained_in': ['8.b1.b1', '12.c1.a1'], 'normal_contains': ['48.b1.a1', '168.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.b1', 'projective_image': '336.165', 'quotient_action_image': '6.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '24.b1.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 110521084
    {'ambient': '672.729', 'aut_centralizer_order': 224, 'aut_label': '24.c1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '12.5', 'aut_weyl_index': 448, 'centralizer': '6.b1.a1', 'complements': ['28.g1.a1', '28.g1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.a1.a1', '12.h1.a1', '12.h1.b1'], 'contains': ['48.c1.a1', '48.d1.a1', '168.c1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1162, 6691, 7823, 1527, 1584, 5394, 7990, 4191], 'generators': [523, 96, 12], 'label': '672.729.24.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': ['8.c1.a1', '12.a1.a1'], 'normal_contains': ['48.c1.a1', '168.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '336.165', 'quotient_action_image': '6.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 110521085
    {'ambient': '672.729', 'aut_centralizer_order': 224, 'aut_label': '24.c1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '12.5', 'aut_weyl_index': 448, 'centralizer': '6.b1.a1', 'complements': ['28.g1.a1', '28.g1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.b1', '12.a1.a1', '12.h1.c1', '12.h1.d1'], 'contains': ['48.c1.a1', '48.d1.b1', '168.c1.b1'], 'core': '24.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1162, 6691, 8803, 673, 1584, 5394, 7797, 4833], 'generators': [187, 96, 12], 'label': '672.729.24.c1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.c1.b1', 'normal_contained_in': ['8.c1.b1', '12.a1.a1'], 'normal_contains': ['48.c1.a1', '168.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.b1', 'projective_image': '336.165', 'quotient_action_image': '6.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '24.c1.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 110521086
    {'ambient': '672.729', 'aut_centralizer_order': 224, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.5', 'aut_weyl_index': 448, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.a1.a1'], 'contains': ['48.a1.a1', '48.d1.a1', '48.d1.b1', '168.d1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3343, -1, 6849, -1, 4238, -1, 6304, -1], 'generators': [187, 96, 348], 'label': '672.729.24.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.d1.a1', 'projective_image': '336.167', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110521087
    {'ambient': '672.729', 'aut_centralizer_order': 112, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.5', 'aut_weyl_index': 448, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.b1.a1'], 'contains': ['48.a1.a1', '48.e1.a1', '168.e1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2120, -1, 3420, -1, 2523, -1, 4209, -1], 'generators': [1, 96, 348], 'label': '672.729.24.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '24.e1.a1', 'projective_image': '336.167', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 110521088
    {'ambient': '672.729', 'aut_centralizer_order': 112, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.5', 'aut_weyl_index': 448, 'centralizer': '12.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.b1', '12.b1.b1'], 'contains': ['48.a1.a1', '48.e1.b1', '168.e1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2120, -1, 5325, -1, 2523, -1, 5127, -1], 'generators': [505, 96, 348], 'label': '672.729.24.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '24.e1.b1', 'projective_image': '336.167', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 110521089
    {'ambient': '672.729', 'aut_centralizer_order': 224, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.5', 'aut_weyl_index': 448, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.a1.a1', '12.f1.a1', '12.f1.b1'], 'contains': ['48.b1.a1', '48.d1.a1', '48.d1.b1', '168.f1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5732, -1, 999, -1, 6547, -1, 1717, -1], 'generators': [187, 96, 336], 'label': '672.729.24.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.f1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110521090
    {'ambient': '672.729', 'aut_centralizer_order': 112, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.5', 'aut_weyl_index': 448, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '12.b1.a1', '12.g1.a1', '12.g1.b1'], 'contains': ['48.b1.a1', '48.e1.a1', '168.g1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6220, -1, 2064, -1, 5609, -1, 2567, -1], 'generators': [1, 96, 336], 'label': '672.729.24.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '24.g1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 110521091
    {'ambient': '672.729', 'aut_centralizer_order': 112, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.5', 'aut_weyl_index': 448, 'centralizer': '12.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.b1', '12.b1.b1', '12.g1.a1', '12.g1.b1'], 'contains': ['48.b1.a1', '48.e1.b1', '168.g1.b1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6220, -1, 2412, -1, 5609, -1, 3010, -1], 'generators': [505, 96, 336], 'label': '672.729.24.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '24.g1.b1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 110521092
    {'ambient': '672.729', 'aut_centralizer_order': 7, 'aut_label': '3.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '768.55643', 'aut_weyl_index': 7, 'centralizer': '24.a1.a1', 'complements': ['224.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.a1.b1', '6.b1.a1', '6.c1.a1', '6.c1.b1', '6.d1.a1', '6.e1.a1', '21.a1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5951, 482, 4078, 8764, 5430, 3298, 4673, 6586], 'generators': [1, 336, 168, 96, 6, 348], 'label': '672.729.3.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.a1', '6.a1.b1', '6.b1.a1', '6.c1.a1', '6.c1.b1', '6.d1.a1', '6.e1.a1', '21.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '168.51', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.15'}
  • id: 110521093
    {'ambient': '672.729', 'aut_centralizer_order': 224, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.5', 'aut_weyl_index': 448, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.d1.a1', '12.f1.a1', '12.f1.b1'], 'contains': ['48.b1.a1', '168.h1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7811, -1, 166, -1, 8119, -1, 1091, -1], 'generators': [355, 336, 96], 'label': '672.729.24.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.h1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110521094
    {'ambient': '672.729', 'aut_centralizer_order': 112, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.5', 'aut_weyl_index': 448, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '12.b1.a1', '12.h1.a1', '12.h1.c1'], 'contains': ['48.c1.a1', '48.e1.a1', '168.i1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [477, -1, 9151, -1, 645, -1, 7059, -1], 'generators': [1, 96, 12], 'label': '672.729.24.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.i1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 110521095
    {'ambient': '672.729', 'aut_centralizer_order': 112, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.5', 'aut_weyl_index': 448, 'centralizer': '12.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.b1', '12.b1.b1', '12.h1.b1', '12.h1.d1'], 'contains': ['48.c1.a1', '48.e1.b1', '168.i1.b1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [477, -1, 8346, -1, 645, -1, 8710, -1], 'generators': [505, 96, 12], 'label': '672.729.24.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '24.i1.b1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 110521096
    {'ambient': '672.729', 'aut_centralizer_order': 112, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.5', 'aut_weyl_index': 448, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '12.e1.a1', '12.h1.b1', '12.h1.d1'], 'contains': ['48.c1.a1', '168.j1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [172, -1, 8162, -1, 70, -1, 9106, -1], 'generators': [6, 12, 96], 'label': '672.729.24.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '24.j1.a1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 110521097
    {'ambient': '672.729', 'aut_centralizer_order': 112, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.5', 'aut_weyl_index': 448, 'centralizer': '12.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.b1', '12.e1.b1', '12.h1.a1', '12.h1.c1'], 'contains': ['48.c1.a1', '168.j1.b1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [172, -1, 9333, -1, 70, -1, 7542, -1], 'generators': [522, 12, 96], 'label': '672.729.24.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.j1.b1', 'projective_image': '336.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 110521098
    {'ambient': '672.729', 'aut_centralizer_order': 192, 'aut_label': '28.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1344, 'centralizer': '14.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '14.a1.a1', '14.a1.b1', '14.b1.a1'], 'contains': ['56.a1.a1', '56.b1.a1', '56.d1.a1', '56.h1.a1', '56.h1.b1', '84.a1.a1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5493, -1, 7378, -1, 5138, -1, 6543, -1], 'generators': [187, 348, 336, 8], 'label': '672.729.28.a1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.a1.a1', 'projective_image': '168.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110521099
    {'ambient': '672.729', 'aut_centralizer_order': 96, 'aut_label': '28.b1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1344, 'centralizer': '28.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '14.a1.a1', '14.c1.a1', '14.d1.a1'], 'contains': ['56.a1.a1', '56.c1.a1', '56.e1.a1', '56.i1.a1', '84.b1.a1'], 'core': '84.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [4346, -1, 3592, -1, 3466, -1, 4351, -1], 'generators': [1, 348, 336, 8], 'label': '672.729.28.b1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.b1.a1', 'projective_image': '168.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110521100
    {'ambient': '672.729', 'aut_centralizer_order': 96, 'aut_label': '28.b1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1344, 'centralizer': '28.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '14.a1.b1', '14.c1.b1', '14.d1.a1'], 'contains': ['56.a1.a1', '56.c1.b1', '56.e1.b1', '56.i1.b1', '84.b1.b1'], 'core': '84.b1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [4346, -1, 4473, -1, 3466, -1, 5251, -1], 'generators': [505, 348, 336, 8], 'label': '672.729.28.b1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.b1.b1', 'projective_image': '168.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110521101
    {'ambient': '672.729', 'aut_centralizer_order': 192, 'aut_label': '28.c1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1344, 'centralizer': '14.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '14.b1.a1', '14.d1.a1', '14.e1.a1'], 'contains': ['56.a1.a1', '56.f1.a1', '56.f1.b1', '84.c1.a1'], 'core': '84.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [9186, -1, 1676, -1, 7557, -1, 3360, -1], 'generators': [348, 168, 8, 336], 'label': '672.729.28.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.c1.a1', 'projective_image': '168.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110521102
    {'ambient': '672.729', 'aut_centralizer_order': 192, 'aut_label': '28.d1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1344, 'centralizer': '14.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '14.b1.a1', '14.c1.a1', '14.c1.b1'], 'contains': ['56.a1.a1', '56.g1.a1', '84.d1.a1'], 'core': '84.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7535, -1, 2809, -1, 8212, -1, 3717, -1], 'generators': [355, 348, 8, 336], 'label': '672.729.28.d1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.d1.a1', 'projective_image': '168.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}