Abstract group data - 672.1158

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 84, 'aut_gen_orders': [6, 12, 21, 6, 6, 6], 'aut_gens': [[1, 2, 4, 24], [169, 18, 404, 577], [169, 2, 436, 600], [504, 18, 388, 25], [504, 10, 100, 385], [168, 354, 196, 313], [504, 346, 388, 385]], 'aut_group': None, 'aut_hash': 3639632427544831545, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 24192, 'aut_permdeg': 26, 'aut_perms': [99628346044197653788773914, 83828221975562034913389844, 392636094831891918032423240, 392504589643243692491367914, 99077557376131533638111104, 4001618371759507927532798], 'aut_phi_ratio': 126.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 6, 1, 1], [2, 14, 1, 1], [2, 42, 3, 1], [3, 2, 1, 1], [4, 2, 3, 1], [4, 6, 3, 1], [4, 14, 3, 1], [4, 42, 1, 1], [6, 2, 1, 1], [6, 14, 2, 1], [7, 2, 3, 1], [12, 4, 3, 1], [12, 28, 3, 1], [14, 2, 3, 1], [14, 6, 6, 1], [21, 4, 3, 1], [28, 4, 9, 1], [28, 12, 9, 1], [42, 4, 3, 1], [84, 8, 9, 1]], 'aut_supersolvable': False, 'aut_tex': '(C_{21}\\times A_4).C_6.C_2^4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '16.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': '1512.792', 'autcentquo_hash': 792, 'autcentquo_nilpotent': False, 'autcentquo_order': 1512, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3^2\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 6, 1], [2, 14, 1], [2, 42, 3], [3, 2, 1], [4, 2, 3], [4, 6, 3], [4, 14, 3], [4, 42, 1], [6, 2, 1], [6, 14, 2], [7, 2, 3], [12, 4, 3], [12, 28, 3], [14, 2, 3], [14, 6, 6], [21, 4, 3], [28, 4, 9], [28, 12, 9], [42, 4, 3], [84, 8, 9]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '336.219', 'commutator_count': 1, 'commutator_label': '42.6', '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': 1158, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 6, 1, 1], [2, 14, 1, 1], [2, 42, 1, 3], [3, 2, 1, 1], [4, 2, 1, 3], [4, 6, 1, 3], [4, 14, 1, 3], [4, 42, 1, 1], [6, 2, 1, 1], [6, 14, 2, 1], [7, 2, 3, 1], [12, 4, 1, 3], [12, 28, 1, 3], [14, 2, 3, 1], [14, 6, 6, 1], [21, 4, 3, 1], [28, 4, 3, 3], [28, 12, 3, 3], [42, 4, 3, 1], [84, 8, 3, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 2489760, 'exponent': 84, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[8, 1, 3]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '336.219', 'hash': 1158, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 42, 'inner_gen_orders': [2, 2, 6, 14], 'inner_gens': [[1, 2, 4, 360], [1, 2, 356, 24], [1, 346, 4, 312], [337, 2, 388, 24]], 'inner_hash': 219, 'inner_nilpotent': False, 'inner_order': 336, 'inner_split': True, 'inner_tex': 'D_6\\times D_{14}', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 8, 'irrQ_degree': 24, 'irrQ_dim': 48, 'irrR_degree': 8, 'irrep_stats': [[1, 16], [2, 32], [4, 21], [8, 3]], 'label': '672.1158', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C84.C2^3', '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': 22, 'number_characteristic_subgroups': 24, 'number_conjugacy_classes': 72, 'number_divisions': 40, 'number_normal_subgroups': 108, 'number_subgroup_autclasses': 128, 'number_subgroup_classes': 292, 'number_subgroups': 1808, 'old_label': None, 'order': 672, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 147], [3, 2], [4, 108], [6, 30], [7, 6], [12, 96], [14, 42], [21, 12], [28, 144], [42, 12], [84, 72]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [2, 6, 6], 'outer_gen_pows': [0, 1, 0], 'outer_gens': [[1, 2, 20, 24], [1, 338, 4, 409], [169, 338, 4, 193]], 'outer_group': '72.48', 'outer_hash': 48, 'outer_nilpotent': False, 'outer_order': 72, 'outer_permdeg': 10, 'outer_perms': [367920, 368065, 806403], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_6\\times D_6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 26, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 8], [4, 1], [6, 8], [8, 1], [12, 4], [24, 2]], 'representations': {'PC': {'code': 5259415908937520251321724552380371264605, 'gens': [1, 2, 3, 5], 'pres': [7, -2, -2, -2, -3, -2, -2, -7, 2352, 3747, 58, 234, 12604, 2748, 102, 6571, 124, 7076]}, 'Perm': {'d': 26, 'gens': [621574835363380685215009, 357022053595426, 3073540589692, 4485203476099, 5626834239961, 6758061133824000, 16754357281155028254720000]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{84}.C_2^3', 'transitive_degree': 336, 'wreath_data': None, 'wreath_product': False}
• gps_conj_classes •

  Column	Type
  aut_label	text
  centralizer	text
  counter	integer
  group_counter	integer
  group_order	numeric
  label	text
  order	integer
  powers	integer[]
  representative	numeric
  size	numeric

  
  
  • id: 139879941
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 1158, 'group_order': 672, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 139879952
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 1158, 'group_order': 672, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 336, 'size': 1}
  • id: 139879963
    {'aut_label': '2B', 'centralizer': '6.d1', 'counter': 3, 'group_counter': 1158, 'group_order': 672, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 2, 'size': 6}
  • id: 139879974
    {'aut_label': '2C', 'centralizer': '14.e1', 'counter': 4, 'group_counter': 1158, 'group_order': 672, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 12, 'size': 14}
  • id: 139879985
    {'aut_label': '2D', 'centralizer': '42.f1', 'counter': 5, 'group_counter': 1158, 'group_order': 672, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 631, 'size': 42}
  • id: 139879996
    {'aut_label': '2D', 'centralizer': '42.f1', 'counter': 6, 'group_counter': 1158, 'group_order': 672, 'label': '2E', 'order': 2, 'powers': [1, 6, 6], 'representative': 270, 'size': 42}
  • id: 139880007
    {'aut_label': '2D', 'centralizer': '42.f1', 'counter': 7, 'group_counter': 1158, 'group_order': 672, 'label': '2F', 'order': 2, 'powers': [1, 7, 7], 'representative': 95, 'size': 42}
  • id: 139880011
    {'aut_label': '3A', 'centralizer': '2.e1', 'counter': 8, 'group_counter': 1158, 'group_order': 672, 'label': '3A', 'order': 3, 'powers': [8, 1, 8], 'representative': 8, 'size': 2}
  • id: 139880012
    {'aut_label': '4A', 'centralizer': '2.a1', 'counter': 9, 'group_counter': 1158, 'group_order': 672, 'label': '4A', 'order': 4, 'powers': [2, 9, 9], 'representative': 504, 'size': 2}
  • id: 139879942
    {'aut_label': '4A', 'centralizer': '2.a1', 'counter': 10, 'group_counter': 1158, 'group_order': 672, 'label': '4B', 'order': 4, 'powers': [2, 10, 10], 'representative': 1, 'size': 2}
  • id: 139879943
    {'aut_label': '4A', 'centralizer': '2.a1', 'counter': 11, 'group_counter': 1158, 'group_order': 672, 'label': '4C', 'order': 4, 'powers': [2, 11, 11], 'representative': 505, 'size': 2}
  • id: 139879944
    {'aut_label': '4D', 'centralizer': '6.c1', 'counter': 12, 'group_counter': 1158, 'group_order': 672, 'label': '4D', 'order': 4, 'powers': [2, 12, 12], 'representative': 170, 'size': 6}
  • id: 139879945
    {'aut_label': '4D', 'centralizer': '6.c1', 'counter': 13, 'group_counter': 1158, 'group_order': 672, 'label': '4E', 'order': 4, 'powers': [2, 13, 13], 'representative': 339, 'size': 6}
  • id: 139879946
    {'aut_label': '4D', 'centralizer': '6.c1', 'counter': 14, 'group_counter': 1158, 'group_order': 672, 'label': '4F', 'order': 4, 'powers': [2, 14, 14], 'representative': 171, 'size': 6}
  • id: 139879947
    {'aut_label': '4G', 'centralizer': '14.d1', 'counter': 15, 'group_counter': 1158, 'group_order': 672, 'label': '4G', 'order': 4, 'powers': [2, 15, 15], 'representative': 349, 'size': 14}
  • id: 139879948
    {'aut_label': '4G', 'centralizer': '14.d1', 'counter': 16, 'group_counter': 1158, 'group_order': 672, 'label': '4H', 'order': 4, 'powers': [2, 16, 16], 'representative': 84, 'size': 14}
  • id: 139879949
    {'aut_label': '4G', 'centralizer': '14.d1', 'counter': 17, 'group_counter': 1158, 'group_order': 672, 'label': '4I', 'order': 4, 'powers': [2, 17, 17], 'representative': 325, 'size': 14}
  • id: 139879950
    {'aut_label': '4J', 'centralizer': '42.g1', 'counter': 18, 'group_counter': 1158, 'group_order': 672, 'label': '4J', 'order': 4, 'powers': [2, 18, 18], 'representative': 646, 'size': 42}
  • id: 139879951
    {'aut_label': '6A', 'centralizer': '2.e1', 'counter': 19, 'group_counter': 1158, 'group_order': 672, 'label': '6A', 'order': 6, 'powers': [8, 2, 19], 'representative': 352, 'size': 2}
  • id: 139879953
    {'aut_label': '6B1', 'centralizer': '14.e1', 'counter': 20, 'group_counter': 1158, 'group_order': 672, 'label': '6B1', 'order': 6, 'powers': [8, 4, 20], 'representative': 4, 'size': 14}
  • id: 139879954
    {'aut_label': '6B1', 'centralizer': '14.e1', 'counter': 21, 'group_counter': 1158, 'group_order': 672, 'label': '6B-1', 'order': 6, 'powers': [8, 4, 21], 'representative': 52, 'size': 14}
  • id: 139879955
    {'aut_label': '7A1', 'centralizer': '2.c1', 'counter': 22, 'group_counter': 1158, 'group_order': 672, 'label': '7A1', 'order': 7, 'powers': [23, 24, 1], 'representative': 192, 'size': 2}
  • id: 139879956
    {'aut_label': '7A1', 'centralizer': '2.c1', 'counter': 23, 'group_counter': 1158, 'group_order': 672, 'label': '7A2', 'order': 7, 'powers': [24, 22, 1], 'representative': 384, 'size': 2}
  • id: 139879957
    {'aut_label': '7A1', 'centralizer': '2.c1', 'counter': 24, 'group_counter': 1158, 'group_order': 672, 'label': '7A3', 'order': 7, 'powers': [22, 23, 1], 'representative': 576, 'size': 2}
  • id: 139879958
    {'aut_label': '12A', 'centralizer': '4.e1', 'counter': 25, 'group_counter': 1158, 'group_order': 672, 'label': '12A', 'order': 12, 'powers': [19, 9, 25], 'representative': 176, 'size': 4}
  • id: 139879959
    {'aut_label': '12A', 'centralizer': '4.e1', 'counter': 26, 'group_counter': 1158, 'group_order': 672, 'label': '12B', 'order': 12, 'powers': [19, 10, 26], 'representative': 345, 'size': 4}
  • id: 139879960
    {'aut_label': '12A', 'centralizer': '4.e1', 'counter': 27, 'group_counter': 1158, 'group_order': 672, 'label': '12C', 'order': 12, 'powers': [19, 11, 27], 'representative': 177, 'size': 4}
  • id: 139879961
    {'aut_label': '12D', 'centralizer': '28.g1', 'counter': 28, 'group_counter': 1158, 'group_order': 672, 'label': '12D', 'order': 12, 'powers': [19, 15, 28], 'representative': 5, 'size': 28}
  • id: 139879962
    {'aut_label': '12D', 'centralizer': '28.g1', 'counter': 29, 'group_counter': 1158, 'group_order': 672, 'label': '12E', 'order': 12, 'powers': [19, 16, 29], 'representative': 412, 'size': 28}
  • id: 139879964
    {'aut_label': '12D', 'centralizer': '28.g1', 'counter': 30, 'group_counter': 1158, 'group_order': 672, 'label': '12F', 'order': 12, 'powers': [19, 17, 30], 'representative': 669, 'size': 28}
  • id: 139879965
    {'aut_label': '14A1', 'centralizer': '2.c1', 'counter': 31, 'group_counter': 1158, 'group_order': 672, 'label': '14A1', 'order': 14, 'powers': [24, 32, 2], 'representative': 48, 'size': 2}
  • id: 139879966
    {'aut_label': '14A1', 'centralizer': '2.c1', 'counter': 32, 'group_counter': 1158, 'group_order': 672, 'label': '14A3', 'order': 14, 'powers': [23, 33, 2], 'representative': 144, 'size': 2}
  • id: 139879967
    {'aut_label': '14A1', 'centralizer': '2.c1', 'counter': 33, 'group_counter': 1158, 'group_order': 672, 'label': '14A5', 'order': 14, 'powers': [22, 31, 2], 'representative': 240, 'size': 2}
  • id: 139879968
    {'aut_label': '14B1', 'centralizer': '6.d1', 'counter': 34, 'group_counter': 1158, 'group_order': 672, 'label': '14B1', 'order': 14, 'powers': [22, 36, 3], 'representative': 98, 'size': 6}
  • id: 139879969
    {'aut_label': '14B1', 'centralizer': '6.d1', 'counter': 35, 'group_counter': 1158, 'group_order': 672, 'label': '14B-1', 'order': 14, 'powers': [22, 37, 3], 'representative': 578, 'size': 6}
  • id: 139879970
    {'aut_label': '14B1', 'centralizer': '6.d1', 'counter': 36, 'group_counter': 1158, 'group_order': 672, 'label': '14B3', 'order': 14, 'powers': [24, 39, 3], 'representative': 50, 'size': 6}
  • id: 139879971
    {'aut_label': '14B1', 'centralizer': '6.d1', 'counter': 37, 'group_counter': 1158, 'group_order': 672, 'label': '14B-3', 'order': 14, 'powers': [24, 38, 3], 'representative': 386, 'size': 6}
  • id: 139879972
    {'aut_label': '14B1', 'centralizer': '6.d1', 'counter': 38, 'group_counter': 1158, 'group_order': 672, 'label': '14B5', 'order': 14, 'powers': [23, 34, 3], 'representative': 482, 'size': 6}
  • id: 139879973
    {'aut_label': '14B1', 'centralizer': '6.d1', 'counter': 39, 'group_counter': 1158, 'group_order': 672, 'label': '14B-5', 'order': 14, 'powers': [23, 35, 3], 'representative': 194, 'size': 6}
  • id: 139879975
    {'aut_label': '21A1', 'centralizer': '4.k1', 'counter': 40, 'group_counter': 1158, 'group_order': 672, 'label': '21A1', 'order': 21, 'powers': [41, 23, 8], 'representative': 104, 'size': 4}
  • id: 139879976
    {'aut_label': '21A1', 'centralizer': '4.k1', 'counter': 41, 'group_counter': 1158, 'group_order': 672, 'label': '21A2', 'order': 21, 'powers': [42, 24, 8], 'representative': 208, 'size': 4}
  • id: 139879977
    {'aut_label': '21A1', 'centralizer': '4.k1', 'counter': 42, 'group_counter': 1158, 'group_order': 672, 'label': '21A4', 'order': 21, 'powers': [40, 22, 8], 'representative': 392, 'size': 4}
  • id: 139879978
    {'aut_label': '28A1', 'centralizer': '4.c1', 'counter': 43, 'group_counter': 1158, 'group_order': 672, 'label': '28A1', 'order': 28, 'powers': [32, 44, 9], 'representative': 72, 'size': 4}
  • id: 139879979
    {'aut_label': '28A1', 'centralizer': '4.c1', 'counter': 44, 'group_counter': 1158, 'group_order': 672, 'label': '28A3', 'order': 28, 'powers': [33, 45, 9], 'representative': 216, 'size': 4}
  • id: 139879980
    {'aut_label': '28A1', 'centralizer': '4.c1', 'counter': 45, 'group_counter': 1158, 'group_order': 672, 'label': '28A5', 'order': 28, 'powers': [31, 43, 9], 'representative': 360, 'size': 4}
  • id: 139879981
    {'aut_label': '28A1', 'centralizer': '4.c1', 'counter': 46, 'group_counter': 1158, 'group_order': 672, 'label': '28B1', 'order': 28, 'powers': [33, 47, 10], 'representative': 625, 'size': 4}
  • id: 139879982
    {'aut_label': '28A1', 'centralizer': '4.c1', 'counter': 47, 'group_counter': 1158, 'group_order': 672, 'label': '28B3', 'order': 28, 'powers': [31, 48, 10], 'representative': 193, 'size': 4}
  • id: 139879983
    {'aut_label': '28A1', 'centralizer': '4.c1', 'counter': 48, 'group_counter': 1158, 'group_order': 672, 'label': '28B5', 'order': 28, 'powers': [32, 46, 10], 'representative': 433, 'size': 4}
  • id: 139879984
    {'aut_label': '28A1', 'centralizer': '4.c1', 'counter': 49, 'group_counter': 1158, 'group_order': 672, 'label': '28C1', 'order': 28, 'powers': [32, 50, 11], 'representative': 73, 'size': 4}
  • id: 139879986
    {'aut_label': '28A1', 'centralizer': '4.c1', 'counter': 50, 'group_counter': 1158, 'group_order': 672, 'label': '28C3', 'order': 28, 'powers': [33, 51, 11], 'representative': 217, 'size': 4}
  • id: 139879987
    {'aut_label': '28A1', 'centralizer': '4.c1', 'counter': 51, 'group_counter': 1158, 'group_order': 672, 'label': '28C5', 'order': 28, 'powers': [31, 49, 11], 'representative': 361, 'size': 4}
  • id: 139879988
    {'aut_label': '28D1', 'centralizer': '12.f1', 'counter': 52, 'group_counter': 1158, 'group_order': 672, 'label': '28D1', 'order': 28, 'powers': [31, 53, 12], 'representative': 26, 'size': 12}
  • id: 139879989
    {'aut_label': '28D1', 'centralizer': '12.f1', 'counter': 53, 'group_counter': 1158, 'group_order': 672, 'label': '28D3', 'order': 28, 'powers': [32, 54, 12], 'representative': 74, 'size': 12}
  • id: 139879990
    {'aut_label': '28D1', 'centralizer': '12.f1', 'counter': 54, 'group_counter': 1158, 'group_order': 672, 'label': '28D5', 'order': 28, 'powers': [33, 52, 12], 'representative': 122, 'size': 12}
  • id: 139879991
    {'aut_label': '28D1', 'centralizer': '12.f1', 'counter': 55, 'group_counter': 1158, 'group_order': 672, 'label': '28E1', 'order': 28, 'powers': [32, 56, 13], 'representative': 99, 'size': 12}
  • id: 139879992
    {'aut_label': '28D1', 'centralizer': '12.f1', 'counter': 56, 'group_counter': 1158, 'group_order': 672, 'label': '28E3', 'order': 28, 'powers': [33, 57, 13], 'representative': 51, 'size': 12}
  • id: 139879993
    {'aut_label': '28D1', 'centralizer': '12.f1', 'counter': 57, 'group_counter': 1158, 'group_order': 672, 'label': '28E5', 'order': 28, 'powers': [31, 55, 13], 'representative': 195, 'size': 12}
  • id: 139879994
    {'aut_label': '28D1', 'centralizer': '12.f1', 'counter': 58, 'group_counter': 1158, 'group_order': 672, 'label': '28F1', 'order': 28, 'powers': [31, 59, 14], 'representative': 27, 'size': 12}
  • id: 139879995
    {'aut_label': '28D1', 'centralizer': '12.f1', 'counter': 59, 'group_counter': 1158, 'group_order': 672, 'label': '28F3', 'order': 28, 'powers': [32, 60, 14], 'representative': 75, 'size': 12}
  • id: 139879997
    {'aut_label': '28D1', 'centralizer': '12.f1', 'counter': 60, 'group_counter': 1158, 'group_order': 672, 'label': '28F5', 'order': 28, 'powers': [33, 58, 14], 'representative': 123, 'size': 12}
  • id: 139879998
    {'aut_label': '42A1', 'centralizer': '4.k1', 'counter': 61, 'group_counter': 1158, 'group_order': 672, 'label': '42A1', 'order': 42, 'powers': [40, 32, 19], 'representative': 64, 'size': 4}
  • id: 139879999
    {'aut_label': '42A1', 'centralizer': '4.k1', 'counter': 62, 'group_counter': 1158, 'group_order': 672, 'label': '42A5', 'order': 42, 'powers': [41, 31, 19], 'representative': 248, 'size': 4}
  • id: 139880000
    {'aut_label': '42A1', 'centralizer': '4.k1', 'counter': 63, 'group_counter': 1158, 'group_order': 672, 'label': '42A11', 'order': 42, 'powers': [42, 33, 19], 'representative': 536, 'size': 4}
  • id: 139880001
    {'aut_label': '84A1', 'centralizer': '8.d1', 'counter': 64, 'group_counter': 1158, 'group_order': 672, 'label': '84A1', 'order': 84, 'powers': [61, 43, 25], 'representative': 32, 'size': 8}
  • id: 139880002
    {'aut_label': '84A1', 'centralizer': '8.d1', 'counter': 65, 'group_counter': 1158, 'group_order': 672, 'label': '84A5', 'order': 84, 'powers': [62, 45, 25], 'representative': 128, 'size': 8}
  • id: 139880003
    {'aut_label': '84A1', 'centralizer': '8.d1', 'counter': 66, 'group_counter': 1158, 'group_order': 672, 'label': '84A11', 'order': 84, 'powers': [63, 44, 25], 'representative': 80, 'size': 8}
  • id: 139880004
    {'aut_label': '84A1', 'centralizer': '8.d1', 'counter': 67, 'group_counter': 1158, 'group_order': 672, 'label': '84B1', 'order': 84, 'powers': [63, 46, 26], 'representative': 105, 'size': 8}
  • id: 139880005
    {'aut_label': '84A1', 'centralizer': '8.d1', 'counter': 68, 'group_counter': 1158, 'group_order': 672, 'label': '84B5', 'order': 84, 'powers': [61, 48, 26], 'representative': 201, 'size': 8}
  • id: 139880006
    {'aut_label': '84A1', 'centralizer': '8.d1', 'counter': 69, 'group_counter': 1158, 'group_order': 672, 'label': '84B11', 'order': 84, 'powers': [62, 47, 26], 'representative': 57, 'size': 8}
  • id: 139880008
    {'aut_label': '84A1', 'centralizer': '8.d1', 'counter': 70, 'group_counter': 1158, 'group_order': 672, 'label': '84C1', 'order': 84, 'powers': [61, 49, 27], 'representative': 33, 'size': 8}
  • id: 139880009
    {'aut_label': '84A1', 'centralizer': '8.d1', 'counter': 71, 'group_counter': 1158, 'group_order': 672, 'label': '84C5', 'order': 84, 'powers': [62, 51, 27], 'representative': 129, 'size': 8}
  • id: 139880010
    {'aut_label': '84A1', 'centralizer': '8.d1', 'counter': 72, 'group_counter': 1158, 'group_order': 672, 'label': '84C11', 'order': 84, 'powers': [63, 50, 27], 'representative': 81, 'size': 8}
• gps_qchar •

  Column	Type
  cdim	integer
  counter	smallint
  faithful	boolean
  group	text
  group_order	numeric
  image	text
  label	text
  multiplicity	smallint
  nt	integer[]
  qdim	integer
  qvalues	integer[]
  schur_index	smallint

  
  
  • id: 12797669
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12797680
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 12797691
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12797702
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 12797704
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12797705
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12797706
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 12797707
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12797708
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.1i', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 12797670
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.1j', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12797671
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.1k', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 12797672
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.1l', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12797673
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.1m', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 12797674
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.1n', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 12797675
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.1o', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12797676
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.1p', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 12797677
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 2, 0, 0, 0, -1, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 0, 0, 0, 0, 0, 0, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12797678
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.2b', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, -2, 0, 0, 0, -1, -2, -2, 2, 0, 0, 0, 2, 2, -2, 0, -1, 1, 1, 2, 2, 2, 1, 1, -1, -1, -1, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, -1, -1, -1, 2, 2, -2, -2, -2, -2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12797679
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.2c', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, -2, 0, 0, 0, -1, -2, 2, -2, 0, 0, 0, -2, 2, 2, 0, -1, 1, 1, 2, 2, 2, 1, -1, 1, 1, -1, -1, 2, 2, 2, 0, 0, 0, 0, 0, 0, -1, -1, -1, -2, -2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 12797681
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, -2, 0, 0, 0, -1, 2, -2, -2, 0, 0, 0, 2, -2, 2, 0, -1, 1, 1, 2, 2, 2, -1, 1, 1, -1, 1, -1, 2, 2, 2, 0, 0, 0, 0, 0, 0, -1, -1, -1, -2, -2, 2, -2, -2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 12797682
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.2e', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, -2, 0, 0, 0, -1, 2, 2, 2, 0, 0, 0, -2, -2, -2, 0, -1, 1, 1, 2, 2, 2, -1, -1, -1, 1, 1, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12797683
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 2, 0, 0, 0, -1, -2, -2, 2, 0, 0, 0, -2, -2, 2, 0, -1, -1, -1, 2, 2, 2, 1, 1, -1, 1, 1, -1, 2, 2, 2, 0, 0, 0, 0, 0, 0, -1, -1, -1, 2, 2, -2, -2, -2, -2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12797684
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.2g', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 2, 0, 0, 0, -1, -2, 2, -2, 0, 0, 0, 2, -2, -2, 0, -1, -1, -1, 2, 2, 2, 1, -1, 1, -1, 1, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, -1, -1, -1, -2, -2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 12797685
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.2h', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 2, 0, 0, 0, -1, 2, -2, -2, 0, 0, 0, -2, 2, -2, 0, -1, -1, -1, 2, 2, 2, -1, 1, 1, 1, -1, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, -1, -1, -1, -2, -2, 2, -2, -2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 12797695
    {'cdim': 4, 'counter': 33, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.4a', 'multiplicity': 1, 'nt': [16, 20], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 12797686
    {'cdim': 2, 'counter': 25, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.2i', 'multiplicity': 3, 'nt': [7, 2], 'qdim': 6, 'qvalues': [6, 6, 6, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 6, 0, 0, -1, -1, -1, 6, 6, 6, 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, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12797687
    {'cdim': 2, 'counter': 26, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.2j', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, -6, 0, 0, 0, 0, 6, -6, -6, 6, 6, -6, 6, 0, 0, 0, 0, 6, 0, 0, -1, -1, -1, -6, -6, 6, 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, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12797688
    {'cdim': 2, 'counter': 27, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.2k', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, -6, 0, 0, 0, 0, 6, -6, 6, -6, -6, 6, 6, 0, 0, 0, 0, 6, 0, 0, -1, -1, -1, -6, 6, -6, 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, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 12797689
    {'cdim': 2, 'counter': 28, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.2l', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, -6, 0, 0, 0, 0, 6, 6, -6, -6, 6, 6, -6, 0, 0, 0, 0, 6, 0, 0, -1, -1, -1, 6, -6, -6, 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, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 12797690
    {'cdim': 2, 'counter': 29, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.2m', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, -6, 0, 0, 0, 0, 6, 6, 6, 6, -6, -6, -6, 0, 0, 0, 0, 6, 0, 0, -1, -1, -1, 6, 6, 6, 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, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12797692
    {'cdim': 2, 'counter': 30, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.2n', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, 6, 0, 0, 0, 0, 6, -6, -6, 6, -6, 6, -6, 0, 0, 0, 0, 6, 0, 0, -1, -1, -1, -6, -6, 6, 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, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12797693
    {'cdim': 2, 'counter': 31, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.2o', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, 6, 0, 0, 0, 0, 6, -6, 6, -6, 6, -6, -6, 0, 0, 0, 0, 6, 0, 0, -1, -1, -1, -6, 6, -6, 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, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 12797694
    {'cdim': 2, 'counter': 32, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.2p', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, 6, 0, 0, 0, 0, 6, 6, -6, -6, -6, -6, 6, 0, 0, 0, 0, 6, 0, 0, -1, -1, -1, 6, -6, -6, 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, 1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 12797696
    {'cdim': 4, 'counter': 34, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.4b', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12797697
    {'cdim': 4, 'counter': 35, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.4c', 'multiplicity': 3, 'nt': [21, 8], 'qdim': 12, 'qvalues': [12, 12, 0, 0, 0, 0, 0, -6, 12, 12, 12, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, -2, -2, -2, -6, -6, -6, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 1, 1, 1, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12797698
    {'cdim': 4, 'counter': 36, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.4d', 'multiplicity': 3, 'nt': [42, 36], 'qdim': 12, 'qvalues': [12, 12, 0, 0, 0, 0, 0, -6, -12, -12, 12, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, -2, -2, -2, 6, 6, -6, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 1, 1, 1, -2, -2, 2, 2, 2, 2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12797699
    {'cdim': 4, 'counter': 37, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.4e', 'multiplicity': 3, 'nt': [42, 36], 'qdim': 12, 'qvalues': [12, 12, 0, 0, 0, 0, 0, -6, -12, 12, -12, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, -2, -2, -2, 6, -6, 6, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 12797700
    {'cdim': 4, 'counter': 38, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.4f', 'multiplicity': 3, 'nt': [42, 36], 'qdim': 12, 'qvalues': [12, 12, 0, 0, 0, 0, 0, -6, 12, -12, -12, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, -2, -2, -2, -6, 6, 6, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, -2, 2, 2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 12797701
    {'cdim': 4, 'counter': 39, 'faithful': False, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.4g', 'multiplicity': 6, 'nt': [112, 0], 'qdim': 24, 'qvalues': [24, -24, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 12797703
    {'cdim': 8, 'counter': 40, 'faithful': True, 'group': '672.1158', 'group_order': 672, 'image': None, 'label': '672.1158.8a', 'multiplicity': 3, 'nt': [336, 0], 'qdim': 24, 'qvalues': [24, -24, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
• gps_char •

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

  
  
  • id: 29598305
    {'center': '1.a1', 'center_index': 1, 'center_order': 672, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 672, 'label': '672.1158.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 29598316
    {'center': '1.a1', 'center_index': 1, 'center_order': 672, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 336, 'label': '672.1158.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 29598327
    {'center': '1.a1', 'center_index': 1, 'center_order': 672, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 336, 'label': '672.1158.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 29598338
    {'center': '1.a1', 'center_index': 1, 'center_order': 672, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 336, 'label': '672.1158.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 29598349
    {'center': '1.a1', 'center_index': 1, 'center_order': 672, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1', 'kernel_order': 336, 'label': '672.1158.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 29598360
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  • id: 29598371
    {'center': '1.a1', 'center_index': 1, 'center_order': 672, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 336, 'label': '672.1158.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 29598375
    {'center': '1.a1', 'center_index': 1, 'center_order': 672, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 336, 'label': '672.1158.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 29598376
    {'center': '1.a1', 'center_index': 1, 'center_order': 672, 'counter': 9, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 336, 'label': '672.1158.1i', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 29598306
    {'center': '1.a1', 'center_index': 1, 'center_order': 672, 'counter': 10, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 336, 'label': '672.1158.1j', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 29598307
    {'center': '1.a1', 'center_index': 1, 'center_order': 672, 'counter': 11, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 336, 'label': '672.1158.1k', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 29598308
    {'center': '1.a1', 'center_index': 1, 'center_order': 672, 'counter': 12, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 336, 'label': '672.1158.1l', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 29598309
    {'center': '1.a1', 'center_index': 1, 'center_order': 672, 'counter': 13, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 336, 'label': '672.1158.1m', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 29598310
    {'center': '1.a1', 'center_index': 1, 'center_order': 672, 'counter': 14, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 336, 'label': '672.1158.1n', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 29598311
    {'center': '1.a1', 'center_index': 1, 'center_order': 672, 'counter': 15, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 336, 'label': '672.1158.1o', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 29598312
    {'center': '1.a1', 'center_index': 1, 'center_order': 672, 'counter': 16, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 336, 'label': '672.1158.1p', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 29598313
    {'center': '6.a1', 'center_index': 6, 'center_order': 112, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 112, 'label': '672.1158.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 29598314
    {'center': '6.a1', 'center_index': 6, 'center_order': 112, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1', 'kernel_order': 56, 'label': '672.1158.2b', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 29598315
    {'center': '6.a1', 'center_index': 6, 'center_order': 112, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1', 'kernel_order': 56, 'label': '672.1158.2c', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 29598317
    {'center': '6.a1', 'center_index': 6, 'center_order': 112, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1', 'kernel_order': 56, 'label': '672.1158.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 29598318
    {'center': '6.a1', 'center_index': 6, 'center_order': 112, 'counter': 21, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1', 'kernel_order': 56, 'label': '672.1158.2e', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 29598319
    {'center': '6.a1', 'center_index': 6, 'center_order': 112, 'counter': 22, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 56, 'label': '672.1158.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 29598320
    {'center': '6.a1', 'center_index': 6, 'center_order': 112, 'counter': 23, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 56, 'label': '672.1158.2g', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 29598321
    {'center': '6.a1', 'center_index': 6, 'center_order': 112, 'counter': 24, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 56, 'label': '672.1158.2h', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 29598322
    {'center': '14.a1', 'center_index': 14, 'center_order': 48, 'counter': 25, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '14.1', 'image_order': 14, 'indicator': 1, 'kernel': '14.a1', 'kernel_order': 48, 'label': '672.1158.2i1', 'nt': [7, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]]]}
  • id: 29598323
    {'center': '14.a1', 'center_index': 14, 'center_order': 48, 'counter': 26, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '14.1', 'image_order': 14, 'indicator': 1, 'kernel': '14.a1', 'kernel_order': 48, 'label': '672.1158.2i2', 'nt': [7, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]]]}
  • id: 29598324
    {'center': '14.a1', 'center_index': 14, 'center_order': 48, 'counter': 27, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '14.1', 'image_order': 14, 'indicator': 1, 'kernel': '14.a1', 'kernel_order': 48, 'label': '672.1158.2i3', 'nt': [7, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]]]}
  • id: 29598325
    {'center': '14.a1', 'center_index': 14, 'center_order': 48, 'counter': 28, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1', 'kernel_order': 24, 'label': '672.1158.2j1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]]]}
  • id: 29598326
    {'center': '14.a1', 'center_index': 14, 'center_order': 48, 'counter': 29, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1', 'kernel_order': 24, 'label': '672.1158.2j2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]]]}
  • id: 29598328
    {'center': '14.a1', 'center_index': 14, 'center_order': 48, 'counter': 30, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1', 'kernel_order': 24, 'label': '672.1158.2j3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]]]}
  • id: 29598329
    {'center': '14.a1', 'center_index': 14, 'center_order': 48, 'counter': 31, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1', 'kernel_order': 24, 'label': '672.1158.2k1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]]]}
  • id: 29598330
    {'center': '14.a1', 'center_index': 14, 'center_order': 48, 'counter': 32, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1', 'kernel_order': 24, 'label': '672.1158.2k2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]]]}
  • id: 29598331
    {'center': '14.a1', 'center_index': 14, 'center_order': 48, 'counter': 33, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1', 'kernel_order': 24, 'label': '672.1158.2k3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]]]}
  • id: 29598332
    {'center': '14.a1', 'center_index': 14, 'center_order': 48, 'counter': 34, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1', 'kernel_order': 24, 'label': '672.1158.2l1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]]]}
  • id: 29598333
    {'center': '14.a1', 'center_index': 14, 'center_order': 48, 'counter': 35, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1', 'kernel_order': 24, 'label': '672.1158.2l2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]]]}
  • id: 29598334
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  • id: 29598335
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  • id: 29598336
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  • id: 29598337
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  • id: 29598339
    {'center': '14.a1', 'center_index': 14, 'center_order': 48, 'counter': 40, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1', 'kernel_order': 24, 'label': '672.1158.2n1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]]]}
  • id: 29598340
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  • id: 29598341
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  • id: 29598342
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  • id: 29598343
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  • id: 29598344
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  • id: 29598345
    {'center': '14.a1', 'center_index': 14, 'center_order': 48, 'counter': 46, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1', 'kernel_order': 24, 'label': '672.1158.2p1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]]]}
  • id: 29598346
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  • id: 29598347
    {'center': '14.a1', 'center_index': 14, 'center_order': 48, 'counter': 48, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1', 'kernel_order': 24, 'label': '672.1158.2p3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]]]}
  • id: 29598348
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  • id: 29598350
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  • id: 29598351
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  • id: 29598352
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  • id: 29598353
    {'center': '84.a1', 'center_index': 84, 'center_order': 8, 'counter': 53, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '84.8', 'image_order': 84, 'indicator': 1, 'kernel': '84.a1', 'kernel_order': 8, 'label': '672.1158.4c2', 'nt': [21, 8], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]]]}
  • id: 29598354
    {'center': '84.a1', 'center_index': 84, 'center_order': 8, 'counter': 54, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '84.8', 'image_order': 84, 'indicator': 1, 'kernel': '84.a1', 'kernel_order': 8, 'label': '672.1158.4c3', 'nt': [21, 8], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]]]}
  • id: 29598355
    {'center': '84.a1', 'center_index': 84, 'center_order': 8, 'counter': 55, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.a1', 'kernel_order': 4, 'label': '672.1158.4d1', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]]]}
  • id: 29598356
    {'center': '84.a1', 'center_index': 84, 'center_order': 8, 'counter': 56, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.a1', 'kernel_order': 4, 'label': '672.1158.4d2', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]]]}
  • id: 29598357
    {'center': '84.a1', 'center_index': 84, 'center_order': 8, 'counter': 57, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.a1', 'kernel_order': 4, 'label': '672.1158.4d3', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]]]}
  • id: 29598358
    {'center': '84.a1', 'center_index': 84, 'center_order': 8, 'counter': 58, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.a1', 'kernel_order': 4, 'label': '672.1158.4e1', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]]]}
  • id: 29598359
    {'center': '84.a1', 'center_index': 84, 'center_order': 8, 'counter': 59, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.a1', 'kernel_order': 4, 'label': '672.1158.4e2', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]]]}
  • id: 29598361
    {'center': '84.a1', 'center_index': 84, 'center_order': 8, 'counter': 60, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.a1', 'kernel_order': 4, 'label': '672.1158.4e3', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]]]}
  • id: 29598362
    {'center': '84.a1', 'center_index': 84, 'center_order': 8, 'counter': 61, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.a1', 'kernel_order': 4, 'label': '672.1158.4f1', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[2, 2], [2, -2]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]]]}
  • id: 29598363
    {'center': '84.a1', 'center_index': 84, 'center_order': 8, 'counter': 62, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.a1', 'kernel_order': 4, 'label': '672.1158.4f2', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[2, 1], [2, -1]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]]]}
  • id: 29598364
    {'center': '84.a1', 'center_index': 84, 'center_order': 8, 'counter': 63, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.a1', 'kernel_order': 4, 'label': '672.1158.4f3', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[2, 3], [2, -3]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]]]}
  • id: 29598365
    {'center': '112.a1', 'center_index': 112, 'center_order': 6, 'counter': 64, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '224.183', 'image_order': 224, 'indicator': 0, 'kernel': '224.a1', 'kernel_order': 3, 'label': '672.1158.4g1', 'nt': [112, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 3], [2, -3]], [[2, 1], [-2, -1]], [[2, 2], [-2, -2]], [[2, 3], [-2, -3]], [[-2, 1], [2, -1]], [[-2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29598366
    {'center': '112.a1', 'center_index': 112, 'center_order': 6, 'counter': 65, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '224.183', 'image_order': 224, 'indicator': 0, 'kernel': '224.a1', 'kernel_order': 3, 'label': '672.1158.4g2', 'nt': [112, 6], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[2, 3], [-2, -3]], [[-2, 1], [2, -1]], [[-2, 2], [2, -2]], [[-2, 3], [2, -3]], [[2, 1], [-2, -1]], [[2, 2], [-2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29598367
    {'center': '112.a1', 'center_index': 112, 'center_order': 6, 'counter': 66, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '224.183', 'image_order': 224, 'indicator': 0, 'kernel': '224.a1', 'kernel_order': 3, 'label': '672.1158.4g3', 'nt': [112, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 2], [2, -2]], [[2, 3], [-2, -3]], [[-2, 1], [2, -1]], [[2, 2], [-2, -2]], [[-2, 3], [2, -3]], [[2, 1], [-2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29598368
    {'center': '112.a1', 'center_index': 112, 'center_order': 6, 'counter': 67, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '224.183', 'image_order': 224, 'indicator': 0, 'kernel': '224.a1', 'kernel_order': 3, 'label': '672.1158.4g4', 'nt': [112, 6], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[2, 2], [-2, -2]], [[-2, 3], [2, -3]], [[2, 1], [-2, -1]], [[-2, 2], [2, -2]], [[2, 3], [-2, -3]], [[-2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29598369
    {'center': '112.a1', 'center_index': 112, 'center_order': 6, 'counter': 68, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '224.183', 'image_order': 224, 'indicator': 0, 'kernel': '224.a1', 'kernel_order': 3, 'label': '672.1158.4g5', 'nt': [112, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [2, -1]], [[-2, 2], [2, -2]], [[2, 3], [-2, -3]], [[2, 1], [-2, -1]], [[2, 2], [-2, -2]], [[-2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29598370
    {'center': '112.a1', 'center_index': 112, 'center_order': 6, 'counter': 69, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '224.183', 'image_order': 224, 'indicator': 0, 'kernel': '224.a1', 'kernel_order': 3, 'label': '672.1158.4g6', 'nt': [112, 6], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[2, 1], [-2, -1]], [[2, 2], [-2, -2]], [[-2, 3], [2, -3]], [[-2, 1], [2, -1]], [[-2, 2], [2, -2]], [[2, 3], [-2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29598372
    {'center': '336.a1', 'center_index': 336, 'center_order': 2, 'counter': 70, 'cyclotomic_n': 7, 'dim': 8, 'faithful': True, 'field': [1, -2, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '672.1158', 'image_order': 672, 'indicator': 1, 'kernel': '672.a1', 'kernel_order': 1, 'label': '672.1158.8a1', 'nt': [336, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 3], [4, -3]], [[4, 1], [4, -1]], [[4, 2], [4, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 2], [-4, -2]], [[-4, 1], [-4, -1]], [[-4, 3], [-4, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29598373
    {'center': '336.a1', 'center_index': 336, 'center_order': 2, 'counter': 71, 'cyclotomic_n': 7, 'dim': 8, 'faithful': True, 'field': [1, -2, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '672.1158', 'image_order': 672, 'indicator': 1, 'kernel': '672.a1', 'kernel_order': 1, 'label': '672.1158.8a2', 'nt': [336, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 2], [4, -2]], [[4, 3], [4, -3]], [[4, 1], [4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 1], [-4, -1]], [[-4, 3], [-4, -3]], [[-4, 2], [-4, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29598374
    {'center': '336.a1', 'center_index': 336, 'center_order': 2, 'counter': 72, 'cyclotomic_n': 7, 'dim': 8, 'faithful': True, 'field': [1, -2, -1, 1], 'group': '672.1158', 'group_counter': 1158, 'group_order': 672, 'image': None, 'image_isoclass': '672.1158', 'image_order': 672, 'indicator': 1, 'kernel': '672.a1', 'kernel_order': 1, 'label': '672.1158.8a3', 'nt': [336, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 1], [4, -1]], [[4, 2], [4, -2]], [[4, 3], [4, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 3], [-4, -3]], [[-4, 2], [-4, -2]], [[-4, 1], [-4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• 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: 110432349
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 672, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 42, 'label': '672.1158.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.1158', 'subgroup_hash': 1158, 'subgroup_order': 672, 'subgroup_tex': 'C_{84}.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 110432389
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 336, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.144', 'subgroup_hash': 144, 'subgroup_order': 336, 'subgroup_tex': 'C_{12}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110432400
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.142', 'subgroup_hash': 142, 'subgroup_order': 336, 'subgroup_tex': 'D_{84}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110432411
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': True, 'core_order': 336, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.190', 'subgroup_hash': 190, 'subgroup_order': 336, 'subgroup_tex': 'C_{28}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110432422
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.2.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.146', 'subgroup_hash': 146, 'subgroup_order': 336, 'subgroup_tex': 'D_{84}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110432433
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 336, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.2.e1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.180', 'subgroup_hash': 180, 'subgroup_order': 336, 'subgroup_tex': 'C_{12}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110432444
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.2.f1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.143', 'subgroup_hash': 143, 'subgroup_order': 336, 'subgroup_tex': 'D_{21}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 110432455
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 336, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.2.g1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.201', 'subgroup_hash': 201, 'subgroup_order': 336, 'subgroup_tex': 'D_{84}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110432466
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 112, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 14, 'label': '672.1158.3.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '224.183', 'subgroup_hash': 183, 'subgroup_order': 224, 'subgroup_tex': 'Q_8.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110432350
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': True, 'core_order': 168, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.15', 'subgroup_hash': 15, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110432361
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.17', 'subgroup_hash': 17, 'subgroup_order': 168, 'subgroup_tex': 'C_7:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110432372
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 168, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.30', 'subgroup_hash': 30, 'subgroup_order': 168, 'subgroup_tex': 'S_3\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 110432382
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.4.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.16', 'subgroup_hash': 16, 'subgroup_order': 168, 'subgroup_tex': 'C_3:D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 110432383
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 168, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.4.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.25', 'subgroup_hash': 25, 'subgroup_order': 168, 'subgroup_tex': 'C_{12}\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 110432384
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.4.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.35', 'subgroup_hash': 35, 'subgroup_order': 168, 'subgroup_tex': 'C_4\\times D_{21}', 'supersolvable': True, 'sylow': 0}
  • id: 110432385
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 168, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.4.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.14', 'subgroup_hash': 14, 'subgroup_order': 168, 'subgroup_tex': 'D_{21}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110432386
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 168, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.4.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.36', 'subgroup_hash': 36, 'subgroup_order': 168, 'subgroup_tex': 'D_{84}', 'supersolvable': True, 'sylow': 0}
  • id: 110432387
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 168, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.4.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.29', 'subgroup_hash': 29, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 110432388
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 168, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.4.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.24', 'subgroup_hash': 24, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 110432390
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 42, 'characteristic': True, 'core_order': 168, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.4.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['F', 'C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.41', 'subgroup_hash': 41, 'subgroup_order': 168, 'subgroup_tex': 'Q_8\\times C_{21}', 'supersolvable': True, 'sylow': 0}
  • id: 110432391
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.4.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.18', 'subgroup_hash': 18, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 110432392
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 112, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '112.33', 'subgroup_hash': 33, 'subgroup_order': 112, 'subgroup_tex': 'Q_8\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 110432393
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.6.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.30', 'subgroup_hash': 30, 'subgroup_order': 112, 'subgroup_tex': 'D_{28}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110432394
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.6.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.30', 'subgroup_hash': 30, 'subgroup_order': 112, 'subgroup_tex': 'D_{28}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110432395
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 56, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.6.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.39', 'subgroup_hash': 39, 'subgroup_order': 112, 'subgroup_tex': 'Q_8\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110432396
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 56, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.6.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.34', 'subgroup_hash': 34, 'subgroup_order': 112, 'subgroup_tex': 'D_{28}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110432397
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 56, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.6.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.33', 'subgroup_hash': 33, 'subgroup_order': 112, 'subgroup_tex': 'Q_8\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 110432398
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 56, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.6.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.34', 'subgroup_hash': 34, 'subgroup_order': 112, 'subgroup_tex': 'D_{28}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110432399
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '672.1158.7.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.214', 'subgroup_hash': 214, 'subgroup_order': 96, 'subgroup_tex': 'Q_8.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110432401
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 84, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.13', 'subgroup_hash': 13, 'subgroup_order': 84, 'subgroup_tex': 'S_3\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110432402
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 84, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.8.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.12', 'subgroup_hash': 12, 'subgroup_order': 84, 'subgroup_tex': 'C_3\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110432403
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.8.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.14', 'subgroup_hash': 14, 'subgroup_order': 84, 'subgroup_tex': 'D_{42}', 'supersolvable': True, 'sylow': 0}
  • id: 110432404
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': False, 'core_order': 84, 'counter': 33, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '672.1158.8.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.6', 'subgroup_hash': 6, 'subgroup_order': 84, 'subgroup_tex': 'C_{84}', 'supersolvable': True, 'sylow': 0}
  • id: 110432405
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 84, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.8.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.3', 'subgroup_hash': 3, 'subgroup_order': 84, 'subgroup_tex': 'C_3:C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 110432406
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 84, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.8.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.4', 'subgroup_hash': 4, 'subgroup_order': 84, 'subgroup_tex': 'C_7:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110432407
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 84, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.8.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.5', 'subgroup_hash': 5, 'subgroup_order': 84, 'subgroup_tex': 'C_{21}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110432408
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 56, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.4', 'subgroup_hash': 4, 'subgroup_order': 56, 'subgroup_tex': 'C_4\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 110432409
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 56, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.3', 'subgroup_hash': 3, 'subgroup_order': 56, 'subgroup_tex': 'C_7:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 110432410
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': True, 'core_order': 56, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.12.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.10', 'subgroup_hash': 10, 'subgroup_order': 56, 'subgroup_tex': 'C_7\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 110432412
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.12.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.7', 'subgroup_hash': 7, 'subgroup_order': 56, 'subgroup_tex': 'C_7:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110432413
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.12.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.7', 'subgroup_hash': 7, 'subgroup_order': 56, 'subgroup_tex': 'C_7:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110432414
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 28, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.12.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 110432415
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 28, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.12.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.5', 'subgroup_hash': 5, 'subgroup_order': 56, 'subgroup_tex': 'D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 110432416
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 28, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.12.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.4', 'subgroup_hash': 4, 'subgroup_order': 56, 'subgroup_tex': 'C_4\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 110432417
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 28, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.12.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.4', 'subgroup_hash': 4, 'subgroup_order': 56, 'subgroup_tex': 'C_4\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 110432418
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 28, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.12.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.5', 'subgroup_hash': 5, 'subgroup_order': 56, 'subgroup_tex': 'D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 110432419
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 28, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.12.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.10', 'subgroup_hash': 10, 'subgroup_order': 56, 'subgroup_tex': 'C_7\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 110432420
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 28, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.12.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.3', 'subgroup_hash': 3, 'subgroup_order': 56, 'subgroup_tex': 'C_7:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 110432421
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': True, 'core_order': 48, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.14.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '14.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '14.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 14, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_7', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 110432423
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.14.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.37', 'subgroup_hash': 37, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110432424
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.14.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.41', 'subgroup_hash': 41, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110432425
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.14.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.37', 'subgroup_hash': 37, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110432426
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.14.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.46', 'subgroup_hash': 46, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 110432427
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.14.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 110432428
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.14.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.41', 'subgroup_hash': 41, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110432429
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 42, 'counter': 56, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '672.1158.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'S', 'L1', 'D1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '42.6', 'subgroup_hash': 6, 'subgroup_order': 42, 'subgroup_tex': 'C_{42}', 'supersolvable': True, 'sylow': 0}
  • id: 110432430
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 21, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.16.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.3', 'subgroup_hash': 3, 'subgroup_order': 42, 'subgroup_tex': 'S_3\\times C_7', 'supersolvable': True, 'sylow': 0}
  • id: 110432431
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 21, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.16.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.4', 'subgroup_hash': 4, 'subgroup_order': 42, 'subgroup_tex': 'C_3\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 110432432
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 21, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.16.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.5', 'subgroup_hash': 5, 'subgroup_order': 42, 'subgroup_tex': 'D_{21}', 'supersolvable': True, 'sylow': 0}
  • id: 110432434
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '672.1158.21.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '21.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 21, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.50', 'subgroup_hash': 50, 'subgroup_order': 32, 'subgroup_tex': 'C_4.C_2^3', 'supersolvable': True, 'sylow': 2}
  • id: 110432435
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 28, 'counter': 61, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.24.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110432436
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 28, 'counter': 62, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '672.1158.24.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 110432437
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 28, 'counter': 63, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.24.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '28.1', 'subgroup_hash': 1, 'subgroup_order': 28, 'subgroup_tex': 'C_7:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110432438
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 14, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.24.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110432439
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.24.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110432440
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 14, 'counter': 66, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.1158.24.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 110432441
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.24.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '28.1', 'subgroup_hash': 1, 'subgroup_order': 28, 'subgroup_tex': 'C_7:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110432442
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 24, 'counter': 68, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.28.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '28.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110432443
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 24, 'counter': 69, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.28.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '28.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 110432445
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': True, 'core_order': 24, 'counter': 70, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.28.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '28.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 110432446
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.28.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110432447
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.28.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110432448
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.28.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110432449
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.28.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110432450
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.28.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110432451
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.28.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110432452
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.28.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110432453
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.28.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 110432454
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.28.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 110432456
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 21, 'counter': 80, 'cyclic': True, 'direct': False, 'hall': 21, 'label': '672.1158.32.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.50', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 50, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4.C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['L2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '21.2', 'subgroup_hash': 2, 'subgroup_order': 21, 'subgroup_tex': 'C_{21}', 'supersolvable': True, 'sylow': 0}
  • id: 110432457
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.42.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110432458
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.42.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110432459
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 8, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.42.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 110432460
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.42.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110432461
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.42.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 110432462
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.42.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 110432463
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.42.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110432464
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 14, 'counter': 88, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '672.1158.48.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.51', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 51, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['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: 110432465
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 7, 'counter': 89, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.1158.48.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 110432467
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 7, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.48.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
  • id: 110432468
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 7, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.48.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
  • id: 110432469
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 12, 'counter': 92, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.56.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '56.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '56.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110432470
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 12, 'counter': 93, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '672.1158.56.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '56.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '56.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110432471
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 12, 'counter': 94, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.56.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '56.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '56.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110432472
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.56.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110432473
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.56.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110432474
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 97, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.1158.56.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110432475
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.56.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110432476
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': True, 'centralizer_order': 168, 'characteristic': True, 'core_order': 8, 'counter': 99, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1158.84.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '84.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '84.8', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 84, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_7', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 110432351
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.84.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 110432352
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.84.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 110432353
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 4, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.84.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110432354
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.84.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110432355
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.84.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110432356
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.84.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110432357
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.84.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110432358
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.84.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110432359
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 4, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.84.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 110432360
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.84.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 110432362
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.84.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 110432363
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 7, 'counter': 111, 'cyclic': True, 'direct': False, 'hall': 7, 'label': '672.1158.96.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '96.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '96.214', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 214, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8.D_6', 'simple': True, 'solvable': True, 'special_labels': ['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: 110432364
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 6, 'counter': 112, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '672.1158.112.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '112.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '112.42', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 42, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110432365
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 3, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.112.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110432366
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 114, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.1158.112.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110432367
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.112.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110432368
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 4, 'counter': 116, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '672.1158.168.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '168.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '168.50', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 50, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 168, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110432369
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 2, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.168.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 110432370
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.168.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 110432371
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1158.168.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 110432373
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 2, 'counter': 120, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.1158.168.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110432374
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 121, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.1158.168.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110432375
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 122, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.1158.168.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110432376
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 3, 'counter': 123, 'cyclic': True, 'direct': False, 'hall': 3, 'label': '672.1158.224.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '224.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '224.183', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 183, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 224, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8.D_{14}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
  • id: 110432377
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 2, 'counter': 124, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '672.1158.336.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '336.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '336.219', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 219, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 336, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6\\times D_{14}', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'Phi', 'U1'], '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: 110432378
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 1, 'counter': 125, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.1158.336.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 110432379
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 126, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.1158.336.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 110432380
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 127, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.1158.336.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 110432381
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1158', 'ambient_counter': 1158, 'ambient_order': 672, 'ambient_tex': 'C_{84}.C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 1, 'counter': 128, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '672.1158.672.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '672.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '672.1158', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1158, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 672, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{84}.C_2^3', '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: 110432349
    {'ambient': '672.1158', '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': '336.a1', 'complements': ['672.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '2.d1', '2.e1', '2.f1', '2.g1', '3.a1', '7.a1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7118, 4013, 4639, 5040], 'generators': [1, 8, 12, 168, 2, 96, 336], 'label': '672.1158.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1', '2.d1', '2.e1', '2.f1', '2.g1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '336.219'}
  • id: 110432350
    {'ambient': '672.1158', 'aut_centralizer_order': 24, 'aut_label': '4.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 24, 'centralizer': '84.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['8.a1', '8.b1', '8.g1', '12.d1', '28.d1'], 'core': '4.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1834, 9575, 795, 262], 'generators': [2, 336, 8, 12, 96], 'label': '672.1158.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['8.a1', '8.b1', '8.g1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '84.8'}
  • id: 110432351
    {'ambient': '672.1158', 'aut_centralizer_order': 288, 'aut_label': '84.b1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '4.2', 'aut_weyl_index': 6048, 'centralizer': '84.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1', '28.d1', '42.a1'], 'contains': ['168.b1', '168.c1', '168.g1'], 'core': '336.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [2732, -1, 5402, -1], 'generators': [2, 12], 'label': '672.1158.84.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '84.b1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110432352
    {'ambient': '672.1158', 'aut_centralizer_order': 96, 'aut_label': '84.c1', 'aut_quo_index': None, 'aut_stab_index': 63, 'aut_weyl_group': '4.2', 'aut_weyl_index': 6048, 'centralizer': '84.j1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.e1', '28.e1', '42.a1', '42.b1'], 'contains': ['168.b1', '168.d1', '168.f1'], 'core': '336.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [5016, -1, 6275, -1], 'generators': [13, 2], 'label': '672.1158.84.c1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '84.c1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110432353
    {'ambient': '672.1158', 'aut_centralizer_order': 672, 'aut_label': '84.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 6048, 'centralizer': '12.f1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.f1', '28.a1', '42.a1', '42.b1', '42.c1'], 'contains': ['168.a1', '168.b1', '168.e1'], 'core': '168.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7938, -1, 7157, -1], 'generators': [1, 2], 'label': '672.1158.84.d1', 'mobius_quo': None, 'mobius_sub': 14, 'normal_closure': '28.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '84.d1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110432354
    {'ambient': '672.1158', 'aut_centralizer_order': 96, 'aut_label': '84.e1', 'aut_quo_index': None, 'aut_stab_index': 63, 'aut_weyl_group': '4.2', 'aut_weyl_index': 6048, 'centralizer': '84.k1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.g1', '28.f1', '42.a1', '42.d1'], 'contains': ['168.c1', '168.d1', '168.e1'], 'core': '336.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [3964, -1, 6116, -1], 'generators': [3, 12], 'label': '672.1158.84.e1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '84.e1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.e1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110432355
    {'ambient': '672.1158', 'aut_centralizer_order': 288, 'aut_label': '84.f1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '4.2', 'aut_weyl_index': 6048, 'centralizer': '28.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.a1', '28.g1', '42.a1', '42.d1', '42.e1'], 'contains': ['168.a1', '168.c1', '168.f1'], 'core': '168.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [6851, -1, 6858, -1], 'generators': [1, 12], 'label': '672.1158.84.f1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '84.f1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110432356
    {'ambient': '672.1158', 'aut_centralizer_order': 96, 'aut_label': '84.g1', 'aut_quo_index': None, 'aut_stab_index': 63, 'aut_weyl_group': '4.2', 'aut_weyl_index': 6048, 'centralizer': '84.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.h1', '28.h1', '42.a1', '42.f1', '42.g1'], 'contains': ['168.a1', '168.d1', '168.g1'], 'core': '168.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [6289, -1, 7457, -1], 'generators': [1, 358], 'label': '672.1158.84.g1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '84.g1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110432357
    {'ambient': '672.1158', 'aut_centralizer_order': 48, 'aut_label': '84.h1', 'aut_quo_index': None, 'aut_stab_index': 126, 'aut_weyl_group': '4.2', 'aut_weyl_index': 6048, 'centralizer': '84.h1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.i1', '28.i1', '42.b1', '42.d1', '42.f1'], 'contains': ['168.d1', '168.e1', '168.f1'], 'core': '336.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [7168, -1, 7757, -1], 'generators': [3, 324], 'label': '672.1158.84.h1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '84.h1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.h1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110432358
    {'ambient': '672.1158', 'aut_centralizer_order': 48, 'aut_label': '84.i1', 'aut_quo_index': None, 'aut_stab_index': 63, 'aut_weyl_group': '8.3', 'aut_weyl_index': 3024, 'centralizer': '84.l1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.j1', '28.j1', '42.b1', '42.d1', '42.g1'], 'contains': ['168.a1', '168.d1'], 'core': '168.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [7717, -1, 7987, -1], 'generators': [359, 504], 'label': '672.1158.84.i1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '84.i1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.i1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110432359
    {'ambient': '672.1158', 'aut_centralizer_order': 336, 'aut_label': '84.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.3', 'aut_weyl_index': 3024, 'centralizer': '12.e1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.k1', '28.b1', '42.c1', '42.d1', '42.f1'], 'contains': ['168.a1', '168.e1'], 'core': '168.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8656, -1, 8304, -1], 'generators': [3, 504], 'label': '672.1158.84.j1', 'mobius_quo': None, 'mobius_sub': 14, 'normal_closure': '28.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '84.j1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.j1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110432360
    {'ambient': '672.1158', 'aut_centralizer_order': 144, 'aut_label': '84.k1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '8.3', 'aut_weyl_index': 3024, 'centralizer': '28.f1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.b1', '28.k1', '42.b1', '42.e1', '42.f1'], 'contains': ['168.a1', '168.f1'], 'core': '168.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [8509, -1, 8145, -1], 'generators': [13, 504], 'label': '672.1158.84.k1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '84.k1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.k1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110432361
    {'ambient': '672.1158', 'aut_centralizer_order': 8, 'aut_label': '4.b1', 'aut_quo_index': 3, 'aut_stab_index': 3, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 24, 'centralizer': '168.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['2.a1', '2.b1'], 'contains': ['8.a1', '8.c1', '8.f1', '12.e1', '28.e1'], 'core': '4.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [2654, 8190, 1366, 878], 'generators': [349, 336, 8, 2, 96], 'label': '672.1158.4.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': ['2.a1', '2.b1'], 'normal_contains': ['8.a1', '8.c1', '8.f1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
  • id: 110432362
    {'ambient': '672.1158', 'aut_centralizer_order': 96, 'aut_label': '84.l1', 'aut_quo_index': None, 'aut_stab_index': 63, 'aut_weyl_group': '4.2', 'aut_weyl_index': 6048, 'centralizer': '84.i1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.l1', '28.l1', '42.a1', '42.f1'], 'contains': ['168.e1', '168.f1', '168.g1'], 'core': '336.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [6503, -1, 6434, -1], 'generators': [3, 350], 'label': '672.1158.84.l1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '84.l1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.l1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110432363
    {'ambient': '672.1158', 'aut_centralizer_order': 4032, 'aut_label': '96.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 4032, 'centralizer': '2.c1', 'complements': ['7.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1', '48.a1', '48.b1', '48.c1', '48.d1'], 'contains': ['672.a1'], 'core': '96.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [713, 5480, 2919, 4988], 'generators': [96], 'label': '672.1158.96.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '96.a1', 'normal_contained_in': ['32.a1', '48.a1'], 'normal_contains': ['672.a1'], 'normalizer': '1.a1', 'old_label': '96.a1', 'projective_image': '672.1158', 'quotient_action_image': '2.1', 'quotient_action_kernel': '48.40', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '96.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110432364
    {'ambient': '672.1158', 'aut_centralizer_order': 12096, 'aut_label': '112.a1', 'aut_quo_index': 224, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 12096, 'centralizer': '2.e1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '56.a1', '56.b1', '56.c1', '56.d1', '56.e1', '56.f1', '56.g1'], 'contains': ['224.a1', '336.a1'], 'core': '112.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2322, 4305, 5135, 5735], 'generators': [336, 8], 'label': '672.1158.112.a1', 'mobius_quo': 1, 'mobius_sub': -448, 'normal_closure': '112.a1', 'normal_contained_in': ['16.a1', '56.a1', '56.b1', '56.c1'], 'normal_contains': ['224.a1', '336.a1'], 'normalizer': '1.a1', 'old_label': '112.a1', 'projective_image': '336.219', 'quotient_action_image': '2.1', 'quotient_action_kernel': '56.12', 'quotient_action_kernel_order': 56, 'quotient_fusion': None, 'short_label': '112.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110432365
    {'ambient': '672.1158', 'aut_centralizer_order': 2016, 'aut_label': '112.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 4032, 'centralizer': '12.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1', '56.a1'], 'contains': ['224.a1', '336.b1'], 'core': '224.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [242, -1, 4253, -1], 'generators': [2, 8], 'label': '672.1158.112.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '56.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '112.b1', 'projective_image': '672.1158', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110432366
    {'ambient': '672.1158', 'aut_centralizer_order': 864, 'aut_label': '112.c1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '2.1', 'aut_weyl_index': 12096, 'centralizer': '14.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1', '56.d1'], 'contains': ['224.a1', '336.c1'], 'core': '224.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [493, -1, 4015, -1], 'generators': [12, 8], 'label': '672.1158.112.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.e1', 'old_label': '112.c1', 'projective_image': '672.1158', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110432367
    {'ambient': '672.1158', 'aut_centralizer_order': 96, 'aut_label': '112.d1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '6.1', 'aut_weyl_index': 4032, 'centralizer': '84.k1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['16.d1', '56.e1'], 'contains': ['224.a1', '336.d1'], 'core': '224.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [940, -1, 4451, -1], 'generators': [359, 8], 'label': '672.1158.112.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.f1', 'old_label': '112.d1', 'projective_image': '672.1158', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110432368
    {'ambient': '672.1158', 'aut_centralizer_order': 4032, 'aut_label': '168.a1', 'aut_quo_index': 4, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 12096, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['24.b1', '56.b1', '84.a1', '84.d1', '84.f1', '84.g1', '84.i1', '84.j1', '84.k1'], 'contains': ['336.a1'], 'core': '168.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7831, 2475, 7307, 6616], 'generators': [1], 'label': '672.1158.168.a1', 'mobius_quo': 0, 'mobius_sub': -168, 'normal_closure': '168.a1', 'normal_contained_in': ['24.b1', '56.b1', '84.a1'], 'normal_contains': ['336.a1'], 'normalizer': '1.a1', 'old_label': '168.a1', 'projective_image': '336.219', 'quotient_action_image': '2.1', 'quotient_action_kernel': '84.8', 'quotient_action_kernel_order': 84, 'quotient_fusion': None, 'short_label': '168.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110432369
    {'ambient': '672.1158', 'aut_centralizer_order': 4032, 'aut_label': '168.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 12096, 'centralizer': '6.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1', '56.a1', '84.b1', '84.c1', '84.d1'], 'contains': ['336.a1', '336.b1'], 'core': '336.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2673, -1, 5486, -1], 'generators': [2, 336], 'label': '672.1158.168.b1', 'mobius_quo': None, 'mobius_sub': -56, 'normal_closure': '56.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '168.b1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110432370
    {'ambient': '672.1158', 'aut_centralizer_order': 1728, 'aut_label': '168.c1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '2.1', 'aut_weyl_index': 12096, 'centralizer': '14.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1', '56.d1', '84.b1', '84.e1', '84.f1'], 'contains': ['336.a1', '336.c1'], 'core': '336.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [2908, -1, 5305, -1], 'generators': [12, 336], 'label': '672.1158.168.c1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '168.c1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110432371
    {'ambient': '672.1158', 'aut_centralizer_order': 192, 'aut_label': '168.d1', 'aut_quo_index': None, 'aut_stab_index': 63, 'aut_weyl_group': '2.1', 'aut_weyl_index': 12096, 'centralizer': '42.f1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.e1', '56.e1', '84.c1', '84.e1', '84.g1', '84.h1', '84.i1'], 'contains': ['336.a1', '336.d1'], 'core': '336.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [4077, -1, 6105, -1], 'generators': [359, 336], 'label': '672.1158.168.d1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '168.d1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110432372
    {'ambient': '672.1158', 'aut_centralizer_order': 56, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 3, 'aut_weyl_group': '144.195', 'aut_weyl_index': 168, 'centralizer': '24.b1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['2.a1', '2.b1', '2.c1'], 'contains': ['8.a1', '8.d1', '8.e1', '12.f1', '28.a1'], 'core': '4.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [4864, 4048, 3236, 5164], 'generators': [1, 96, 336, 2, 8], 'label': '672.1158.4.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': ['2.a1', '2.b1', '2.c1'], 'normal_contains': ['8.a1', '8.d1', '8.e1', '28.a1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 110432373
    {'ambient': '672.1158', 'aut_centralizer_order': 1344, 'aut_label': '168.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 12096, 'centralizer': '6.c1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.f1', '56.c1', '84.d1', '84.e1', '84.h1', '84.j1', '84.l1'], 'contains': ['336.a1'], 'core': '336.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7018, -1, 6434, -1], 'generators': [3], 'label': '672.1158.168.e1', 'mobius_quo': None, 'mobius_sub': -56, 'normal_closure': '56.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '168.e1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110432374
    {'ambient': '672.1158', 'aut_centralizer_order': 576, 'aut_label': '168.f1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '2.1', 'aut_weyl_index': 12096, 'centralizer': '14.d1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.c1', '56.f1', '84.c1', '84.f1', '84.h1', '84.k1', '84.l1'], 'contains': ['336.a1'], 'core': '336.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [6542, -1, 6275, -1], 'generators': [13], 'label': '672.1158.168.f1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '168.f1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110432375
    {'ambient': '672.1158', 'aut_centralizer_order': 576, 'aut_label': '168.g1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '2.1', 'aut_weyl_index': 12096, 'centralizer': '42.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1', '56.g1', '84.b1', '84.g1', '84.l1'], 'contains': ['336.a1'], 'core': '336.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [3287, -1, 5656, -1], 'generators': [358], 'label': '672.1158.168.g1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '168.g1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110432412
    {'ambient': '672.1158', 'aut_centralizer_order': 48, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '168.47', 'aut_weyl_index': 144, 'centralizer': '84.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '6.b1'], 'contains': ['24.a1', '24.d1', '24.g1', '84.b1'], 'core': '24.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2112, -1, 773, -1], 'generators': [2, 336, 96, 12], 'label': '672.1158.12.d1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.d1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 110432376
    {'ambient': '672.1158', 'aut_centralizer_order': 12096, 'aut_label': '224.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 12096, 'centralizer': '2.e1', 'complements': ['3.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1', '112.a1', '112.b1', '112.c1', '112.d1'], 'contains': ['672.a1'], 'core': '224.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [456, 5498, 4134, 5361], 'generators': [8], 'label': '672.1158.224.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '224.a1', 'normal_contained_in': ['32.a1', '112.a1'], 'normal_contains': ['672.a1'], 'normalizer': '1.a1', 'old_label': '224.a1', 'projective_image': '672.1158', 'quotient_action_image': '2.1', 'quotient_action_kernel': '112.33', 'quotient_action_kernel_order': 112, 'quotient_fusion': None, 'short_label': '224.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110432377
    {'ambient': '672.1158', 'aut_centralizer_order': 24192, 'aut_label': '336.a1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 24192, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1', '112.a1', '168.a1', '168.b1', '168.c1', '168.d1', '168.e1', '168.f1', '168.g1'], 'contains': ['672.a1'], 'core': '336.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3131, 4531, 5569, 5735], 'generators': [336], 'label': '672.1158.336.a1', 'mobius_quo': -1, 'mobius_sub': 1344, 'normal_closure': '336.a1', 'normal_contained_in': ['48.a1', '112.a1', '168.a1'], 'normal_contains': ['672.a1'], 'normalizer': '1.a1', 'old_label': '336.a1', 'projective_image': '336.219', 'quotient_action_image': '1.1', 'quotient_action_kernel': '336.219', 'quotient_action_kernel_order': 336, 'quotient_fusion': None, 'short_label': '336.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110432378
    {'ambient': '672.1158', 'aut_centralizer_order': 4032, 'aut_label': '336.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 24192, 'centralizer': '6.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1', '112.b1', '168.b1'], 'contains': ['672.a1'], 'core': '672.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [252, -1, 4293, -1], 'generators': [2], 'label': '672.1158.336.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '56.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '336.b1', 'projective_image': '672.1158', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110432379
    {'ambient': '672.1158', 'aut_centralizer_order': 1728, 'aut_label': '336.c1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '1.1', 'aut_weyl_index': 24192, 'centralizer': '14.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1', '112.c1', '168.c1'], 'contains': ['672.a1'], 'core': '672.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [693, -1, 3975, -1], 'generators': [12], 'label': '672.1158.336.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.e1', 'old_label': '336.c1', 'projective_image': '672.1158', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110432380
    {'ambient': '672.1158', 'aut_centralizer_order': 192, 'aut_label': '336.d1', 'aut_quo_index': None, 'aut_stab_index': 126, 'aut_weyl_group': '1.1', 'aut_weyl_index': 24192, 'centralizer': '42.f1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.d1', '112.d1', '168.d1'], 'contains': ['672.a1'], 'core': '672.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [999, -1, 4451, -1], 'generators': [359], 'label': '672.1158.336.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.f1', 'old_label': '336.d1', 'projective_image': '672.1158', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110432381
    {'ambient': '672.1158', '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', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['96.a1', '224.a1', '336.a1', '336.b1', '336.c1', '336.d1'], 'contains': [], 'core': '672.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [771, 5498, 4213, 5361], 'generators': [], 'label': '672.1158.672.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '672.a1', 'normal_contained_in': ['96.a1', '224.a1', '336.a1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '672.a1', 'projective_image': '672.1158', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110432382
    {'ambient': '672.1158', 'aut_centralizer_order': 8, 'aut_label': '4.d1', 'aut_quo_index': 3, 'aut_stab_index': 3, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 24, 'centralizer': '168.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['2.a1', '2.d1'], 'contains': ['8.b1', '8.c1', '8.e1', '12.g1', '28.f1'], 'core': '4.d1', 'coset_action_label': None, 'count': 3, 'diagramx': [2342, 6535, 1104, 2112], 'generators': [3, 336, 8, 12, 96], 'label': '672.1158.4.d1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1', 'normal_contained_in': ['2.a1', '2.d1'], 'normal_contains': ['8.b1', '8.c1', '8.e1'], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
  • id: 110432383
    {'ambient': '672.1158', 'aut_centralizer_order': 24, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 3, 'aut_weyl_group': '336.216', 'aut_weyl_index': 72, 'centralizer': '56.b1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['2.a1', '2.d1', '2.e1'], 'contains': ['8.b1', '8.d1', '8.f1', '12.a1', '28.g1'], 'core': '4.e1', 'coset_action_label': None, 'count': 3, 'diagramx': [4380, 2575, 1942, 4320], 'generators': [1, 8, 336, 12, 96], 'label': '672.1158.4.e1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1', 'normal_contained_in': ['2.a1', '2.d1', '2.e1'], 'normal_contains': ['8.b1', '8.d1', '8.f1', '12.a1'], 'normalizer': '1.a1', 'old_label': '4.e1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 110432384
    {'ambient': '672.1158', 'aut_centralizer_order': 8, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 3, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 24, 'centralizer': '168.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['2.a1', '2.f1', '2.g1'], 'contains': ['8.c1', '8.d1', '8.g1', '12.h1', '28.h1'], 'core': '4.f1', 'coset_action_label': None, 'count': 3, 'diagramx': [4031, 7362, 2303, 2848], 'generators': [1, 336, 8, 358, 96], 'label': '672.1158.4.f1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1', 'normal_contained_in': ['2.a1', '2.f1', '2.g1'], 'normal_contains': ['8.c1', '8.d1', '8.g1'], 'normalizer': '1.a1', 'old_label': '4.f1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
  • id: 110432385
    {'ambient': '672.1158', 'aut_centralizer_order': 4, 'aut_label': '4.g1', 'aut_quo_index': 6, 'aut_stab_index': 6, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 24, 'centralizer': '336.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['2.b1', '2.d1', '2.f1'], 'contains': ['8.c1', '8.e1', '8.f1', '12.i1', '28.i1'], 'core': '4.g1', 'coset_action_label': None, 'count': 6, 'diagramx': [3730, 5842, 2925, 3584], 'generators': [3, 336, 8, 660, 96], 'label': '672.1158.4.g1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1', 'normal_contained_in': ['2.b1', '2.d1', '2.f1'], 'normal_contains': ['8.c1', '8.e1', '8.f1'], 'normalizer': '1.a1', 'old_label': '4.g1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1', 'subgroup_fusion': None, 'weyl_group': '336.219'}
  • id: 110432386
    {'ambient': '672.1158', 'aut_centralizer_order': 4, 'aut_label': '4.h1', 'aut_quo_index': 6, 'aut_stab_index': 3, 'aut_weyl_group': '2016.eo', 'aut_weyl_index': 12, 'centralizer': '336.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['2.b1', '2.d1', '2.g1'], 'contains': ['8.c1', '8.d1', '12.j1', '28.j1'], 'core': '4.h1', 'coset_action_label': None, 'count': 3, 'diagramx': [5407, 3314, 3514, 5817], 'generators': [359, 336, 8, 168, 96], 'label': '672.1158.4.h1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.h1', 'normal_contained_in': ['2.b1', '2.d1', '2.g1'], 'normal_contains': ['8.c1', '8.d1'], 'normalizer': '1.a1', 'old_label': '4.h1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1', 'subgroup_fusion': None, 'weyl_group': '336.219'}
  • id: 110432387
    {'ambient': '672.1158', 'aut_centralizer_order': 28, 'aut_label': '4.i1', 'aut_quo_index': 6, 'aut_stab_index': 3, 'aut_weyl_group': '288.992', 'aut_weyl_index': 84, 'centralizer': '48.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['2.c1', '2.d1', '2.f1'], 'contains': ['8.d1', '8.e1', '12.k1', '28.b1'], 'core': '4.i1', 'coset_action_label': None, 'count': 3, 'diagramx': [5671, 1608, 4738, 7347], 'generators': [3, 96, 336, 168, 8], 'label': '672.1158.4.i1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.i1', 'normal_contained_in': ['2.c1', '2.d1', '2.f1'], 'normal_contains': ['8.d1', '8.e1', '28.b1'], 'normalizer': '1.a1', 'old_label': '4.i1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 110432388
    {'ambient': '672.1158', 'aut_centralizer_order': 12, 'aut_label': '4.j1', 'aut_quo_index': 6, 'aut_stab_index': 3, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 36, 'centralizer': '112.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['2.b1', '2.e1', '2.f1'], 'contains': ['8.d1', '8.f1', '12.b1', '28.k1'], 'core': '4.j1', 'coset_action_label': None, 'count': 3, 'diagramx': [6092, 5008, 4059, 6481], 'generators': [349, 8, 336, 168, 96], 'label': '672.1158.4.j1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.j1', 'normal_contained_in': ['2.b1', '2.e1', '2.f1'], 'normal_contains': ['8.d1', '8.f1', '12.b1'], 'normalizer': '1.a1', 'old_label': '4.j1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1', 'subgroup_fusion': None, 'weyl_group': '112.42'}
  • id: 110432389
    {'ambient': '672.1158', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 12, 'centralizer': '168.a1', 'complements': ['336.d1'], 'conjugacy_class_count': 3, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1', '4.f1', '4.l1', '6.b1', '14.b1'], 'core': '2.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3704, 6978, 2123, 2428], 'generators': [1, 96, 12, 336, 2, 8], 'label': '672.1158.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1', '4.f1', '4.l1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '336.219', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
  • id: 110432390
    {'ambient': '672.1158', 'aut_centralizer_order': 84, 'aut_label': '4.k1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '288.1033', 'aut_weyl_index': 84, 'centralizer': '16.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '2.e1', '2.g1'], 'contains': ['8.d1', '12.c1', '28.c1'], 'core': '4.k1', 'coset_action_label': None, 'count': 1, 'diagramx': [9422, 425, 5708, 8917], 'generators': [1, 8, 96, 168, 336], 'label': '672.1158.4.k1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.k1', 'normal_contained_in': ['2.c1', '2.e1', '2.g1'], 'normal_contains': ['8.d1', '12.c1', '28.c1'], 'normalizer': '1.a1', 'old_label': '4.k1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.k1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 110432391
    {'ambient': '672.1158', 'aut_centralizer_order': 8, 'aut_label': '4.l1', 'aut_quo_index': 3, 'aut_stab_index': 3, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 24, 'centralizer': '168.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['2.a1', '2.f1'], 'contains': ['8.e1', '8.f1', '8.g1', '12.l1', '28.l1'], 'core': '4.l1', 'coset_action_label': None, 'count': 3, 'diagramx': [3476, 8883, 1629, 1495], 'generators': [3, 336, 8, 358, 96], 'label': '672.1158.4.l1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.l1', 'normal_contained_in': ['2.a1', '2.f1'], 'normal_contains': ['8.e1', '8.f1', '8.g1'], 'normalizer': '1.a1', 'old_label': '4.l1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.l1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
  • id: 110432392
    {'ambient': '672.1158', 'aut_centralizer_order': 12, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2016.dc', 'aut_weyl_index': 12, 'centralizer': '112.a1', 'complements': ['112.b1', '112.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1', '3.a1'], 'contains': ['12.a1', '12.b1', '12.c1', '42.e1'], 'core': '6.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9843, 1095, 5375, 8134], 'generators': [1, 168, 336, 12, 96], 'label': '672.1158.6.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1', 'normal_contained_in': ['2.e1'], 'normal_contains': ['12.a1', '12.b1', '12.c1'], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': '336.219', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.a1', 'subgroup_fusion': None, 'weyl_group': '112.42'}
  • id: 110432393
    {'ambient': '672.1158', 'aut_centralizer_order': 8, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '336.216', 'aut_weyl_index': 72, 'centralizer': '168.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['2.a1', '3.a1'], 'contains': ['12.a1', '12.d1', '12.e1', '12.f1', '12.g1', '12.h1', '12.l1', '42.a1'], 'core': '12.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6005, -1, 2639, -1], 'generators': [1, 12, 336, 2, 96], 'label': '672.1158.6.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.b1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 110432394
    {'ambient': '672.1158', 'aut_centralizer_order': 4, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 36, 'centralizer': '168.e1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['2.b1', '3.a1'], 'contains': ['12.b1', '12.e1', '12.f1', '12.i1', '12.j1', '42.b1'], 'core': '12.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [8226, -1, 4398, -1], 'generators': [13, 168, 336, 2, 96], 'label': '672.1158.6.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.c1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 110432395
    {'ambient': '672.1158', 'aut_centralizer_order': 28, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1033', 'aut_weyl_index': 84, 'centralizer': '24.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '3.a1'], 'contains': ['12.c1', '12.f1', '12.k1', '42.c1'], 'core': '12.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [8901, -1, 6335, -1], 'generators': [1, 168, 96, 2, 336], 'label': '672.1158.6.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.d1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 110432396
    {'ambient': '672.1158', 'aut_centralizer_order': 4, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 36, 'centralizer': '336.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['2.d1', '3.a1'], 'contains': ['12.a1', '12.g1', '12.i1', '12.j1', '12.k1', '42.d1'], 'core': '12.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7476, -1, 3743, -1], 'generators': [3, 168, 336, 12, 96], 'label': '672.1158.6.e1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.e1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1', 'subgroup_fusion': None, 'weyl_group': '112.42'}
  • id: 110432397
    {'ambient': '672.1158', 'aut_centralizer_order': 4, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 36, 'centralizer': '336.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['2.f1', '3.a1'], 'contains': ['12.b1', '12.h1', '12.i1', '12.k1', '12.l1', '42.f1'], 'core': '12.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [8513, -1, 5073, -1], 'generators': [3, 168, 336, 350, 96], 'label': '672.1158.6.f1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.f1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1', 'subgroup_fusion': None, 'weyl_group': '112.42'}
  • id: 110432398
    {'ambient': '672.1158', 'aut_centralizer_order': 4, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2016.dc', 'aut_weyl_index': 12, 'centralizer': '336.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1', '3.a1'], 'contains': ['12.c1', '12.h1', '12.j1', '42.g1'], 'core': '12.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [9528, -1, 6022, -1], 'generators': [1, 168, 336, 358, 96], 'label': '672.1158.6.g1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.g1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1', 'subgroup_fusion': None, 'weyl_group': '112.42'}
  • id: 110432399
    {'ambient': '672.1158', 'aut_centralizer_order': 6, 'aut_label': '7.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 42, 'centralizer': '336.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['14.a1', '14.b1', '14.c1', '14.d1', '14.e1', '14.f1', '14.g1', '21.a1'], 'core': '14.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7118, -1, 7442, -1], 'generators': [1, 8, 336, 2, 12, 504], 'label': '672.1158.7.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '7.a1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 110432400
    {'ambient': '672.1158', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '336.a1', 'complements': ['336.c1', '336.d1'], 'conjugacy_class_count': 3, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.c1', '4.g1', '4.h1', '4.j1', '6.c1', '14.c1'], 'core': '2.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5504, 4957, 3898, 3584], 'generators': [349, 96, 168, 336, 2, 8], 'label': '672.1158.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.c1', '4.g1', '4.h1', '4.j1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '336.219', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '336.219'}
  • id: 110432401
    {'ambient': '672.1158', 'aut_centralizer_order': 336, 'aut_label': '8.a1', 'aut_quo_index': 28, 'aut_stab_index': 1, 'aut_weyl_group': '72.48', 'aut_weyl_index': 336, 'centralizer': '12.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.b1', '4.c1'], 'contains': ['16.a1', '16.b1', '24.d1', '56.a1'], 'core': '8.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1123, 7718, 462, 2407], 'generators': [2, 96, 8, 336], 'label': '672.1158.8.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1', '4.b1', '4.c1'], 'normal_contains': ['16.a1', '56.a1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110432402
    {'ambient': '672.1158', 'aut_centralizer_order': 144, 'aut_label': '8.b1', 'aut_quo_index': 28, 'aut_stab_index': 1, 'aut_weyl_group': '168.47', 'aut_weyl_index': 144, 'centralizer': '28.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.d1', '4.e1'], 'contains': ['16.a1', '16.c1', '24.a1', '56.d1'], 'core': '8.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1432, 6325, 131, 1630], 'generators': [12, 8, 96, 336], 'label': '672.1158.8.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1', 'normal_contained_in': ['4.a1', '4.d1', '4.e1'], 'normal_contains': ['16.a1', '24.a1'], 'normalizer': '1.a1', 'old_label': '8.b1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 110432403
    {'ambient': '672.1158', 'aut_centralizer_order': 16, 'aut_label': '8.c1', 'aut_quo_index': 84, 'aut_stab_index': 3, 'aut_weyl_group': '504.162', 'aut_weyl_index': 48, 'centralizer': '168.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['4.b1', '4.d1', '4.f1', '4.g1', '4.h1'], 'contains': ['16.a1', '16.d1', '24.e1', '56.e1'], 'core': '8.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [2237, 6983, 1265, 3060], 'generators': [359, 8, 96, 336], 'label': '672.1158.8.c1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.c1', 'normal_contained_in': ['4.b1', '4.d1', '4.f1', '4.g1', '4.h1'], 'normal_contains': ['16.a1'], 'normalizer': '1.a1', 'old_label': '8.c1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
  • id: 110432404
    {'ambient': '672.1158', 'aut_centralizer_order': 336, 'aut_label': '8.d1', 'aut_quo_index': 168, 'aut_stab_index': 3, 'aut_weyl_group': '24.15', 'aut_weyl_index': 1008, 'centralizer': '8.d1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['4.c1', '4.e1', '4.f1', '4.h1', '4.i1', '4.j1', '4.k1'], 'contains': ['16.a1', '24.b1', '56.b1'], 'core': '8.d1', 'coset_action_label': None, 'count': 3, 'diagramx': [5472, 2848, 3164, 5963], 'generators': [1, 96, 336, 8], 'label': '672.1158.8.d1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.d1', 'normal_contained_in': ['4.c1', '4.e1', '4.f1', '4.h1', '4.i1', '4.j1', '4.k1'], 'normal_contains': ['16.a1', '24.b1', '56.b1'], 'normalizer': '1.a1', 'old_label': '8.d1', 'projective_image': '336.219', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.d1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 110432405
    {'ambient': '672.1158', 'aut_centralizer_order': 112, 'aut_label': '8.e1', 'aut_quo_index': 84, 'aut_stab_index': 3, 'aut_weyl_group': '72.48', 'aut_weyl_index': 336, 'centralizer': '24.b1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['4.c1', '4.d1', '4.g1', '4.i1', '4.l1'], 'contains': ['16.a1', '24.f1', '56.c1'], 'core': '8.e1', 'coset_action_label': None, 'count': 3, 'diagramx': [3754, 4468, 2374, 4589], 'generators': [3, 336, 8, 96], 'label': '672.1158.8.e1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.e1', 'normal_contained_in': ['4.c1', '4.d1', '4.g1', '4.i1', '4.l1'], 'normal_contains': ['16.a1', '56.c1'], 'normalizer': '1.a1', 'old_label': '8.e1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 110432406
    {'ambient': '672.1158', 'aut_centralizer_order': 48, 'aut_label': '8.f1', 'aut_quo_index': 84, 'aut_stab_index': 3, 'aut_weyl_group': '168.47', 'aut_weyl_index': 144, 'centralizer': '56.b1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['4.b1', '4.e1', '4.g1', '4.j1', '4.l1'], 'contains': ['16.a1', '24.c1', '56.f1'], 'core': '8.f1', 'coset_action_label': None, 'count': 3, 'diagramx': [3264, 5440, 1743, 3724], 'generators': [349, 336, 96, 8], 'label': '672.1158.8.f1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.f1', 'normal_contained_in': ['4.b1', '4.e1', '4.g1', '4.j1', '4.l1'], 'normal_contains': ['16.a1', '24.c1'], 'normalizer': '1.a1', 'old_label': '8.f1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 110432407
    {'ambient': '672.1158', 'aut_centralizer_order': 48, 'aut_label': '8.g1', 'aut_quo_index': 28, 'aut_stab_index': 1, 'aut_weyl_group': '504.162', 'aut_weyl_index': 48, 'centralizer': '84.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.f1', '4.l1'], 'contains': ['16.a1', '24.g1', '56.g1'], 'core': '8.g1', 'coset_action_label': None, 'count': 1, 'diagramx': [2531, 8736, 1035, 967], 'generators': [358, 8, 96, 336], 'label': '672.1158.8.g1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.g1', 'normal_contained_in': ['4.a1', '4.f1', '4.l1'], 'normal_contains': ['16.a1'], 'normalizer': '1.a1', 'old_label': '8.g1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1', 'subgroup_fusion': None, 'weyl_group': '84.8'}
  • id: 110432408
    {'ambient': '672.1158', 'aut_centralizer_order': 48, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 3, 'aut_weyl_group': '168.47', 'aut_weyl_index': 144, 'centralizer': '56.b1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['4.e1', '6.a1', '6.b1', '6.e1'], 'contains': ['24.a1', '24.b1', '24.c1', '84.f1'], 'core': '12.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7001, 2120, 2914, 5377], 'generators': [1, 336, 96, 12], 'label': '672.1158.12.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1', 'normal_contained_in': ['4.e1', '6.a1'], 'normal_contains': ['24.a1', '24.b1', '24.c1'], 'normalizer': '1.a1', 'old_label': '12.a1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 110432409
    {'ambient': '672.1158', 'aut_centralizer_order': 24, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 3, 'aut_weyl_group': '336.125', 'aut_weyl_index': 72, 'centralizer': '56.c1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['4.j1', '6.a1', '6.c1', '6.f1'], 'contains': ['24.b1', '24.c1', '84.k1'], 'core': '12.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [9188, 3233, 4524, 6429], 'generators': [13, 336, 96, 168], 'label': '672.1158.12.b1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1', 'normal_contained_in': ['4.j1', '6.a1'], 'normal_contains': ['24.b1', '24.c1'], 'normalizer': '1.a1', 'old_label': '12.b1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 110432410
    {'ambient': '672.1158', 'aut_centralizer_order': 168, 'aut_label': '12.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '144.188', 'aut_weyl_index': 168, 'centralizer': '8.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.k1', '6.a1', '6.d1', '6.g1'], 'contains': ['24.b1', '84.a1'], 'core': '12.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [9880, 1095, 5080, 8207], 'generators': [1, 96, 336, 168], 'label': '672.1158.12.c1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.c1', 'normal_contained_in': ['4.k1', '6.a1'], 'normal_contains': ['24.b1', '84.a1'], 'normalizer': '1.a1', 'old_label': '12.c1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 110432411
    {'ambient': '672.1158', 'aut_centralizer_order': 14, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1728.47893', 'aut_weyl_index': 14, 'centralizer': '48.a1', 'complements': ['336.c1', '336.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.c1', '4.i1', '4.k1', '6.d1', '14.a1'], 'core': '2.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [7658, 1112, 5706, 7621], 'generators': [1, 8, 168, 96, 2, 336], 'label': '672.1158.2.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.c1', '4.i1', '4.k1', '14.a1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '336.219', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 110432413
    {'ambient': '672.1158', 'aut_centralizer_order': 16, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '168.47', 'aut_weyl_index': 144, 'centralizer': '84.j1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.b1', '6.b1', '6.c1'], 'contains': ['24.c1', '24.d1', '24.e1', '84.c1'], 'core': '24.c1', 'coset_action_label': None, 'count': 9, 'diagramx': [3946, -1, 2059, -1], 'generators': [13, 336, 96, 2], 'label': '672.1158.12.e1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.e1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 110432414
    {'ambient': '672.1158', 'aut_centralizer_order': 112, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.15', 'aut_weyl_index': 1008, 'centralizer': '12.f1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.c1', '6.b1', '6.c1', '6.d1'], 'contains': ['24.b1', '24.d1', '24.f1', '84.d1'], 'core': '24.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [8224, -1, 3743, -1], 'generators': [1, 96, 336, 2], 'label': '672.1158.12.f1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.f1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110432415
    {'ambient': '672.1158', 'aut_centralizer_order': 16, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '168.47', 'aut_weyl_index': 144, 'centralizer': '168.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.d1', '6.b1', '6.e1'], 'contains': ['24.a1', '24.e1', '24.f1', '84.e1'], 'core': '24.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3464, -1, 1461, -1], 'generators': [3, 336, 96, 12], 'label': '672.1158.12.g1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.g1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 110432416
    {'ambient': '672.1158', 'aut_centralizer_order': 16, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '168.47', 'aut_weyl_index': 144, 'centralizer': '168.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.f1', '6.b1', '6.f1', '6.g1'], 'contains': ['24.b1', '24.e1', '24.g1', '84.g1'], 'core': '24.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [5980, -1, 3413, -1], 'generators': [1, 336, 96, 358], 'label': '672.1158.12.h1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.h1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 110432417
    {'ambient': '672.1158', 'aut_centralizer_order': 8, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '168.47', 'aut_weyl_index': 144, 'centralizer': '168.e1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['4.g1', '6.c1', '6.e1', '6.f1'], 'contains': ['24.c1', '24.e1', '24.f1', '84.h1'], 'core': '24.c1', 'coset_action_label': None, 'count': 18, 'diagramx': [7283, -1, 4074, -1], 'generators': [3, 336, 96, 324], 'label': '672.1158.12.i1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.i1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 110432418
    {'ambient': '672.1158', 'aut_centralizer_order': 8, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '336.125', 'aut_weyl_index': 72, 'centralizer': '168.e1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.h1', '6.c1', '6.e1', '6.g1'], 'contains': ['24.b1', '24.e1', '84.i1'], 'core': '24.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [8483, -1, 4324, -1], 'generators': [359, 336, 96, 168], 'label': '672.1158.12.j1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.j1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 110432419
    {'ambient': '672.1158', 'aut_centralizer_order': 56, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.45', 'aut_weyl_index': 504, 'centralizer': '24.d1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.i1', '6.d1', '6.e1', '6.f1'], 'contains': ['24.b1', '24.f1', '84.j1'], 'core': '24.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [8772, -1, 4778, -1], 'generators': [3, 96, 336, 168], 'label': '672.1158.12.k1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.k1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 110432420
    {'ambient': '672.1158', 'aut_centralizer_order': 16, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '168.47', 'aut_weyl_index': 144, 'centralizer': '168.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.l1', '6.b1', '6.f1'], 'contains': ['24.c1', '24.f1', '24.g1', '84.l1'], 'core': '24.c1', 'coset_action_label': None, 'count': 9, 'diagramx': [6530, -1, 2661, -1], 'generators': [3, 336, 96, 350], 'label': '672.1158.12.l1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.l1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 110432421
    {'ambient': '672.1158', 'aut_centralizer_order': 84, 'aut_label': '14.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 84, 'centralizer': '48.a1', 'complements': ['48.c1', '48.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '7.a1'], 'contains': ['28.a1', '28.b1', '28.c1', '42.c1'], 'core': '14.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7728, 612, 8046, 9694], 'generators': [1, 8, 2, 504, 336], 'label': '672.1158.14.a1', 'mobius_quo': 0, 'mobius_sub': 7, 'normal_closure': '14.a1', 'normal_contained_in': ['2.c1'], 'normal_contains': ['28.a1', '28.b1', '28.c1'], 'normalizer': '1.a1', 'old_label': '14.a1', 'projective_image': '336.219', 'quotient_action_image': '2.1', 'quotient_action_kernel': '7.1', 'quotient_action_kernel_order': 7, 'quotient_fusion': None, 'short_label': '14.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 110432422
    {'ambient': '672.1158', 'aut_centralizer_order': 2, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '336.a1', 'complements': ['336.b1', '336.d1'], 'conjugacy_class_count': 3, 'contained_in': ['1.a1'], 'contains': ['4.d1', '4.e1', '4.g1', '4.h1', '4.i1', '6.e1', '14.d1'], 'core': '2.d1', 'coset_action_label': None, 'count': 3, 'diagramx': [4806, 3314, 3516, 5040], 'generators': [3, 96, 168, 336, 12, 8], 'label': '672.1158.2.d1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.d1', '4.e1', '4.g1', '4.h1', '4.i1'], 'normalizer': '1.a1', 'old_label': '2.d1', 'projective_image': '336.219', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1', 'subgroup_fusion': None, 'weyl_group': '336.219'}
  • id: 110432423
    {'ambient': '672.1158', 'aut_centralizer_order': 24, 'aut_label': '14.b1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '48.51', 'aut_weyl_index': 504, 'centralizer': '168.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['2.a1', '7.a1'], 'contains': ['28.a1', '28.d1', '28.e1', '28.f1', '28.g1', '28.h1', '28.l1', '42.a1'], 'core': '28.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [3170, -1, 6648, -1], 'generators': [1, 8, 2, 12, 336], 'label': '672.1158.14.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '14.b1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 110432424
    {'ambient': '672.1158', 'aut_centralizer_order': 12, 'aut_label': '14.c1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '96.209', 'aut_weyl_index': 252, 'centralizer': '336.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['2.b1', '7.a1'], 'contains': ['28.a1', '28.e1', '28.i1', '28.j1', '28.k1', '42.b1'], 'core': '28.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [5354, -1, 7166, -1], 'generators': [349, 8, 2, 504, 336], 'label': '672.1158.14.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '14.c1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.c1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 110432425
    {'ambient': '672.1158', 'aut_centralizer_order': 12, 'aut_label': '14.d1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '96.209', 'aut_weyl_index': 252, 'centralizer': '168.f1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['2.d1', '7.a1'], 'contains': ['28.b1', '28.f1', '28.g1', '28.i1', '28.j1', '42.d1'], 'core': '28.b1', 'coset_action_label': None, 'count': 21, 'diagramx': [5103, -1, 6910, -1], 'generators': [3, 8, 12, 504, 336], 'label': '672.1158.14.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '14.d1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.d1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 110432426
    {'ambient': '672.1158', 'aut_centralizer_order': 36, 'aut_label': '14.e1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '96.226', 'aut_weyl_index': 252, 'centralizer': '56.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1', '7.a1'], 'contains': ['28.c1', '28.g1', '28.k1', '42.e1'], 'core': '28.c1', 'coset_action_label': None, 'count': 7, 'diagramx': [8131, -1, 7744, -1], 'generators': [1, 336, 12, 504, 8], 'label': '672.1158.14.e1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '14.e1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.e1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 110432427
    {'ambient': '672.1158', 'aut_centralizer_order': 12, 'aut_label': '14.f1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '96.209', 'aut_weyl_index': 252, 'centralizer': '336.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['2.f1', '7.a1'], 'contains': ['28.b1', '28.h1', '28.i1', '28.k1', '28.l1', '42.f1'], 'core': '28.b1', 'coset_action_label': None, 'count': 21, 'diagramx': [4817, -1, 7442, -1], 'generators': [3, 8, 358, 504, 336], 'label': '672.1158.14.f1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '14.f1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.f1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 110432428
    {'ambient': '672.1158', 'aut_centralizer_order': 12, 'aut_label': '14.g1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 84, 'centralizer': '336.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1', '7.a1'], 'contains': ['28.c1', '28.h1', '28.j1', '42.g1'], 'core': '28.c1', 'coset_action_label': None, 'count': 7, 'diagramx': [8398, -1, 8322, -1], 'generators': [1, 8, 358, 504, 336], 'label': '672.1158.14.g1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '14.g1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.g1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 110432429
    {'ambient': '672.1158', 'aut_centralizer_order': 2016, 'aut_label': '16.a1', 'aut_quo_index': 3360, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 2016, 'centralizer': '4.k1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '8.b1', '8.c1', '8.d1', '8.e1', '8.f1', '8.g1'], 'contains': ['32.a1', '48.a1', '112.a1'], 'core': '16.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1467, 5633, 2584, 4081], 'generators': [336, 96, 8], 'label': '672.1158.16.a1', 'mobius_quo': -1, 'mobius_sub': 64, 'normal_closure': '16.a1', 'normal_contained_in': ['8.a1', '8.b1', '8.c1', '8.d1', '8.e1', '8.f1', '8.g1'], 'normal_contains': ['32.a1', '48.a1', '112.a1'], 'normalizer': '1.a1', 'old_label': '16.a1', 'projective_image': '336.219', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110432430
    {'ambient': '672.1158', 'aut_centralizer_order': 336, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '36.12', 'aut_weyl_index': 672, 'centralizer': '12.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1'], 'contains': ['32.a1', '48.b1', '112.b1'], 'core': '32.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [120, -1, 1944, -1], 'generators': [2, 8, 96], 'label': '672.1158.16.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.b1', 'projective_image': '672.1158', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110432431
    {'ambient': '672.1158', 'aut_centralizer_order': 144, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '84.7', 'aut_weyl_index': 288, 'centralizer': '28.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1'], 'contains': ['32.a1', '48.c1', '112.c1'], 'core': '32.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [400, -1, 1644, -1], 'generators': [12, 96, 8], 'label': '672.1158.16.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '16.c1', 'projective_image': '672.1158', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
  • id: 110432432
    {'ambient': '672.1158', 'aut_centralizer_order': 16, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '252.26', 'aut_weyl_index': 96, 'centralizer': '168.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['8.c1'], 'contains': ['32.a1', '48.d1', '112.d1'], 'core': '32.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [738, -1, 2191, -1], 'generators': [359, 96, 8], 'label': '672.1158.16.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1', 'old_label': '16.d1', 'projective_image': '672.1158', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1', 'subgroup_fusion': None, 'weyl_group': '84.8'}
  • id: 110432452
    {'ambient': '672.1158', 'aut_centralizer_order': 24, 'aut_label': '28.j1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '48.38', 'aut_weyl_index': 504, 'centralizer': '168.f1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.h1', '14.c1', '14.d1', '14.g1'], 'contains': ['56.b1', '56.e1', '84.i1'], 'core': '56.b1', 'coset_action_label': None, 'count': 21, 'diagramx': [5486, -1, 7596, -1], 'generators': [359, 504, 336, 8], 'label': '672.1158.28.j1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '28.j1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.j1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 110432433
    {'ambient': '672.1158', 'aut_centralizer_order': 6, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4032.dm', 'aut_weyl_index': 6, 'centralizer': '112.a1', 'complements': ['336.b1', '336.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.e1', '4.j1', '4.k1', '6.a1', '14.e1'], 'core': '2.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [8374, 2347, 4639, 6522], 'generators': [1, 96, 168, 8, 12, 336], 'label': '672.1158.2.e1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.e1', '4.j1', '4.k1', '6.a1'], 'normalizer': '1.a1', 'old_label': '2.e1', 'projective_image': '336.219', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1', 'subgroup_fusion': None, 'weyl_group': '112.42'}
  • id: 110432434
    {'ambient': '672.1158', 'aut_centralizer_order': 12, 'aut_label': '21.a1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '96.226', 'aut_weyl_index': 252, 'centralizer': '336.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1', '7.a1'], 'contains': ['42.a1', '42.b1', '42.c1', '42.d1', '42.e1', '42.f1', '42.g1'], 'core': '84.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [9266, -1, 8571, -1], 'generators': [1, 2, 12, 504], 'label': '672.1158.21.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '21.a1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '21.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 110432435
    {'ambient': '672.1158', 'aut_centralizer_order': 288, 'aut_label': '24.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '84.7', 'aut_weyl_index': 288, 'centralizer': '28.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '12.a1', '12.d1', '12.g1'], 'contains': ['48.a1', '48.c1', '168.c1'], 'core': '24.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2146, 3786, 2387, 4838], 'generators': [12, 96, 336], 'label': '672.1158.24.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.a1', 'normal_contained_in': ['8.b1', '12.a1'], 'normal_contains': ['48.a1'], 'normalizer': '1.a1', 'old_label': '24.a1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 110432436
    {'ambient': '672.1158', 'aut_centralizer_order': 672, 'aut_label': '24.b1', 'aut_quo_index': 24, 'aut_stab_index': 3, 'aut_weyl_group': '12.5', 'aut_weyl_index': 2016, 'centralizer': '4.c1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['8.d1', '12.a1', '12.b1', '12.c1', '12.f1', '12.h1', '12.j1', '12.k1'], 'contains': ['48.a1', '168.a1'], 'core': '24.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [8483, 2307, 4129, 6149], 'generators': [1, 336, 96], 'label': '672.1158.24.b1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.b1', 'normal_contained_in': ['8.d1', '12.a1', '12.b1', '12.c1'], 'normal_contains': ['48.a1', '168.a1'], 'normalizer': '1.a1', 'old_label': '24.b1', 'projective_image': '336.219', 'quotient_action_image': '4.2', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '24.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110432437
    {'ambient': '672.1158', 'aut_centralizer_order': 96, 'aut_label': '24.c1', 'aut_quo_index': 12, 'aut_stab_index': 3, 'aut_weyl_group': '84.7', 'aut_weyl_index': 288, 'centralizer': '28.b1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['8.f1', '12.a1', '12.b1', '12.e1', '12.i1', '12.l1'], 'contains': ['48.a1', '168.f1'], 'core': '24.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [6505, 4316, 3545, 5310], 'generators': [13, 96, 336], 'label': '672.1158.24.c1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.c1', 'normal_contained_in': ['8.f1', '12.a1', '12.b1'], 'normal_contains': ['48.a1'], 'normalizer': '1.a1', 'old_label': '24.c1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 110432438
    {'ambient': '672.1158', 'aut_centralizer_order': 672, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.5', 'aut_weyl_index': 2016, 'centralizer': '6.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.d1', '12.e1', '12.f1'], 'contains': ['48.a1', '48.b1', '168.b1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1728, -1, 2861, -1], 'generators': [2, 96, 336], 'label': '672.1158.24.d1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.d1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110432439
    {'ambient': '672.1158', 'aut_centralizer_order': 32, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '84.7', 'aut_weyl_index': 288, 'centralizer': '84.j1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['8.c1', '12.e1', '12.g1', '12.h1', '12.i1', '12.j1'], 'contains': ['48.a1', '48.d1', '168.d1'], 'core': '48.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3398, -1, 3344, -1], 'generators': [359, 96, 336], 'label': '672.1158.24.e1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.e1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 110432440
    {'ambient': '672.1158', 'aut_centralizer_order': 224, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.5', 'aut_weyl_index': 2016, 'centralizer': '12.f1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['8.e1', '12.f1', '12.g1', '12.i1', '12.k1', '12.l1'], 'contains': ['48.a1', '168.e1'], 'core': '48.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6802, -1, 3743, -1], 'generators': [3, 336, 96], 'label': '672.1158.24.f1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.f1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110432441
    {'ambient': '672.1158', 'aut_centralizer_order': 96, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '84.7', 'aut_weyl_index': 288, 'centralizer': '84.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1', '12.d1', '12.h1', '12.l1'], 'contains': ['48.a1', '168.g1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3684, -1, 3144, -1], 'generators': [358, 96, 336], 'label': '672.1158.24.g1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.g1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 110432442
    {'ambient': '672.1158', 'aut_centralizer_order': 336, 'aut_label': '28.a1', 'aut_quo_index': 2, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1008, 'centralizer': '24.b1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['4.c1', '14.a1', '14.b1', '14.c1'], 'contains': ['56.a1', '56.b1', '56.c1', '84.d1'], 'core': '28.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5255, 2813, 6549, 7020], 'generators': [1, 2, 336, 8], 'label': '672.1158.28.a1', 'mobius_quo': 0, 'mobius_sub': -14, 'normal_closure': '28.a1', 'normal_contained_in': ['4.c1', '14.a1'], 'normal_contains': ['56.a1', '56.b1', '56.c1'], 'normalizer': '1.a1', 'old_label': '28.a1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 110432443
    {'ambient': '672.1158', 'aut_centralizer_order': 168, 'aut_label': '28.b1', 'aut_quo_index': 2, 'aut_stab_index': 3, 'aut_weyl_group': '48.38', 'aut_weyl_index': 504, 'centralizer': '24.c1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['4.i1', '14.a1', '14.d1', '14.f1'], 'contains': ['56.b1', '56.c1', '84.j1'], 'core': '28.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5850, 1700, 8099, 7611], 'generators': [3, 504, 336, 8], 'label': '672.1158.28.b1', 'mobius_quo': 0, 'mobius_sub': -14, 'normal_closure': '28.b1', 'normal_contained_in': ['4.i1', '14.a1'], 'normal_contains': ['56.b1', '56.c1'], 'normalizer': '1.a1', 'old_label': '28.b1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 110432444
    {'ambient': '672.1158', 'aut_centralizer_order': 2, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '336.a1', 'complements': ['336.c1', '336.b1', '336.d1'], 'conjugacy_class_count': 3, 'contained_in': ['1.a1'], 'contains': ['4.f1', '4.g1', '4.i1', '4.j1', '4.l1', '6.f1', '14.f1'], 'core': '2.f1', 'coset_action_label': None, 'count': 3, 'diagramx': [5836, 5895, 4266, 4418], 'generators': [3, 96, 168, 336, 358, 8], 'label': '672.1158.2.f1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.f1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.f1', '4.g1', '4.i1', '4.j1', '4.l1'], 'normalizer': '1.a1', 'old_label': '2.f1', 'projective_image': '336.219', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.f1', 'subgroup_fusion': None, 'weyl_group': '336.219'}
  • id: 110432445
    {'ambient': '672.1158', 'aut_centralizer_order': 504, 'aut_label': '28.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 504, 'centralizer': '8.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.k1', '14.a1', '14.e1', '14.g1'], 'contains': ['56.b1', '84.a1'], 'core': '28.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [8094, 577, 9060, 8917], 'generators': [1, 504, 8, 336], 'label': '672.1158.28.c1', 'mobius_quo': 0, 'mobius_sub': -14, 'normal_closure': '28.c1', 'normal_contained_in': ['4.k1', '14.a1'], 'normal_contains': ['56.b1', '84.a1'], 'normalizer': '1.a1', 'old_label': '28.c1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 110432446
    {'ambient': '672.1158', 'aut_centralizer_order': 144, 'aut_label': '28.d1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1008, 'centralizer': '84.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '14.b1'], 'contains': ['56.a1', '56.d1', '56.g1', '84.b1'], 'core': '56.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [1587, -1, 5334, -1], 'generators': [2, 12, 336, 8], 'label': '672.1158.28.d1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '28.d1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110432447
    {'ambient': '672.1158', 'aut_centralizer_order': 48, 'aut_label': '28.e1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1008, 'centralizer': '168.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.b1', '14.b1', '14.c1'], 'contains': ['56.a1', '56.e1', '56.f1', '84.c1'], 'core': '56.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [2591, -1, 5737, -1], 'generators': [349, 2, 336, 8], 'label': '672.1158.28.e1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '28.e1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.e1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 110432448
    {'ambient': '672.1158', 'aut_centralizer_order': 48, 'aut_label': '28.f1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1008, 'centralizer': '84.k1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.d1', '14.b1', '14.d1'], 'contains': ['56.c1', '56.d1', '56.e1', '84.e1'], 'core': '56.c1', 'coset_action_label': None, 'count': 21, 'diagramx': [2357, -1, 5536, -1], 'generators': [3, 12, 336, 8], 'label': '672.1158.28.f1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '28.f1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.f1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110432449
    {'ambient': '672.1158', 'aut_centralizer_order': 144, 'aut_label': '28.g1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '8.5', 'aut_weyl_index': 3024, 'centralizer': '28.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.e1', '14.b1', '14.d1', '14.e1'], 'contains': ['56.b1', '56.d1', '56.f1', '84.f1'], 'core': '56.b1', 'coset_action_label': None, 'count': 21, 'diagramx': [4868, -1, 6220, -1], 'generators': [1, 12, 8, 336], 'label': '672.1158.28.g1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '28.g1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110432450
    {'ambient': '672.1158', 'aut_centralizer_order': 48, 'aut_label': '28.h1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1008, 'centralizer': '168.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.f1', '14.b1', '14.f1', '14.g1'], 'contains': ['56.b1', '56.e1', '56.g1', '84.g1'], 'core': '56.b1', 'coset_action_label': None, 'count': 21, 'diagramx': [4324, -1, 6846, -1], 'generators': [1, 358, 336, 8], 'label': '672.1158.28.h1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '28.h1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.h1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 110432451
    {'ambient': '672.1158', 'aut_centralizer_order': 24, 'aut_label': '28.i1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1008, 'centralizer': '168.f1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['4.g1', '14.c1', '14.d1', '14.f1'], 'contains': ['56.c1', '56.e1', '56.f1', '84.h1'], 'core': '56.c1', 'coset_action_label': None, 'count': 42, 'diagramx': [4047, -1, 7144, -1], 'generators': [3, 660, 336, 8], 'label': '672.1158.28.i1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '28.i1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.i1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 110432453
    {'ambient': '672.1158', 'aut_centralizer_order': 72, 'aut_label': '28.k1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1512, 'centralizer': '56.d1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.j1', '14.c1', '14.e1', '14.f1'], 'contains': ['56.b1', '56.f1', '84.k1'], 'core': '56.b1', 'coset_action_label': None, 'count': 21, 'diagramx': [6087, -1, 7845, -1], 'generators': [349, 504, 8, 336], 'label': '672.1158.28.k1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '28.k1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.k1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 110432454
    {'ambient': '672.1158', 'aut_centralizer_order': 48, 'aut_label': '28.l1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1008, 'centralizer': '168.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.l1', '14.b1', '14.f1'], 'contains': ['56.c1', '56.f1', '56.g1', '84.l1'], 'core': '56.c1', 'coset_action_label': None, 'count': 21, 'diagramx': [3500, -1, 5938, -1], 'generators': [3, 358, 336, 8], 'label': '672.1158.28.l1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '28.l1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.l1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 110432455
    {'ambient': '672.1158', 'aut_centralizer_order': 2, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '336.a1', 'complements': ['336.c1', '336.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.f1', '4.h1', '4.k1', '6.g1', '14.g1'], 'core': '2.g1', 'coset_action_label': None, 'count': 1, 'diagramx': [9155, 4013, 5005, 5662], 'generators': [1, 96, 168, 336, 358, 8], 'label': '672.1158.2.g1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.f1', '4.h1', '4.k1'], 'normalizer': '1.a1', 'old_label': '2.g1', 'projective_image': '336.219', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.g1', 'subgroup_fusion': None, 'weyl_group': '336.219'}
  • id: 110432456
    {'ambient': '672.1158', 'aut_centralizer_order': 2016, 'aut_label': '32.a1', 'aut_quo_index': 20, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 2016, 'centralizer': '4.k1', 'complements': ['21.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.b1', '16.c1', '16.d1'], 'contains': ['96.a1', '224.a1'], 'core': '32.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [452, 5801, 2575, 4854], 'generators': [8, 96], 'label': '672.1158.32.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': ['16.a1'], 'normal_contains': ['96.a1', '224.a1'], 'normalizer': '1.a1', 'old_label': '32.a1', 'projective_image': '672.1158', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.4', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110432457
    {'ambient': '672.1158', 'aut_centralizer_order': 48, 'aut_label': '42.a1', 'aut_quo_index': None, 'aut_stab_index': 63, 'aut_weyl_group': '8.5', 'aut_weyl_index': 3024, 'centralizer': '168.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.b1', '14.b1', '21.a1'], 'contains': ['84.b1', '84.c1', '84.d1', '84.e1', '84.f1', '84.g1', '84.l1'], 'core': '168.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [6291, -1, 7395, -1], 'generators': [1, 2, 12], 'label': '672.1158.42.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '42.a1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 110432458
    {'ambient': '672.1158', 'aut_centralizer_order': 24, 'aut_label': '42.b1', 'aut_quo_index': None, 'aut_stab_index': 63, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1512, 'centralizer': '168.e1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.c1', '14.c1', '21.a1'], 'contains': ['84.c1', '84.d1', '84.h1', '84.i1', '84.k1'], 'core': '168.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [8276, -1, 8505, -1], 'generators': [13, 2, 504], 'label': '672.1158.42.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '42.b1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 110432459
    {'ambient': '672.1158', 'aut_centralizer_order': 168, 'aut_label': '42.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.48', 'aut_weyl_index': 504, 'centralizer': '24.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '14.a1', '21.a1'], 'contains': ['84.a1', '84.d1', '84.j1'], 'core': '84.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9682, -1, 9665, -1], 'generators': [1, 2, 504], 'label': '672.1158.42.c1', 'mobius_quo': None, 'mobius_sub': -7, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '42.c1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 110432460
    {'ambient': '672.1158', 'aut_centralizer_order': 24, 'aut_label': '42.d1', 'aut_quo_index': None, 'aut_stab_index': 63, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1512, 'centralizer': '168.f1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.e1', '14.d1', '21.a1'], 'contains': ['84.e1', '84.f1', '84.h1', '84.i1', '84.j1'], 'core': '168.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [7310, -1, 8302, -1], 'generators': [3, 12, 504], 'label': '672.1158.42.d1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '42.d1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.d1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 110432461
    {'ambient': '672.1158', 'aut_centralizer_order': 72, 'aut_label': '42.e1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '48.48', 'aut_weyl_index': 504, 'centralizer': '56.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '14.e1', '21.a1'], 'contains': ['84.a1', '84.f1', '84.k1'], 'core': '84.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [9400, -1, 9363, -1], 'generators': [1, 12, 504], 'label': '672.1158.42.e1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '42.e1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.e1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 110432462
    {'ambient': '672.1158', 'aut_centralizer_order': 24, 'aut_label': '42.f1', 'aut_quo_index': None, 'aut_stab_index': 63, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1512, 'centralizer': '168.d1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.f1', '14.f1', '21.a1'], 'contains': ['84.g1', '84.h1', '84.j1', '84.k1', '84.l1'], 'core': '168.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [7689, -1, 8758, -1], 'generators': [3, 350, 504], 'label': '672.1158.42.f1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '42.f1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.f1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 110432463
    {'ambient': '672.1158', 'aut_centralizer_order': 24, 'aut_label': '42.g1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '48.48', 'aut_weyl_index': 504, 'centralizer': '168.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1', '14.g1', '21.a1'], 'contains': ['84.a1', '84.g1', '84.i1'], 'core': '84.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [9083, -1, 9918, -1], 'generators': [1, 358, 504], 'label': '672.1158.42.g1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '42.g1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.g1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 110432464
    {'ambient': '672.1158', 'aut_centralizer_order': 4032, 'aut_label': '48.a1', 'aut_quo_index': 224, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 4032, 'centralizer': '2.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '24.a1', '24.b1', '24.c1', '24.d1', '24.e1', '24.f1', '24.g1'], 'contains': ['96.a1', '336.a1'], 'core': '48.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3464, 4415, 3280, 5310], 'generators': [336, 96], 'label': '672.1158.48.a1', 'mobius_quo': 1, 'mobius_sub': -192, 'normal_closure': '48.a1', 'normal_contained_in': ['16.a1', '24.a1', '24.b1', '24.c1'], 'normal_contains': ['96.a1', '336.a1'], 'normalizer': '1.a1', 'old_label': '48.a1', 'projective_image': '336.219', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.14', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110432465
    {'ambient': '672.1158', 'aut_centralizer_order': 672, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 4032, 'centralizer': '6.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1', '24.d1'], 'contains': ['96.a1', '336.b1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [296, -1, 2877, -1], 'generators': [2, 96], 'label': '672.1158.48.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '48.b1', 'projective_image': '672.1158', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110432466
    {'ambient': '672.1158', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4032.dm', 'aut_weyl_index': 6, 'centralizer': '336.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.a1', '6.b1', '6.c1', '6.d1', '6.e1', '6.f1', '6.g1', '21.a1'], 'core': '6.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8912, -1, 5303, -1], 'generators': [1, 96, 12, 168, 2, 336], 'label': '672.1158.3.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '3.a1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1', 'subgroup_fusion': None, 'weyl_group': '112.42'}
  • id: 110432467
    {'ambient': '672.1158', 'aut_centralizer_order': 288, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '42.1', 'aut_weyl_index': 576, 'centralizer': '28.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1', '24.a1'], 'contains': ['96.a1', '336.c1'], 'core': '96.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [674, -1, 2394, -1], 'generators': [12, 96], 'label': '672.1158.48.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '48.c1', 'projective_image': '672.1158', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
  • id: 110432468
    {'ambient': '672.1158', 'aut_centralizer_order': 32, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '42.1', 'aut_weyl_index': 576, 'centralizer': '84.j1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['16.d1', '24.e1'], 'contains': ['96.a1', '336.d1'], 'core': '96.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [905, -1, 3071, -1], 'generators': [359, 96], 'label': '672.1158.48.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.d1', 'projective_image': '672.1158', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
  • id: 110432469
    {'ambient': '672.1158', 'aut_centralizer_order': 2016, 'aut_label': '56.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 2016, 'centralizer': '12.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '28.a1', '28.d1', '28.e1'], 'contains': ['112.a1', '112.b1', '168.b1'], 'core': '56.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1296, 4252, 5040, 5735], 'generators': [2, 336, 8], 'label': '672.1158.56.a1', 'mobius_quo': 0, 'mobius_sub': 56, 'normal_closure': '56.a1', 'normal_contained_in': ['8.a1', '28.a1'], 'normal_contains': ['112.a1'], 'normalizer': '1.a1', 'old_label': '56.a1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110432470
    {'ambient': '672.1158', 'aut_centralizer_order': 2016, 'aut_label': '56.b1', 'aut_quo_index': 24, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 6048, 'centralizer': '4.e1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['8.d1', '28.a1', '28.b1', '28.c1', '28.g1', '28.h1', '28.j1', '28.k1'], 'contains': ['112.a1', '168.a1'], 'core': '56.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5486, 2726, 6610, 7082], 'generators': [1, 8, 336], 'label': '672.1158.56.b1', 'mobius_quo': 0, 'mobius_sub': 56, 'normal_closure': '56.b1', 'normal_contained_in': ['8.d1', '28.a1', '28.b1', '28.c1'], 'normal_contains': ['112.a1', '168.a1'], 'normalizer': '1.a1', 'old_label': '56.b1', 'projective_image': '336.219', 'quotient_action_image': '4.2', 'quotient_action_kernel': '14.1', 'quotient_action_kernel_order': 14, 'quotient_fusion': None, 'short_label': '56.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110432471
    {'ambient': '672.1158', 'aut_centralizer_order': 672, 'aut_label': '56.c1', 'aut_quo_index': 12, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 2016, 'centralizer': '12.b1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['8.e1', '28.a1', '28.b1', '28.f1', '28.i1', '28.l1'], 'contains': ['112.a1', '168.e1'], 'core': '56.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [4211, 3483, 5936, 6616], 'generators': [3, 336, 8], 'label': '672.1158.56.c1', 'mobius_quo': 0, 'mobius_sub': 56, 'normal_closure': '56.c1', 'normal_contained_in': ['8.e1', '28.a1', '28.b1'], 'normal_contains': ['112.a1'], 'normalizer': '1.a1', 'old_label': '56.c1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110432472
    {'ambient': '672.1158', 'aut_centralizer_order': 864, 'aut_label': '56.d1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '4.2', 'aut_weyl_index': 6048, 'centralizer': '14.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '28.d1', '28.f1', '28.g1'], 'contains': ['112.a1', '112.c1', '168.c1'], 'core': '112.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [1675, -1, 4811, -1], 'generators': [12, 336, 8], 'label': '672.1158.56.d1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '56.d1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110432473
    {'ambient': '672.1158', 'aut_centralizer_order': 96, 'aut_label': '56.e1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '12.4', 'aut_weyl_index': 2016, 'centralizer': '84.k1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['8.c1', '28.e1', '28.f1', '28.h1', '28.i1', '28.j1'], 'contains': ['112.a1', '112.d1', '168.d1'], 'core': '112.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [2447, -1, 5561, -1], 'generators': [359, 336, 8], 'label': '672.1158.56.e1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '56.e1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.e1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110432474
    {'ambient': '672.1158', 'aut_centralizer_order': 288, 'aut_label': '56.f1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '4.2', 'aut_weyl_index': 6048, 'centralizer': '28.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['8.f1', '28.e1', '28.g1', '28.i1', '28.k1', '28.l1'], 'contains': ['112.a1', '168.f1'], 'core': '112.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [3615, -1, 5737, -1], 'generators': [349, 8, 336], 'label': '672.1158.56.f1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '56.f1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110432475
    {'ambient': '672.1158', 'aut_centralizer_order': 288, 'aut_label': '56.g1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '12.4', 'aut_weyl_index': 2016, 'centralizer': '84.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1', '28.d1', '28.h1', '28.l1'], 'contains': ['112.a1', '168.g1'], 'core': '112.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [2274, -1, 5221, -1], 'generators': [358, 336, 8], 'label': '672.1158.56.g1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '56.g1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.g1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110432476
    {'ambient': '672.1158', 'aut_centralizer_order': 1008, 'aut_label': '84.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 1008, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.c1', '28.c1', '42.c1', '42.e1', '42.g1'], 'contains': ['168.a1'], 'core': '84.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9361, 1165, 9211, 8207], 'generators': [1, 504], 'label': '672.1158.84.a1', 'mobius_quo': 0, 'mobius_sub': 42, 'normal_closure': '84.a1', 'normal_contained_in': ['12.c1', '28.c1'], 'normal_contains': ['168.a1'], 'normalizer': '1.a1', 'old_label': '84.a1', 'projective_image': '336.219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}