Abstract group data - 1344.9508

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 84, 'aut_gen_orders': [2, 12, 12, 12, 12, 6, 6, 12], 'aut_gens': [[1, 2, 4, 16], [673, 2, 676, 16], [9, 2, 228, 16], [1009, 434, 788, 1040], [337, 914, 1244, 1040], [681, 1154, 900, 176], [673, 1154, 900, 208], [1009, 1106, 1020, 1072], [1009, 1202, 1020, 976]], 'aut_group': None, 'aut_hash': 9161810123478319507, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 32256, 'aut_permdeg': 48, 'aut_perms': [11648936930353593519684687135876904220572945936238361919480621, 527908962168242638241083403061569679475798933206561734098715, 9413804797748589598387012826192031614313155571327719660277001, 3790129942773302638284287326521825267478397839173746517210705, 12243352715382366147044471042193821392295469197283616613395830, 11648943908888853122765337599383844506011239809762212731283109, 9460832921465935415837322822113967551219940825918748563076934, 9460822740217609446779996229948037080179808854673713625437658], 'aut_phi_ratio': 84.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 4, 2, 1], [2, 12, 1, 1], [2, 14, 2, 1], [2, 28, 1, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 12, 1, 1], [4, 14, 2, 1], [4, 28, 1, 1], [4, 84, 2, 1], [6, 2, 1, 1], [6, 4, 1, 1], [6, 4, 4, 1], [6, 28, 2, 2], [7, 2, 3, 1], [8, 12, 2, 1], [8, 42, 2, 1], [8, 84, 1, 1], [12, 4, 1, 2], [12, 28, 2, 2], [14, 2, 3, 1], [14, 4, 3, 1], [14, 8, 6, 1], [14, 24, 3, 1], [21, 4, 3, 1], [28, 4, 3, 2], [28, 24, 3, 1], [42, 4, 3, 1], [42, 4, 6, 1], [42, 8, 12, 1], [56, 24, 6, 1], [84, 8, 3, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_{42}.(C_2^5\\times C_6).C_2^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '16.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': None, 'autcentquo_hash': 5451351369529179689, 'autcentquo_nilpotent': False, 'autcentquo_order': 2016, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^3\\times S_3\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 4, 2], [2, 12, 1], [2, 14, 2], [2, 28, 1], [3, 2, 1], [4, 2, 2], [4, 12, 1], [4, 14, 2], [4, 28, 1], [4, 84, 2], [6, 2, 1], [6, 4, 5], [6, 28, 4], [7, 2, 3], [8, 12, 2], [8, 42, 2], [8, 84, 1], [12, 4, 2], [12, 28, 4], [14, 2, 3], [14, 4, 3], [14, 8, 6], [14, 24, 3], [21, 4, 3], [28, 4, 6], [28, 24, 3], [42, 4, 9], [42, 8, 12], [56, 24, 6], [84, 8, 6]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '672.1175', 'commutator_count': 1, 'commutator_label': '84.6', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '7.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 9508, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 4, 1, 2], [2, 12, 1, 1], [2, 14, 1, 2], [2, 28, 1, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 12, 1, 1], [4, 14, 1, 2], [4, 28, 1, 1], [4, 84, 1, 2], [6, 2, 1, 1], [6, 4, 1, 1], [6, 4, 2, 2], [6, 28, 1, 2], [6, 28, 2, 1], [7, 2, 3, 1], [8, 12, 1, 2], [8, 42, 2, 1], [8, 84, 1, 1], [12, 4, 1, 2], [12, 28, 1, 2], [12, 28, 2, 1], [14, 2, 3, 1], [14, 4, 3, 1], [14, 8, 3, 2], [14, 24, 3, 1], [21, 4, 3, 1], [28, 4, 3, 2], [28, 24, 3, 1], [42, 4, 3, 1], [42, 4, 6, 1], [42, 8, 6, 2], [56, 24, 3, 2], [84, 8, 3, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 29877120, 'exponent': 168, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[8, -1, 6]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '336.219', 'hash': 9508, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 84, 'inner_gen_orders': [2, 2, 4, 42], 'inner_gens': [[1, 2, 12, 688], [1, 2, 4, 880], [681, 2, 4, 1136], [673, 482, 228, 16]], 'inner_hash': 1175, 'inner_nilpotent': False, 'inner_order': 672, 'inner_split': True, 'inner_tex': 'D_{42}:C_2^3', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 8, 'irrQ_degree': 48, 'irrQ_dim': 96, 'irrR_degree': 16, 'irrep_stats': [[1, 16], [2, 44], [4, 32], [8, 10]], 'label': '1344.9508', 'linC_count': 822, 'linC_degree': 8, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 8, 'linQ_dim': 16, 'linQ_dim_count': 64, 'linR_count': 204, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C84.C2^4', 'ngens': 8, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 41, 'number_characteristic_subgroups': 66, 'number_conjugacy_classes': 102, 'number_divisions': 52, 'number_normal_subgroups': 136, 'number_subgroup_autclasses': 364, 'number_subgroup_classes': 516, 'number_subgroups': 3828, 'old_label': None, 'order': 1344, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 79], [3, 2], [4, 240], [6, 134], [7, 6], [8, 192], [12, 120], [14, 138], [21, 12], [28, 96], [42, 132], [56, 144], [84, 48]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 2, 6], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[1, 2, 4, 464], [1, 674, 4, 16], [1, 2, 4, 688], [337, 338, 340, 496]], 'outer_group': '48.52', 'outer_hash': 52, 'outer_nilpotent': True, 'outer_order': 48, 'outer_permdeg': 11, 'outer_perms': [40320, 3628800, 24, 723], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 26, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 12], [4, 4], [6, 8], [8, 2], [12, 6], [24, 3], [48, 1]], 'representations': {'PC': {'code': 32639160586683898635377709456563383868530378900830298649459723, 'gens': [1, 2, 3, 5], 'pres': [8, -2, -2, -2, -2, -2, -2, -3, -7, 290, 66, 21763, 2715, 27524, 17612, 11380, 116, 9997, 11157, 141, 23310, 7190, 222, 36879]}, 'Perm': {'d': 26, 'gens': [621574835364353135884942, 358674298805615, 1589467762739, 1349575118545, 4404334373095, 5808412632349, 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_2^4', '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: 117134407
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 9508, 'group_order': 1344, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 117134421
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 9508, 'group_order': 1344, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 672, 'size': 1}
  • id: 117134432
    {'aut_label': '2B', 'centralizer': '2.c1.a1', 'counter': 3, 'group_counter': 9508, 'group_order': 1344, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 344, 'size': 2}
  • id: 117134443
    {'aut_label': '2C', 'centralizer': '4.x1.a1', 'counter': 4, 'group_counter': 9508, 'group_order': 1344, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 1, 'size': 4}
  • id: 117134454
    {'aut_label': '2C', 'centralizer': '4.x1.b1', 'counter': 5, 'group_counter': 9508, 'group_order': 1344, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 337, 'size': 4}
  • id: 117134465
    {'aut_label': '2E', 'centralizer': '12.s1.a1', 'counter': 6, 'group_counter': 9508, 'group_order': 1344, 'label': '2E', 'order': 2, 'powers': [1, 6, 6], 'representative': 789, 'size': 12}
  • id: 117134476
    {'aut_label': '2F', 'centralizer': '14.j1.a1', 'counter': 7, 'group_counter': 9508, 'group_order': 1344, 'label': '2F', 'order': 2, 'powers': [1, 7, 7], 'representative': 962, 'size': 14}
  • id: 117134487
    {'aut_label': '2F', 'centralizer': '14.j1.b1', 'counter': 8, 'group_counter': 9508, 'group_order': 1344, 'label': '2G', 'order': 2, 'powers': [1, 8, 8], 'representative': 914, 'size': 14}
  • id: 117134498
    {'aut_label': '2H', 'centralizer': '28.n1.a1', 'counter': 9, 'group_counter': 9508, 'group_order': 1344, 'label': '2H', 'order': 2, 'powers': [1, 9, 9], 'representative': 963, 'size': 28}
  • id: 117134408
    {'aut_label': '3A', 'centralizer': '2.b1.a1', 'counter': 10, 'group_counter': 9508, 'group_order': 1344, 'label': '3A', 'order': 3, 'powers': [10, 1, 10], 'representative': 896, 'size': 2}
  • id: 117134412
    {'aut_label': '4A', 'centralizer': '2.f1.a1', 'counter': 11, 'group_counter': 9508, 'group_order': 1344, 'label': '4A', 'order': 4, 'powers': [2, 11, 11], 'representative': 680, 'size': 2}
  • id: 117134413
    {'aut_label': '4B', 'centralizer': '2.e1.a1', 'counter': 12, 'group_counter': 9508, 'group_order': 1344, 'label': '4B', 'order': 4, 'powers': [2, 12, 12], 'representative': 336, 'size': 2}
  • id: 117134414
    {'aut_label': '4C', 'centralizer': '12.r1.a1', 'counter': 13, 'group_counter': 9508, 'group_order': 1344, 'label': '4C', 'order': 4, 'powers': [2, 13, 13], 'representative': 677, 'size': 12}
  • id: 117134415
    {'aut_label': '4D', 'centralizer': '14.i1.b1', 'counter': 14, 'group_counter': 9508, 'group_order': 1344, 'label': '4D', 'order': 4, 'powers': [2, 14, 14], 'representative': 298, 'size': 14}
  • id: 117134416
    {'aut_label': '4D', 'centralizer': '14.i1.a1', 'counter': 15, 'group_counter': 9508, 'group_order': 1344, 'label': '4E', 'order': 4, 'powers': [2, 15, 15], 'representative': 250, 'size': 14}
  • id: 117134417
    {'aut_label': '4F', 'centralizer': '28.o1.a1', 'counter': 16, 'group_counter': 9508, 'group_order': 1344, 'label': '4F', 'order': 4, 'powers': [2, 16, 16], 'representative': 243, 'size': 28}
  • id: 117134418
    {'aut_label': '4G', 'centralizer': '84.c1.b1', 'counter': 17, 'group_counter': 9508, 'group_order': 1344, 'label': '4G', 'order': 4, 'powers': [2, 17, 17], 'representative': 1015, 'size': 84}
  • id: 117134419
    {'aut_label': '4G', 'centralizer': '84.c1.a1', 'counter': 18, 'group_counter': 9508, 'group_order': 1344, 'label': '4H', 'order': 4, 'powers': [2, 18, 18], 'representative': 719, 'size': 84}
  • id: 117134420
    {'aut_label': '6A', 'centralizer': '2.b1.a1', 'counter': 19, 'group_counter': 9508, 'group_order': 1344, 'label': '6A', 'order': 6, 'powers': [10, 2, 19], 'representative': 224, 'size': 2}
  • id: 117134422
    {'aut_label': '6B', 'centralizer': '4.a1.a1', 'counter': 20, 'group_counter': 9508, 'group_order': 1344, 'label': '6B', 'order': 6, 'powers': [10, 3, 20], 'representative': 792, 'size': 4}
  • id: 117134423
    {'aut_label': '6C1', 'centralizer': '4.x1.a1', 'counter': 21, 'group_counter': 9508, 'group_order': 1344, 'label': '6C1', 'order': 6, 'powers': [10, 4, 21], 'representative': 449, 'size': 4}
  • id: 117134424
    {'aut_label': '6C1', 'centralizer': '4.x1.a1', 'counter': 22, 'group_counter': 9508, 'group_order': 1344, 'label': '6C-1', 'order': 6, 'powers': [10, 4, 22], 'representative': 897, 'size': 4}
  • id: 117134425
    {'aut_label': '6C1', 'centralizer': '4.x1.b1', 'counter': 23, 'group_counter': 9508, 'group_order': 1344, 'label': '6D1', 'order': 6, 'powers': [10, 5, 23], 'representative': 785, 'size': 4}
  • id: 117134426
    {'aut_label': '6C1', 'centralizer': '4.x1.b1', 'counter': 24, 'group_counter': 9508, 'group_order': 1344, 'label': '6D-1', 'order': 6, 'powers': [10, 5, 24], 'representative': 1233, 'size': 4}
  • id: 117134427
    {'aut_label': '6E', 'centralizer': '28.l1.a1', 'counter': 25, 'group_counter': 9508, 'group_order': 1344, 'label': '6E', 'order': 6, 'powers': [10, 7, 25], 'representative': 66, 'size': 28}
  • id: 117134428
    {'aut_label': '6E', 'centralizer': '28.l1.b1', 'counter': 26, 'group_counter': 9508, 'group_order': 1344, 'label': '6F', 'order': 6, 'powers': [10, 8, 26], 'representative': 18, 'size': 28}
  • id: 117134429
    {'aut_label': '6G1', 'centralizer': '28.n1.a1', 'counter': 27, 'group_counter': 9508, 'group_order': 1344, 'label': '6G1', 'order': 6, 'powers': [10, 9, 27], 'representative': 67, 'size': 28}
  • id: 117134430
    {'aut_label': '6G1', 'centralizer': '28.n1.a1', 'counter': 28, 'group_counter': 9508, 'group_order': 1344, 'label': '6G-1', 'order': 6, 'powers': [10, 9, 28], 'representative': 35, 'size': 28}
  • id: 117134431
    {'aut_label': '7A1', 'centralizer': '2.a1.a1', 'counter': 29, 'group_counter': 9508, 'group_order': 1344, 'label': '7A1', 'order': 7, 'powers': [30, 31, 1], 'representative': 1152, 'size': 2}
  • id: 117134433
    {'aut_label': '7A1', 'centralizer': '2.a1.a1', 'counter': 30, 'group_counter': 9508, 'group_order': 1344, 'label': '7A2', 'order': 7, 'powers': [31, 29, 1], 'representative': 960, 'size': 2}
  • id: 117134434
    {'aut_label': '7A1', 'centralizer': '2.a1.a1', 'counter': 31, 'group_counter': 9508, 'group_order': 1344, 'label': '7A3', 'order': 7, 'powers': [29, 30, 1], 'representative': 768, 'size': 2}
  • id: 117134435
    {'aut_label': '8A', 'centralizer': '12.x1.a1', 'counter': 32, 'group_counter': 9508, 'group_order': 1344, 'label': '8A', 'order': 8, 'powers': [11, 32, 32], 'representative': 684, 'size': 12}
  • id: 117134436
    {'aut_label': '8A', 'centralizer': '12.x1.b1', 'counter': 33, 'group_counter': 9508, 'group_order': 1344, 'label': '8B', 'order': 8, 'powers': [11, 33, 33], 'representative': 124, 'size': 12}
  • id: 117134437
    {'aut_label': '8C1', 'centralizer': '42.f1.a1', 'counter': 34, 'group_counter': 9508, 'group_order': 1344, 'label': '8C1', 'order': 8, 'powers': [11, 34, 35], 'representative': 710, 'size': 42}
  • id: 117134438
    {'aut_label': '8C1', 'centralizer': '42.f1.a1', 'counter': 35, 'group_counter': 9508, 'group_order': 1344, 'label': '8C-1', 'order': 8, 'powers': [11, 35, 34], 'representative': 46, 'size': 42}
  • id: 117134439
    {'aut_label': '8D', 'centralizer': '84.i1.a1', 'counter': 36, 'group_counter': 9508, 'group_order': 1344, 'label': '8D', 'order': 8, 'powers': [11, 36, 36], 'representative': 1206, 'size': 84}
  • id: 117134440
    {'aut_label': '12A', 'centralizer': '4.d1.a1', 'counter': 37, 'group_counter': 9508, 'group_order': 1344, 'label': '12A', 'order': 12, 'powers': [19, 12, 37], 'representative': 112, 'size': 4}
  • id: 117134441
    {'aut_label': '12B', 'centralizer': '4.c1.a1', 'counter': 38, 'group_counter': 9508, 'group_order': 1344, 'label': '12B', 'order': 12, 'powers': [19, 11, 38], 'representative': 1128, 'size': 4}
  • id: 117134442
    {'aut_label': '12C', 'centralizer': '28.m1.b1', 'counter': 39, 'group_counter': 9508, 'group_order': 1344, 'label': '12C', 'order': 12, 'powers': [19, 14, 39], 'representative': 74, 'size': 28}
  • id: 117134444
    {'aut_label': '12C', 'centralizer': '28.m1.a1', 'counter': 40, 'group_counter': 9508, 'group_order': 1344, 'label': '12D', 'order': 12, 'powers': [19, 15, 40], 'representative': 26, 'size': 28}
  • id: 117134445
    {'aut_label': '12E1', 'centralizer': '28.o1.a1', 'counter': 41, 'group_counter': 9508, 'group_order': 1344, 'label': '12E1', 'order': 12, 'powers': [19, 16, 41], 'representative': 19, 'size': 28}
  • id: 117134446
    {'aut_label': '12E1', 'centralizer': '28.o1.a1', 'counter': 42, 'group_counter': 9508, 'group_order': 1344, 'label': '12E-1', 'order': 12, 'powers': [19, 16, 42], 'representative': 83, 'size': 28}
  • id: 117134447
    {'aut_label': '14A1', 'centralizer': '2.a1.a1', 'counter': 43, 'group_counter': 9508, 'group_order': 1344, 'label': '14A1', 'order': 14, 'powers': [31, 44, 2], 'representative': 1056, 'size': 2}
  • id: 117134448
    {'aut_label': '14A1', 'centralizer': '2.a1.a1', 'counter': 44, 'group_counter': 9508, 'group_order': 1344, 'label': '14A3', 'order': 14, 'powers': [30, 45, 2], 'representative': 480, 'size': 2}
  • id: 117134449
    {'aut_label': '14A1', 'centralizer': '2.a1.a1', 'counter': 45, 'group_counter': 9508, 'group_order': 1344, 'label': '14A5', 'order': 14, 'powers': [29, 43, 2], 'representative': 1248, 'size': 2}
  • id: 117134450
    {'aut_label': '14B1', 'centralizer': '4.a1.a1', 'counter': 46, 'group_counter': 9508, 'group_order': 1344, 'label': '14B1', 'order': 14, 'powers': [31, 47, 3], 'representative': 728, 'size': 4}
  • id: 117134451
    {'aut_label': '14B1', 'centralizer': '4.a1.a1', 'counter': 47, 'group_counter': 9508, 'group_order': 1344, 'label': '14B3', 'order': 14, 'powers': [30, 48, 3], 'representative': 152, 'size': 4}
  • id: 117134452
    {'aut_label': '14B1', 'centralizer': '4.a1.a1', 'counter': 48, 'group_counter': 9508, 'group_order': 1344, 'label': '14B5', 'order': 14, 'powers': [29, 46, 3], 'representative': 920, 'size': 4}
  • id: 117134453
    {'aut_label': '14C1', 'centralizer': '8.o1.a1', 'counter': 49, 'group_counter': 9508, 'group_order': 1344, 'label': '14C1', 'order': 14, 'powers': [30, 50, 4], 'representative': 193, 'size': 8}
  • id: 117134455
    {'aut_label': '14C1', 'centralizer': '8.o1.a1', 'counter': 50, 'group_counter': 9508, 'group_order': 1344, 'label': '14C3', 'order': 14, 'powers': [29, 51, 4], 'representative': 577, 'size': 8}
  • id: 117134456
    {'aut_label': '14C1', 'centralizer': '8.o1.a1', 'counter': 51, 'group_counter': 9508, 'group_order': 1344, 'label': '14C5', 'order': 14, 'powers': [31, 49, 4], 'representative': 961, 'size': 8}
  • id: 117134457
    {'aut_label': '14C1', 'centralizer': '8.o1.a1', 'counter': 52, 'group_counter': 9508, 'group_order': 1344, 'label': '14D1', 'order': 14, 'powers': [31, 53, 5], 'representative': 721, 'size': 8}
  • id: 117134458
    {'aut_label': '14C1', 'centralizer': '8.o1.a1', 'counter': 53, 'group_counter': 9508, 'group_order': 1344, 'label': '14D3', 'order': 14, 'powers': [30, 54, 5], 'representative': 145, 'size': 8}
  • id: 117134459
    {'aut_label': '14C1', 'centralizer': '8.o1.a1', 'counter': 54, 'group_counter': 9508, 'group_order': 1344, 'label': '14D5', 'order': 14, 'powers': [29, 52, 5], 'representative': 913, 'size': 8}
  • id: 117134460
    {'aut_label': '14E1', 'centralizer': '24.s1.a1', 'counter': 55, 'group_counter': 9508, 'group_order': 1344, 'label': '14E1', 'order': 14, 'powers': [29, 56, 6], 'representative': 21, 'size': 24}
  • id: 117134461
    {'aut_label': '14E1', 'centralizer': '24.s1.a1', 'counter': 56, 'group_counter': 9508, 'group_order': 1344, 'label': '14E3', 'order': 14, 'powers': [31, 57, 6], 'representative': 53, 'size': 24}
  • id: 117134462
    {'aut_label': '14E1', 'centralizer': '24.s1.a1', 'counter': 57, 'group_counter': 9508, 'group_order': 1344, 'label': '14E5', 'order': 14, 'powers': [30, 55, 6], 'representative': 85, 'size': 24}
  • id: 117134463
    {'aut_label': '21A1', 'centralizer': '4.a1.a1', 'counter': 58, 'group_counter': 9508, 'group_order': 1344, 'label': '21A1', 'order': 21, 'powers': [59, 31, 10], 'representative': 704, 'size': 4}
  • id: 117134464
    {'aut_label': '21A1', 'centralizer': '4.a1.a1', 'counter': 59, 'group_counter': 9508, 'group_order': 1344, 'label': '21A2', 'order': 21, 'powers': [60, 29, 10], 'representative': 64, 'size': 4}
  • id: 117134466
    {'aut_label': '21A1', 'centralizer': '4.a1.a1', 'counter': 60, 'group_counter': 9508, 'group_order': 1344, 'label': '21A4', 'order': 21, 'powers': [58, 30, 10], 'representative': 128, 'size': 4}
  • id: 117134467
    {'aut_label': '28A1', 'centralizer': '4.f1.a1', 'counter': 61, 'group_counter': 9508, 'group_order': 1344, 'label': '28A1', 'order': 28, 'powers': [45, 62, 11], 'representative': 392, 'size': 4}
  • id: 117134468
    {'aut_label': '28A1', 'centralizer': '4.f1.a1', 'counter': 62, 'group_counter': 9508, 'group_order': 1344, 'label': '28A3', 'order': 28, 'powers': [43, 63, 11], 'representative': 488, 'size': 4}
  • id: 117134469
    {'aut_label': '28A1', 'centralizer': '4.f1.a1', 'counter': 63, 'group_counter': 9508, 'group_order': 1344, 'label': '28A5', 'order': 28, 'powers': [44, 61, 11], 'representative': 584, 'size': 4}
  • id: 117134470
    {'aut_label': '28B1', 'centralizer': '4.b1.a1', 'counter': 64, 'group_counter': 9508, 'group_order': 1344, 'label': '28B1', 'order': 28, 'powers': [45, 65, 12], 'representative': 48, 'size': 4}
  • id: 117134471
    {'aut_label': '28B1', 'centralizer': '4.b1.a1', 'counter': 65, 'group_counter': 9508, 'group_order': 1344, 'label': '28B3', 'order': 28, 'powers': [43, 66, 12], 'representative': 144, 'size': 4}
  • id: 117134472
    {'aut_label': '28B1', 'centralizer': '4.b1.a1', 'counter': 66, 'group_counter': 9508, 'group_order': 1344, 'label': '28B5', 'order': 28, 'powers': [44, 64, 12], 'representative': 240, 'size': 4}
  • id: 117134473
    {'aut_label': '28C1', 'centralizer': '24.s1.a1', 'counter': 67, 'group_counter': 9508, 'group_order': 1344, 'label': '28C1', 'order': 28, 'powers': [43, 68, 13], 'representative': 197, 'size': 24}
  • id: 117134474
    {'aut_label': '28C1', 'centralizer': '24.s1.a1', 'counter': 68, 'group_counter': 9508, 'group_order': 1344, 'label': '28C3', 'order': 28, 'powers': [44, 69, 13], 'representative': 133, 'size': 24}
  • id: 117134475
    {'aut_label': '28C1', 'centralizer': '24.s1.a1', 'counter': 69, 'group_counter': 9508, 'group_order': 1344, 'label': '28C5', 'order': 28, 'powers': [45, 67, 13], 'representative': 69, 'size': 24}
  • id: 117134477
    {'aut_label': '42A1', 'centralizer': '4.a1.a1', 'counter': 70, 'group_counter': 9508, 'group_order': 1344, 'label': '42A1', 'order': 42, 'powers': [59, 45, 19], 'representative': 32, 'size': 4}
  • id: 117134478
    {'aut_label': '42A1', 'centralizer': '4.a1.a1', 'counter': 71, 'group_counter': 9508, 'group_order': 1344, 'label': '42A5', 'order': 42, 'powers': [60, 44, 19], 'representative': 160, 'size': 4}
  • id: 117134479
    {'aut_label': '42A1', 'centralizer': '4.a1.a1', 'counter': 72, 'group_counter': 9508, 'group_order': 1344, 'label': '42A11', 'order': 42, 'powers': [58, 43, 19], 'representative': 352, 'size': 4}
  • id: 117134480
    {'aut_label': '42B1', 'centralizer': '4.a1.a1', 'counter': 73, 'group_counter': 9508, 'group_order': 1344, 'label': '42B1', 'order': 42, 'powers': [58, 46, 20], 'representative': 24, 'size': 4}
  • id: 117134481
    {'aut_label': '42B1', 'centralizer': '4.a1.a1', 'counter': 74, 'group_counter': 9508, 'group_order': 1344, 'label': '42B5', 'order': 42, 'powers': [59, 48, 20], 'representative': 88, 'size': 4}
  • id: 117134482
    {'aut_label': '42B1', 'centralizer': '4.a1.a1', 'counter': 75, 'group_counter': 9508, 'group_order': 1344, 'label': '42B11', 'order': 42, 'powers': [60, 47, 20], 'representative': 1176, 'size': 4}
  • id: 117134483
    {'aut_label': '42B1', 'centralizer': '4.a1.a1', 'counter': 76, 'group_counter': 9508, 'group_order': 1344, 'label': '42B13', 'order': 42, 'powers': [58, 46, 20], 'representative': 216, 'size': 4}
  • id: 117134484
    {'aut_label': '42B1', 'centralizer': '4.a1.a1', 'counter': 77, 'group_counter': 9508, 'group_order': 1344, 'label': '42B17', 'order': 42, 'powers': [60, 47, 20], 'representative': 408, 'size': 4}
  • id: 117134485
    {'aut_label': '42B1', 'centralizer': '4.a1.a1', 'counter': 78, 'group_counter': 9508, 'group_order': 1344, 'label': '42B19', 'order': 42, 'powers': [59, 48, 20], 'representative': 984, 'size': 4}
  • id: 117134486
    {'aut_label': '42C1', 'centralizer': '8.o1.a1', 'counter': 79, 'group_counter': 9508, 'group_order': 1344, 'label': '42C1', 'order': 42, 'powers': [60, 49, 21], 'representative': 65, 'size': 8}
  • id: 117134488
    {'aut_label': '42C1', 'centralizer': '8.o1.a1', 'counter': 80, 'group_counter': 9508, 'group_order': 1344, 'label': '42C-1', 'order': 42, 'powers': [60, 49, 22], 'representative': 73, 'size': 8}
  • id: 117134489
    {'aut_label': '42C1', 'centralizer': '8.o1.a1', 'counter': 81, 'group_counter': 9508, 'group_order': 1344, 'label': '42C5', 'order': 42, 'powers': [58, 51, 22], 'representative': 129, 'size': 8}
  • id: 117134490
    {'aut_label': '42C1', 'centralizer': '8.o1.a1', 'counter': 82, 'group_counter': 9508, 'group_order': 1344, 'label': '42C-5', 'order': 42, 'powers': [58, 51, 21], 'representative': 137, 'size': 8}
  • id: 117134491
    {'aut_label': '42C1', 'centralizer': '8.o1.a1', 'counter': 83, 'group_counter': 9508, 'group_order': 1344, 'label': '42C11', 'order': 42, 'powers': [59, 50, 22], 'representative': 33, 'size': 8}
  • id: 117134492
    {'aut_label': '42C1', 'centralizer': '8.o1.a1', 'counter': 84, 'group_counter': 9508, 'group_order': 1344, 'label': '42C-11', 'order': 42, 'powers': [59, 50, 21], 'representative': 257, 'size': 8}
  • id: 117134493
    {'aut_label': '42C1', 'centralizer': '8.o1.a1', 'counter': 85, 'group_counter': 9508, 'group_order': 1344, 'label': '42D1', 'order': 42, 'powers': [58, 52, 23], 'representative': 17, 'size': 8}
  • id: 117134494
    {'aut_label': '42C1', 'centralizer': '8.o1.a1', 'counter': 86, 'group_counter': 9508, 'group_order': 1344, 'label': '42D-1', 'order': 42, 'powers': [58, 52, 24], 'representative': 25, 'size': 8}
  • id: 117134495
    {'aut_label': '42C1', 'centralizer': '8.o1.a1', 'counter': 87, 'group_counter': 9508, 'group_order': 1344, 'label': '42D5', 'order': 42, 'powers': [59, 54, 24], 'representative': 81, 'size': 8}
  • id: 117134496
    {'aut_label': '42C1', 'centralizer': '8.o1.a1', 'counter': 88, 'group_counter': 9508, 'group_order': 1344, 'label': '42D-5', 'order': 42, 'powers': [59, 54, 23], 'representative': 593, 'size': 8}
  • id: 117134497
    {'aut_label': '42C1', 'centralizer': '8.o1.a1', 'counter': 89, 'group_counter': 9508, 'group_order': 1344, 'label': '42D11', 'order': 42, 'powers': [60, 53, 24], 'representative': 273, 'size': 8}
  • id: 117134499
    {'aut_label': '42C1', 'centralizer': '8.o1.a1', 'counter': 90, 'group_counter': 9508, 'group_order': 1344, 'label': '42D-11', 'order': 42, 'powers': [60, 53, 23], 'representative': 401, 'size': 8}
  • id: 117134500
    {'aut_label': '56A1', 'centralizer': '24.z1.a1', 'counter': 91, 'group_counter': 9508, 'group_order': 1344, 'label': '56A1', 'order': 56, 'powers': [61, 92, 32], 'representative': 196, 'size': 24}
  • id: 117134501
    {'aut_label': '56A1', 'centralizer': '24.z1.a1', 'counter': 92, 'group_counter': 9508, 'group_order': 1344, 'label': '56A3', 'order': 56, 'powers': [62, 93, 32], 'representative': 132, 'size': 24}
  • id: 117134502
    {'aut_label': '56A1', 'centralizer': '24.z1.a1', 'counter': 93, 'group_counter': 9508, 'group_order': 1344, 'label': '56A5', 'order': 56, 'powers': [63, 91, 32], 'representative': 68, 'size': 24}
  • id: 117134503
    {'aut_label': '56A1', 'centralizer': '24.z1.b1', 'counter': 94, 'group_counter': 9508, 'group_order': 1344, 'label': '56B1', 'order': 56, 'powers': [62, 95, 33], 'representative': 20, 'size': 24}
  • id: 117134504
    {'aut_label': '56A1', 'centralizer': '24.z1.b1', 'counter': 95, 'group_counter': 9508, 'group_order': 1344, 'label': '56B3', 'order': 56, 'powers': [63, 96, 33], 'representative': 52, 'size': 24}
  • id: 117134505
    {'aut_label': '56A1', 'centralizer': '24.z1.b1', 'counter': 96, 'group_counter': 9508, 'group_order': 1344, 'label': '56B5', 'order': 56, 'powers': [61, 94, 33], 'representative': 84, 'size': 24}
  • id: 117134506
    {'aut_label': '84A1', 'centralizer': '8.b1.a1', 'counter': 97, 'group_counter': 9508, 'group_order': 1344, 'label': '84A1', 'order': 84, 'powers': [70, 64, 37], 'representative': 16, 'size': 8}
  • id: 117134507
    {'aut_label': '84A1', 'centralizer': '8.b1.a1', 'counter': 98, 'group_counter': 9508, 'group_order': 1344, 'label': '84A5', 'order': 84, 'powers': [71, 66, 37], 'representative': 80, 'size': 8}
  • id: 117134508
    {'aut_label': '84A1', 'centralizer': '8.b1.a1', 'counter': 99, 'group_counter': 9508, 'group_order': 1344, 'label': '84A11', 'order': 84, 'powers': [72, 65, 37], 'representative': 400, 'size': 8}
  • id: 117134409
    {'aut_label': '84B1', 'centralizer': '8.b1.a1', 'counter': 100, 'group_counter': 9508, 'group_order': 1344, 'label': '84B1', 'order': 84, 'powers': [72, 62, 38], 'representative': 72, 'size': 8}
  • id: 117134410
    {'aut_label': '84B1', 'centralizer': '8.b1.a1', 'counter': 101, 'group_counter': 9508, 'group_order': 1344, 'label': '84B5', 'order': 84, 'powers': [70, 61, 38], 'representative': 136, 'size': 8}
  • id: 117134411
    {'aut_label': '84B1', 'centralizer': '8.b1.a1', 'counter': 102, 'group_counter': 9508, 'group_order': 1344, 'label': '84B11', 'order': 84, 'powers': [71, 63, 38], 'representative': 40, '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: 6113154
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6113165
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 6113176
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 6113187
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 6113198
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 6113202
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 6113203
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 6113204
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 6113205
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.1i', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 6113155
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.1j', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6113156
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.1k', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6113157
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.1l', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6113158
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.1m', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6113159
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.1n', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6113160
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.1o', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6113161
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.1p', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6113162
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 0, 2, 2, 2, -1, 2, 2, 0, 2, 2, 2, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, -1, -1, -1, 2, 2, 2, 2, 2, 2, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6113163
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, 0, 0, -2, -2, 0, 2, -2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 2, -2, 0, 0, 2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, 2, 2, 2, -2, -2, 0, 0, 0, 2, -2, -2, 2, -2, -2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 2, -2, 2], 'schur_index': 1}
  • id: 6113164
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, 0, 0, 2, 2, 0, 2, -2, 2, 0, -2, -2, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, -2, 0, 0, -2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, 2, 2, 2, -2, -2, 0, 0, 0, 2, -2, -2, 2, -2, -2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 2, -2, 2], 'schur_index': 1}
  • id: 6113166
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 0, 0, -2, 2, 0, 2, -2, -2, 0, 2, -2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, -2, -2, 0, 0, 2, -2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2], 'schur_index': 1}
  • id: 6113167
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.2e', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 0, 0, 2, -2, 0, 2, -2, -2, 0, -2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, -2, 2, 2, 2, 0, 0, 0, 0, 0, -2, -2, 0, 0, -2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2], 'schur_index': 1}
  • id: 6113168
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 0, -2, 2, 2, -1, 2, -2, 0, -2, 2, -2, 0, 0, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 2, 2, 2, 0, 0, 0, 0, 0, 1, -1, 1, 1, 1, -1, 2, 2, 2, -2, -2, -2, 2, -2, 2, -2, -2, 2, 0, 0, 0, -1, -1, -1, 2, -2, -2, -2, 2, 2, 0, 0, 0, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 6113169
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.2g', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 0, 2, -2, -2, -1, 2, -2, 0, 2, -2, 2, 0, 0, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 2, 2, 2, 0, 0, 0, 0, 0, 1, -1, -1, -1, -1, 1, 2, 2, 2, -2, -2, -2, 2, -2, 2, -2, -2, 2, 0, 0, 0, -1, -1, -1, 2, -2, -2, -2, 2, 2, 0, 0, 0, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 6113170
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.2h', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 2, -2, 0, -2, 2, -2, -1, 2, -2, 0, -2, 2, 2, 0, 0, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 2, 2, 2, 0, 0, 0, 0, 0, 1, -1, -1, -1, 1, -1, 2, 2, 2, -2, -2, -2, -2, 2, -2, 2, 2, -2, 0, 0, 0, -1, -1, -1, 2, -2, -2, -2, 2, 2, 0, 0, 0, -1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 6113171
    {'cdim': 2, 'counter': 25, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.2i', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 2, -2, 0, 2, -2, 2, -1, 2, -2, 0, 2, -2, -2, 0, 0, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 2, 2, 2, 0, 0, 0, 0, 0, 1, -1, 1, 1, -1, 1, 2, 2, 2, -2, -2, -2, -2, 2, -2, 2, 2, -2, 0, 0, 0, -1, -1, -1, 2, -2, -2, -2, 2, 2, 0, 0, 0, -1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 6113172
    {'cdim': 2, 'counter': 26, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.2j', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, -2, -2, 0, -2, -2, 2, -1, 2, 2, 0, -2, -2, 2, 0, 0, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 2, 2, 2, 0, 0, 0, 0, 0, -1, -1, -1, -1, 1, 1, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 0, -1, -1, -1, 2, 2, 2, 2, 2, 2, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6113173
    {'cdim': 2, 'counter': 27, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.2k', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, -2, -2, 0, 2, 2, -2, -1, 2, 2, 0, 2, 2, -2, 0, 0, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 2, 2, 2, 0, 0, 0, 0, 0, -1, -1, 1, 1, -1, -1, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 0, -1, -1, -1, 2, 2, 2, 2, 2, 2, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6113174
    {'cdim': 2, 'counter': 28, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.2l', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 0, -2, -2, -2, -1, 2, 2, 0, -2, -2, -2, 0, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 2, 2, 2, 0, 0, 0, 0, 0, -1, -1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, -1, -1, -1, 2, 2, 2, 2, 2, 2, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6113175
    {'cdim': 2, 'counter': 29, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.2m', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, 4, -4, 0, 0, 0, -4, -4, 0, -2, -4, 4, 0, 4, 4, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 4, 4, 4, 0, 0, 0, 0, 0, -2, 2, 0, 0, -2, -2, 4, 4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -4, 4, 4, 4, -4, -4, 0, 0, 0, -2, 2, 2, -2, 2, 2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, -2, 2, -2], 'schur_index': 1}
  • id: 6113177
    {'cdim': 2, 'counter': 30, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.2n', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, 4, -4, 0, 0, 0, 4, 4, 0, -2, -4, 4, 0, -4, -4, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, -2, -2, 4, 4, 4, 0, 0, 0, 0, 0, -2, 2, 0, 0, 2, 2, 4, 4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -4, 4, 4, 4, -4, -4, 0, 0, 0, -2, 2, 2, -2, 2, 2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, -2, 2, -2], 'schur_index': 1}
  • id: 6113178
    {'cdim': 2, 'counter': 31, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.2o', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, 4, 4, 0, 0, 0, -4, 4, 0, -2, -4, -4, 0, 4, -4, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 2, -2, 4, 4, 4, 0, 0, 0, 0, 0, 2, 2, 0, 0, -2, 2, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -4, -4, -4, -4, -4, -4, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2], 'schur_index': 1}
  • id: 6113179
    {'cdim': 2, 'counter': 32, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.2p', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, 4, 4, 0, 0, 0, 4, -4, 0, -2, -4, -4, 0, -4, 4, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, -2, 2, 4, 4, 4, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, -2, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -4, -4, -4, -4, -4, -4, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2], 'schur_index': 1}
  • id: 6113180
    {'cdim': 2, 'counter': 33, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.2q', 'multiplicity': 3, 'nt': [7, 2], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, 6, 0, 0, 0, 6, 6, 6, 6, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, -1, -1, -1, 6, 6, 0, 0, 0, 6, 6, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 6113181
    {'cdim': 2, 'counter': 34, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.2r', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, -6, -6, 6, -6, 0, 0, 0, 6, 6, -6, 6, 0, 0, 0, 0, 0, 6, 6, 6, -6, -6, -6, 0, 0, 0, 0, -1, -1, -1, -6, 6, 0, 0, 0, -6, 6, 0, 0, 0, 0, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 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: 6113182
    {'cdim': 2, 'counter': 35, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.2s', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, -6, -6, 6, 6, 0, 0, 0, 6, 6, -6, -6, 0, 0, 0, 0, 0, 6, 6, 6, -6, -6, -6, 0, 0, 0, 0, -1, -1, -1, 6, -6, 0, 0, 0, -6, 6, 0, 0, 0, 0, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 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: 6113183
    {'cdim': 2, 'counter': 36, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.2t', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, -6, 6, -6, -6, 0, 0, 0, 6, 6, -6, 6, 0, 0, 0, 0, 0, 6, -6, -6, -6, 6, 6, 0, 0, 0, 0, -1, -1, -1, 6, -6, 0, 0, 0, -6, 6, 0, 0, 0, 0, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, 1, -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: 6113184
    {'cdim': 2, 'counter': 37, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.2u', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, -6, 6, -6, 6, 0, 0, 0, 6, 6, -6, -6, 0, 0, 0, 0, 0, 6, -6, -6, -6, 6, 6, 0, 0, 0, 0, -1, -1, -1, -6, 6, 0, 0, 0, -6, 6, 0, 0, 0, 0, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 1, -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: 6113185
    {'cdim': 2, 'counter': 38, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.2v', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, 6, -6, -6, -6, 0, 0, 0, 6, 6, 6, -6, 0, 0, 0, 0, 0, 6, -6, -6, 6, -6, -6, 0, 0, 0, 0, -1, -1, -1, 6, 6, 0, 0, 0, 6, 6, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 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: 6113186
    {'cdim': 2, 'counter': 39, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.2w', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, 6, -6, -6, 6, 0, 0, 0, 6, 6, 6, 6, 0, 0, 0, 0, 0, 6, -6, -6, 6, -6, -6, 0, 0, 0, 0, -1, -1, -1, -6, -6, 0, 0, 0, 6, 6, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 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: 6113188
    {'cdim': 2, 'counter': 40, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.2x', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, -6, 0, 0, 0, 6, 6, 6, -6, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, -1, -1, -1, -6, -6, 0, 0, 0, 6, 6, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 6113189
    {'cdim': 4, 'counter': 41, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.4a', 'multiplicity': 2, 'nt': [16, 116], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6113199
    {'cdim': 8, 'counter': 50, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.8a', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 6113190
    {'cdim': 4, 'counter': 42, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.4b', 'multiplicity': 3, 'nt': [21, 8], 'qdim': 12, 'qvalues': [12, 12, 12, 12, 12, 0, 0, 0, 0, -6, 12, 12, 0, 0, 0, 0, 0, 0, -6, -6, -6, -6, -6, -6, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, -6, -6, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 1, 1, 1, -2, -2, -2, -2, -2, -2, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6113191
    {'cdim': 4, 'counter': 43, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.4c', 'multiplicity': 3, 'nt': [28, 18], 'qdim': 12, 'qvalues': [12, 12, -12, 0, 0, 0, 0, 0, 0, 12, -12, 12, 0, 0, 0, 0, 0, 0, 12, 0, 0, -12, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 12, -12, 0, 0, 0, 0, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 2, -2, -2, -2, 2, 2, 0, 0, 0, -2, 2, 2, -2, 2, 2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, -2, 2, -2], 'schur_index': 1}
  • id: 6113192
    {'cdim': 4, 'counter': 44, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.4d', 'multiplicity': 3, 'nt': [28, 18], 'qdim': 12, 'qvalues': [12, 12, 12, 0, 0, 0, 0, 0, 0, 12, -12, -12, 0, 0, 0, 0, 0, 0, 12, 0, 0, 12, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, -12, -12, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 2, 2, 2, 2, 2, 2, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2], 'schur_index': 1}
  • id: 6113193
    {'cdim': 4, 'counter': 45, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.4e', 'multiplicity': 3, 'nt': [42, 36], 'qdim': 12, 'qvalues': [12, 12, -12, -12, 12, 0, 0, 0, 0, -6, 12, -12, 0, 0, 0, 0, 0, 0, -6, -6, -6, 6, 6, 6, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, -2, -2, -2, 2, 2, 2, -2, 2, -2, 2, 2, -2, 0, 0, 0, 1, 1, 1, -2, 2, 2, 2, -2, -2, 0, 0, 0, 1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 6113194
    {'cdim': 4, 'counter': 46, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.4f', 'multiplicity': 3, 'nt': [42, 36], 'qdim': 12, 'qvalues': [12, 12, -12, 12, -12, 0, 0, 0, 0, -6, 12, -12, 0, 0, 0, 0, 0, 0, -6, 6, 6, 6, -6, -6, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, -2, -2, -2, 2, 2, 2, 2, -2, 2, -2, -2, 2, 0, 0, 0, 1, 1, 1, -2, 2, 2, 2, -2, -2, 0, 0, 0, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 6113195
    {'cdim': 4, 'counter': 47, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.4g', 'multiplicity': 3, 'nt': [42, 36], 'qdim': 12, 'qvalues': [12, 12, 12, -12, -12, 0, 0, 0, 0, -6, 12, 12, 0, 0, 0, 0, 0, 0, -6, 6, 6, -6, 6, 6, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, -6, -6, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 1, 1, 1, -2, -2, -2, -2, -2, -2, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6113196
    {'cdim': 4, 'counter': 48, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.4h', 'multiplicity': 6, 'nt': [84, 0], 'qdim': 24, 'qvalues': [24, 24, -24, 0, 0, 0, 0, 0, 0, -12, -24, 24, 0, 0, 0, 0, 0, 0, -12, 0, 0, 12, 0, 0, 0, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, -12, 12, 0, 0, 0, 0, -4, -4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 4, -4, -4, -4, 4, 4, 0, 0, 0, 2, -2, -2, 2, -2, -2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 2, -2, 2], 'schur_index': 1}
  • id: 6113197
    {'cdim': 4, 'counter': 49, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.4i', 'multiplicity': 6, 'nt': [84, 0], 'qdim': 24, 'qvalues': [24, 24, 24, 0, 0, 0, 0, 0, 0, -12, -24, -24, 0, 0, 0, 0, 0, 0, -12, 0, 0, -12, 0, 0, 0, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, 12, 12, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 4, 4, 4, 4, 4, 4, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2], 'schur_index': 1}
  • id: 6113200
    {'cdim': 8, 'counter': 51, 'faithful': False, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.8b', 'multiplicity': 3, 'nt': [112, 0], 'qdim': 24, 'qvalues': [24, -24, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 6113201
    {'cdim': 8, 'counter': 52, 'faithful': True, 'group': '1344.9508', 'group_order': 1344, 'image': None, 'label': '1344.9508.8c', 'multiplicity': 6, 'nt': [336, 0], 'qdim': 48, 'qvalues': [48, -48, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], '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: 12719601
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 1344, 'label': '1344.9508.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 12719615
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.j1.b1', 'kernel_order': 672, 'label': '1344.9508.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 12719626
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.k1.b1', 'kernel_order': 672, 'label': '1344.9508.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 12719637
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.h1.b1', 'kernel_order': 672, 'label': '1344.9508.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 12719648
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.i1.b1', 'kernel_order': 672, 'label': '1344.9508.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 12719659
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.k1.a1', 'kernel_order': 672, 'label': '1344.9508.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 12719670
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.j1.a1', 'kernel_order': 672, 'label': '1344.9508.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 12719681
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.i1.a1', 'kernel_order': 672, 'label': '1344.9508.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 12719692
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 9, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.h1.a1', 'kernel_order': 672, 'label': '1344.9508.1i', '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]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 12719602
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 10, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1.a1', 'kernel_order': 672, 'label': '1344.9508.1j', '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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[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: 12719606
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 11, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1.a1', 'kernel_order': 672, 'label': '1344.9508.1k', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 12719607
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 12, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 672, 'label': '1344.9508.1l', '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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 12719608
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 13, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 672, 'label': '1344.9508.1m', '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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 12719609
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 14, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 672, 'label': '1344.9508.1n', '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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-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: 12719610
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 15, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 672, 'label': '1344.9508.1o', '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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-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: 12719611
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 16, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 672, 'label': '1344.9508.1p', '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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 12719612
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 224, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 224, 'label': '1344.9508.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 12719613
    {'center': '4.c1.a1', 'center_index': 4, 'center_order': 336, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.n1.a1', 'kernel_order': 168, 'label': '1344.9508.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 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]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]]]}
  • id: 12719614
    {'center': '4.c1.a1', 'center_index': 4, 'center_order': 336, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.f1.a1', 'kernel_order': 168, 'label': '1344.9508.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 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]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]]]}
  • id: 12719616
    {'center': '4.c1.a1', 'center_index': 4, 'center_order': 336, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1.b1', 'kernel_order': 168, 'label': '1344.9508.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 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]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]]]}
  • id: 12719617
    {'center': '4.c1.a1', 'center_index': 4, 'center_order': 336, 'counter': 21, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1.a1', 'kernel_order': 168, 'label': '1344.9508.2e', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 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]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]]]}
  • id: 12719618
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 224, 'counter': 22, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.d1.b1', 'kernel_order': 112, 'label': '1344.9508.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 12719619
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 224, 'counter': 23, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.e1.b1', 'kernel_order': 112, 'label': '1344.9508.2g', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 12719620
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 224, 'counter': 24, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.e1.a1', 'kernel_order': 112, 'label': '1344.9508.2h', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 12719621
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 224, 'counter': 25, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.d1.a1', 'kernel_order': 112, 'label': '1344.9508.2i', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 12719622
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 224, 'counter': 26, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1.a1', 'kernel_order': 112, 'label': '1344.9508.2j', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 12719623
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 224, 'counter': 27, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1.a1', 'kernel_order': 112, 'label': '1344.9508.2k', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 12719624
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 224, 'counter': 28, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 112, 'label': '1344.9508.2l', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 12719625
    {'center': '12.b1.a1', 'center_index': 12, 'center_order': 112, 'counter': 29, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.h1.a1', 'kernel_order': 56, 'label': '1344.9508.2m1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 12719627
    {'center': '12.b1.a1', 'center_index': 12, 'center_order': 112, 'counter': 30, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.h1.a1', 'kernel_order': 56, 'label': '1344.9508.2m2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 12719628
    {'center': '12.b1.a1', 'center_index': 12, 'center_order': 112, 'counter': 31, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.e1.a1', 'kernel_order': 56, 'label': '1344.9508.2n1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 12719629
    {'center': '12.b1.a1', 'center_index': 12, 'center_order': 112, 'counter': 32, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.e1.a1', 'kernel_order': 56, 'label': '1344.9508.2n2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 12719630
    {'center': '12.b1.a1', 'center_index': 12, 'center_order': 112, 'counter': 33, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1.b1', 'kernel_order': 56, 'label': '1344.9508.2o1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 12719631
    {'center': '12.b1.a1', 'center_index': 12, 'center_order': 112, 'counter': 34, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1.b1', 'kernel_order': 56, 'label': '1344.9508.2o2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 12719632
    {'center': '12.b1.a1', 'center_index': 12, 'center_order': 112, 'counter': 35, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1.a1', 'kernel_order': 56, 'label': '1344.9508.2p1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 12719633
    {'center': '12.b1.a1', 'center_index': 12, 'center_order': 112, 'counter': 36, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1.a1', 'kernel_order': 56, 'label': '1344.9508.2p2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 12719634
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 37, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '14.1', 'image_order': 14, 'indicator': 1, 'kernel': '14.a1.a1', 'kernel_order': 96, 'label': '1344.9508.2q1', 'nt': [7, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]]]}
  • id: 12719635
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 38, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '14.1', 'image_order': 14, 'indicator': 1, 'kernel': '14.a1.a1', 'kernel_order': 96, 'label': '1344.9508.2q2', 'nt': [7, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]]]}
  • id: 12719636
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 39, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '14.1', 'image_order': 14, 'indicator': 1, 'kernel': '14.a1.a1', 'kernel_order': 96, 'label': '1344.9508.2q3', 'nt': [7, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]]]}
  • id: 12719638
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 40, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.e1.b1', 'kernel_order': 48, 'label': '1344.9508.2r1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]]]}
  • id: 12719639
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 41, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.e1.b1', 'kernel_order': 48, 'label': '1344.9508.2r2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]]]}
  • id: 12719640
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 42, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.e1.b1', 'kernel_order': 48, 'label': '1344.9508.2r3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]]]}
  • id: 12719641
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 43, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.d1.b1', 'kernel_order': 48, 'label': '1344.9508.2s1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]]]}
  • id: 12719642
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  • id: 12719643
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  • id: 12719644
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  • id: 12719645
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  • id: 12719646
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  • id: 12719647
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  • id: 12719649
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  • id: 12719650
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 51, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.d1.a1', 'kernel_order': 48, 'label': '1344.9508.2u3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]]]}
  • id: 12719651
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 52, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.c1.a1', 'kernel_order': 48, 'label': '1344.9508.2v1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]]]}
  • id: 12719652
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 53, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.c1.a1', 'kernel_order': 48, 'label': '1344.9508.2v2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]]]}
  • id: 12719653
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 54, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.c1.a1', 'kernel_order': 48, 'label': '1344.9508.2v3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]]]}
  • id: 12719654
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 55, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1.a1', 'kernel_order': 48, 'label': '1344.9508.2w1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]]]}
  • id: 12719655
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 56, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1.a1', 'kernel_order': 48, 'label': '1344.9508.2w2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]]]}
  • id: 12719656
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 57, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1.a1', 'kernel_order': 48, 'label': '1344.9508.2w3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]]]}
  • id: 12719657
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 58, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1.a1', 'kernel_order': 48, 'label': '1344.9508.2x1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]]]}
  • id: 12719658
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 59, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1.a1', 'kernel_order': 48, 'label': '1344.9508.2x2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]]]}
  • id: 12719660
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 60, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1.a1', 'kernel_order': 48, 'label': '1344.9508.2x3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]]]}
  • id: 12719661
    {'center': '32.a1.a1', 'center_index': 32, 'center_order': 42, 'counter': 61, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '64.258', 'image_order': 64, 'indicator': 0, 'kernel': '64.a1.a1', 'kernel_order': 21, 'label': '1344.9508.4a1', 'nt': [16, 116], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12719662
    {'center': '32.a1.a1', 'center_index': 32, 'center_order': 42, 'counter': 62, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '64.258', 'image_order': 64, 'indicator': 0, 'kernel': '64.a1.a1', 'kernel_order': 21, 'label': '1344.9508.4a2', 'nt': [16, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12719663
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 63, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '84.8', 'image_order': 84, 'indicator': 1, 'kernel': '84.a1.a1', 'kernel_order': 16, 'label': '1344.9508.4b1', 'nt': [21, 8], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 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]], [[-2, 0]], [[-2, 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, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]]]}
  • id: 12719664
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 64, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '84.8', 'image_order': 84, 'indicator': 1, 'kernel': '84.a1.a1', 'kernel_order': 16, 'label': '1344.9508.4b2', 'nt': [21, 8], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 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]], [[-2, 0]], [[-2, 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, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]]]}
  • id: 12719665
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 65, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '84.8', 'image_order': 84, 'indicator': 1, 'kernel': '84.a1.a1', 'kernel_order': 16, 'label': '1344.9508.4b3', 'nt': [21, 8], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 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]], [[-2, 0]], [[-2, 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, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]]]}
  • id: 12719666
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 24, 'counter': 66, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '112.31', 'image_order': 112, 'indicator': 1, 'kernel': '112.c1.a1', 'kernel_order': 12, 'label': '1344.9508.4c1', 'nt': [28, 18], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 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]], [[4, 0]], [[-4, 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, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[2, 2], [2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[2, 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]], [[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, 2], [-2, -2]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[2, 1], [2, -1]]]}
  • id: 12719667
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 24, 'counter': 67, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '112.31', 'image_order': 112, 'indicator': 1, 'kernel': '112.c1.a1', 'kernel_order': 12, 'label': '1344.9508.4c2', 'nt': [28, 18], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 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]], [[4, 0]], [[-4, 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, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[2, 3], [2, -3]]]}
  • id: 12719668
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 24, 'counter': 68, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '112.31', 'image_order': 112, 'indicator': 1, 'kernel': '112.c1.a1', 'kernel_order': 12, 'label': '1344.9508.4c3', 'nt': [28, 18], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 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]], [[4, 0]], [[-4, 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, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[2, 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]], [[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, 3], [-2, -3]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[2, 2], [2, -2]]]}
  • id: 12719669
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 24, 'counter': 69, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '112.31', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.a1', 'kernel_order': 12, 'label': '1344.9508.4d1', 'nt': [28, 18], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 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]], [[-4, 0]], [[-4, 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, 3], [2, -3]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 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]], [[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, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]]]}
  • id: 12719671
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 24, 'counter': 70, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '112.31', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.a1', 'kernel_order': 12, 'label': '1344.9508.4d2', 'nt': [28, 18], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 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]], [[-4, 0]], [[-4, 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, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]]]}
  • id: 12719672
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 24, 'counter': 71, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '112.31', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.a1', 'kernel_order': 12, 'label': '1344.9508.4d3', 'nt': [28, 18], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 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]], [[-4, 0]], [[-4, 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, 1], [2, -1]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 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]], [[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, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]]]}
  • id: 12719673
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 72, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.b1.b1', 'kernel_order': 8, 'label': '1344.9508.4e1', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 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]], [[2, 0]], [[-2, 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, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[2, 2], [2, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[2, 2], [2, -2]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]]]}
  • id: 12719674
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 73, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.b1.b1', 'kernel_order': 8, 'label': '1344.9508.4e2', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 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]], [[2, 0]], [[-2, 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, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[2, 1], [2, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]]]}
  • id: 12719675
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 74, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.b1.b1', 'kernel_order': 8, 'label': '1344.9508.4e3', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 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]], [[2, 0]], [[-2, 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, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[2, 3], [2, -3]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]]]}
  • id: 12719676
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 75, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.b1.a1', 'kernel_order': 8, 'label': '1344.9508.4f1', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 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]], [[2, 0]], [[-2, 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, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[-2, 2], [-2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[2, 2], [2, -2]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]]]}
  • id: 12719677
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 76, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.b1.a1', 'kernel_order': 8, 'label': '1344.9508.4f2', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 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]], [[2, 0]], [[-2, 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, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[2, 1], [2, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]]]}
  • id: 12719678
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 77, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.b1.a1', 'kernel_order': 8, 'label': '1344.9508.4f3', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 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]], [[2, 0]], [[-2, 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, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[2, 3], [2, -3]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]]]}
  • id: 12719679
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 78, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.a1.a1', 'kernel_order': 8, 'label': '1344.9508.4g1', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 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]], [[-2, 0]], [[-2, 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, 3], [2, -3]], [[2, 2], [2, -2]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]]]}
  • id: 12719680
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 79, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.a1.a1', 'kernel_order': 8, 'label': '1344.9508.4g2', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 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]], [[-2, 0]], [[-2, 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, 2], [2, -2]], [[2, 1], [2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]]]}
  • id: 12719682
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 80, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.a1.a1', 'kernel_order': 8, 'label': '1344.9508.4g3', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 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]], [[-2, 0]], [[-2, 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, 1], [2, -1]], [[2, 3], [2, -3]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]]]}
  • id: 12719683
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 81, 'cyclotomic_n': 21, 'dim': 4, 'faithful': False, 'field': [1, -2, 5, 0, 3, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '336.161', 'image_order': 336, 'indicator': 0, 'kernel': '336.c1.a1', 'kernel_order': 4, 'label': '1344.9508.4h1', 'nt': [84, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0], [-4, 7]], [[2, 0], [4, 7]], [[2, 0]], [[-2, 0], [-4, 7]], [[2, 0], [4, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 9], [2, -9]], [[2, 3], [2, -3]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 9], [2, -9]], [[2, 6], [2, -6]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[-2, 9], [-2, -9]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-2, 6], [-2, -6]], [[2, 9], [2, -9]], [[2, 6], [2, -6]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[-2, 9], [-2, -9]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 9], [-1, -9]], [[1, 9], [1, -9]], [[1, 9], [1, -9]], [[-1, 6], [-1, -6]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[-1, 9], [-1, -9]], [[1, 9], [1, -9]], [[-1, 3], [-1, -3]]]}
  • id: 12719684
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 82, 'cyclotomic_n': 21, 'dim': 4, 'faithful': False, 'field': [1, -2, 5, 0, 3, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '336.161', 'image_order': 336, 'indicator': 0, 'kernel': '336.c1.a1', 'kernel_order': 4, 'label': '1344.9508.4h2', 'nt': [84, 6], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0], [4, 7]], [[-2, 0], [-4, 7]], [[2, 0]], [[2, 0], [4, 7]], [[-2, 0], [-4, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 9], [2, -9]], [[2, 3], [2, -3]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 9], [2, -9]], [[2, 6], [2, -6]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[-2, 9], [-2, -9]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-2, 6], [-2, -6]], [[2, 9], [2, -9]], [[2, 6], [2, -6]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[-2, 9], [-2, -9]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 9], [-1, -9]], [[1, 9], [1, -9]], [[1, 9], [1, -9]], [[-1, 6], [-1, -6]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[-1, 9], [-1, -9]], [[1, 9], [1, -9]], [[-1, 3], [-1, -3]]]}
  • id: 12719685
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 83, 'cyclotomic_n': 21, 'dim': 4, 'faithful': False, 'field': [1, -2, 5, 0, 3, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '336.161', 'image_order': 336, 'indicator': 0, 'kernel': '336.c1.a1', 'kernel_order': 4, 'label': '1344.9508.4h3', 'nt': [84, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0], [-4, 7]], [[2, 0], [4, 7]], [[2, 0]], [[-2, 0], [-4, 7]], [[2, 0], [4, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 9], [2, -9]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 3], [2, -3]], [[2, 9], [2, -9]], [[-2, 9], [-2, -9]], [[-2, 6], [-2, -6]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, -3]], [[-2, 3], [-2, -3]], [[2, 6], [2, -6]], [[2, 3], [2, -3]], [[2, 9], [2, -9]], [[-2, 9], [-2, -9]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[-1, 3], [-1, -3]], [[1, 9], [1, -9]], [[1, 9], [1, -9]], [[-1, 9], [-1, -9]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 9], [1, -9]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[-1, 9], [-1, -9]]]}
  • id: 12719686
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 84, 'cyclotomic_n': 21, 'dim': 4, 'faithful': False, 'field': [1, -2, 5, 0, 3, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '336.161', 'image_order': 336, 'indicator': 0, 'kernel': '336.c1.a1', 'kernel_order': 4, 'label': '1344.9508.4h4', 'nt': [84, 6], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0], [4, 7]], [[-2, 0], [-4, 7]], [[2, 0]], [[2, 0], [4, 7]], [[-2, 0], [-4, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 9], [2, -9]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 3], [2, -3]], [[2, 9], [2, -9]], [[-2, 9], [-2, -9]], [[-2, 6], [-2, -6]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, -3]], [[-2, 3], [-2, -3]], [[2, 6], [2, -6]], [[2, 3], [2, -3]], [[2, 9], [2, -9]], [[-2, 9], [-2, -9]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[-1, 3], [-1, -3]], [[1, 9], [1, -9]], [[1, 9], [1, -9]], [[-1, 9], [-1, -9]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 9], [1, -9]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[-1, 9], [-1, -9]]]}
  • id: 12719687
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 85, 'cyclotomic_n': 21, 'dim': 4, 'faithful': False, 'field': [1, -2, 5, 0, 3, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '336.161', 'image_order': 336, 'indicator': 0, 'kernel': '336.c1.a1', 'kernel_order': 4, 'label': '1344.9508.4h5', 'nt': [84, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0], [-4, 7]], [[2, 0], [4, 7]], [[2, 0]], [[-2, 0], [-4, 7]], [[2, 0], [4, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 6], [2, -6]], [[2, 9], [2, -9]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 9], [2, -9]], [[2, 6], [2, -6]], [[-2, 6], [-2, -6]], [[-2, 3], [-2, -3]], [[-2, 9], [-2, -9]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 9], [-1, -9]], [[-2, 9], [-2, -9]], [[2, 3], [2, -3]], [[2, 9], [2, -9]], [[2, 6], [2, -6]], [[-2, 6], [-2, -6]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 9], [-1, -9]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[1, 9], [1, -9]], [[1, 9], [1, -9]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[-1, 9], [-1, -9]], [[1, 9], [1, -9]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 6], [-1, -6]]]}
  • id: 12719688
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 86, 'cyclotomic_n': 21, 'dim': 4, 'faithful': False, 'field': [1, -2, 5, 0, 3, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '336.161', 'image_order': 336, 'indicator': 0, 'kernel': '336.c1.a1', 'kernel_order': 4, 'label': '1344.9508.4h6', 'nt': [84, 6], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0], [4, 7]], [[-2, 0], [-4, 7]], [[2, 0]], [[2, 0], [4, 7]], [[-2, 0], [-4, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 6], [2, -6]], [[2, 9], [2, -9]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 9], [2, -9]], [[2, 6], [2, -6]], [[-2, 6], [-2, -6]], [[-2, 3], [-2, -3]], [[-2, 9], [-2, -9]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 9], [-1, -9]], [[-2, 9], [-2, -9]], [[2, 3], [2, -3]], [[2, 9], [2, -9]], [[2, 6], [2, -6]], [[-2, 6], [-2, -6]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 9], [-1, -9]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[1, 9], [1, -9]], [[1, 9], [1, -9]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[-1, 9], [-1, -9]], [[1, 9], [1, -9]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 6], [-1, -6]]]}
  • id: 12719689
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 87, 'cyclotomic_n': 21, 'dim': 4, 'faithful': False, 'field': [1, -2, 5, 0, 3, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '336.161', 'image_order': 336, 'indicator': 0, 'kernel': '336.a1.a1', 'kernel_order': 4, 'label': '1344.9508.4i1', 'nt': [84, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0], [-4, 7]], [[2, 0], [4, 7]], [[-2, 0]], [[2, 0], [4, 7]], [[-2, 0], [-4, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 9], [2, -9]], [[2, 3], [2, -3]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 9], [2, -9]], [[2, 6], [2, -6]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 9], [2, -9]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-2, 6], [-2, -6]], [[-2, 9], [-2, -9]], [[-2, 6], [-2, -6]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-2, 9], [-2, -9]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 9], [-1, -9]], [[-1, 9], [-1, -9]], [[-1, 9], [-1, -9]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 9], [1, -9]], [[1, 9], [1, -9]], [[1, 3], [1, -3]]]}
  • id: 12719690
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 88, 'cyclotomic_n': 21, 'dim': 4, 'faithful': False, 'field': [1, -2, 5, 0, 3, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '336.161', 'image_order': 336, 'indicator': 0, 'kernel': '336.a1.a1', 'kernel_order': 4, 'label': '1344.9508.4i2', 'nt': [84, 6], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0], [4, 7]], [[-2, 0], [-4, 7]], [[-2, 0]], [[-2, 0], [-4, 7]], [[2, 0], [4, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 9], [2, -9]], [[2, 3], [2, -3]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 9], [2, -9]], [[2, 6], [2, -6]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 9], [2, -9]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-2, 6], [-2, -6]], [[-2, 9], [-2, -9]], [[-2, 6], [-2, -6]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-2, 9], [-2, -9]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 9], [-1, -9]], [[-1, 9], [-1, -9]], [[-1, 9], [-1, -9]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 9], [1, -9]], [[1, 9], [1, -9]], [[1, 3], [1, -3]]]}
  • id: 12719691
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 89, 'cyclotomic_n': 21, 'dim': 4, 'faithful': False, 'field': [1, -2, 5, 0, 3, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '336.161', 'image_order': 336, 'indicator': 0, 'kernel': '336.a1.a1', 'kernel_order': 4, 'label': '1344.9508.4i3', 'nt': [84, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0], [-4, 7]], [[2, 0], [4, 7]], [[-2, 0]], [[2, 0], [4, 7]], [[-2, 0], [-4, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 9], [2, -9]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 3], [2, -3]], [[2, 9], [2, -9]], [[2, 9], [2, -9]], [[2, 6], [2, -6]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, -3]], [[-2, 3], [-2, -3]], [[-2, 6], [-2, -6]], [[-2, 3], [-2, -3]], [[-2, 9], [-2, -9]], [[-2, 9], [-2, -9]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[-1, 9], [-1, -9]], [[-1, 9], [-1, -9]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 9], [1, -9]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 9], [1, -9]]]}
  • id: 12719693
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 90, 'cyclotomic_n': 21, 'dim': 4, 'faithful': False, 'field': [1, -2, 5, 0, 3, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '336.161', 'image_order': 336, 'indicator': 0, 'kernel': '336.a1.a1', 'kernel_order': 4, 'label': '1344.9508.4i4', 'nt': [84, 6], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0], [4, 7]], [[-2, 0], [-4, 7]], [[-2, 0]], [[-2, 0], [-4, 7]], [[2, 0], [4, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 9], [2, -9]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 3], [2, -3]], [[2, 9], [2, -9]], [[2, 9], [2, -9]], [[2, 6], [2, -6]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, -3]], [[-2, 3], [-2, -3]], [[-2, 6], [-2, -6]], [[-2, 3], [-2, -3]], [[-2, 9], [-2, -9]], [[-2, 9], [-2, -9]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[-1, 9], [-1, -9]], [[-1, 9], [-1, -9]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 9], [1, -9]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 9], [1, -9]]]}
  • id: 12719694
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 91, 'cyclotomic_n': 21, 'dim': 4, 'faithful': False, 'field': [1, -2, 5, 0, 3, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '336.161', 'image_order': 336, 'indicator': 0, 'kernel': '336.a1.a1', 'kernel_order': 4, 'label': '1344.9508.4i5', 'nt': [84, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0], [-4, 7]], [[2, 0], [4, 7]], [[-2, 0]], [[2, 0], [4, 7]], [[-2, 0], [-4, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 6], [2, -6]], [[2, 9], [2, -9]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 9], [2, -9]], [[2, 6], [2, -6]], [[2, 6], [2, -6]], [[2, 3], [2, -3]], [[2, 9], [2, -9]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 9], [-1, -9]], [[-2, 9], [-2, -9]], [[-2, 3], [-2, -3]], [[-2, 9], [-2, -9]], [[-2, 6], [-2, -6]], [[-2, 6], [-2, -6]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 9], [-1, -9]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 9], [-1, -9]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 9], [1, -9]], [[1, 9], [1, -9]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 6], [1, -6]]]}
  • id: 12719695
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 92, 'cyclotomic_n': 21, 'dim': 4, 'faithful': False, 'field': [1, -2, 5, 0, 3, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '336.161', 'image_order': 336, 'indicator': 0, 'kernel': '336.a1.a1', 'kernel_order': 4, 'label': '1344.9508.4i6', 'nt': [84, 6], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0], [4, 7]], [[-2, 0], [-4, 7]], [[-2, 0]], [[-2, 0], [-4, 7]], [[2, 0], [4, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 6], [2, -6]], [[2, 9], [2, -9]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 9], [2, -9]], [[2, 6], [2, -6]], [[2, 6], [2, -6]], [[2, 3], [2, -3]], [[2, 9], [2, -9]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 9], [-1, -9]], [[-2, 9], [-2, -9]], [[-2, 3], [-2, -3]], [[-2, 9], [-2, -9]], [[-2, 6], [-2, -6]], [[-2, 6], [-2, -6]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 9], [-1, -9]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 9], [-1, -9]], [[-1, 9], [-1, -9]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 9], [1, -9]], [[1, 9], [1, -9]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 6], [1, -6]]]}
  • id: 12719696
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 14, 'counter': 93, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '192.1395', 'image_order': 192, 'indicator': -1, 'kernel': '192.a1.a1', 'kernel_order': 7, 'label': '1344.9508.8a', 'nt': [48, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[8, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12719697
    {'center': '224.a1.a1', 'center_index': 224, 'center_order': 6, 'counter': 94, 'cyclotomic_n': 7, 'dim': 8, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '448.1228', 'image_order': 448, 'indicator': -1, 'kernel': '448.a1.a1', 'kernel_order': 3, 'label': '1344.9508.8b1', 'nt': [112, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 3], [-4, -3]], [[0, 0]], [[0, 0]], [[-4, 2], [-4, -2]], [[0, 0]], [[0, 0]], [[-4, 1], [-4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12719698
    {'center': '224.a1.a1', 'center_index': 224, 'center_order': 6, 'counter': 95, 'cyclotomic_n': 7, 'dim': 8, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '448.1228', 'image_order': 448, 'indicator': -1, 'kernel': '448.a1.a1', 'kernel_order': 3, 'label': '1344.9508.8b2', 'nt': [112, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 2], [-4, -2]], [[0, 0]], [[0, 0]], [[-4, 1], [-4, -1]], [[0, 0]], [[0, 0]], [[-4, 3], [-4, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12719699
    {'center': '224.a1.a1', 'center_index': 224, 'center_order': 6, 'counter': 96, 'cyclotomic_n': 7, 'dim': 8, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '448.1228', 'image_order': 448, 'indicator': -1, 'kernel': '448.a1.a1', 'kernel_order': 3, 'label': '1344.9508.8b3', 'nt': [112, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 1], [-4, -1]], [[0, 0]], [[0, 0]], [[-4, 3], [-4, -3]], [[0, 0]], [[0, 0]], [[-4, 2], [-4, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12719700
    {'center': '672.a1.a1', 'center_index': 672, 'center_order': 2, 'counter': 97, 'cyclotomic_n': 21, 'dim': 8, 'faithful': True, 'field': [1, -8, 8, 6, -6, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '1344.9508', 'image_order': 1344, 'indicator': -1, 'kernel': '1344.a1.a1', 'kernel_order': 1, 'label': '1344.9508.8c1', 'nt': [336, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[4, 9], [4, -9]], [[4, 3], [4, -3]], [[4, 6], [4, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 9], [-4, -9]], [[-4, 6], [-4, -6]], [[-4, 3], [-4, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 9], [-2, -9]], [[-2, 3], [-2, -3]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 9], [2, -9]], [[-2, 0], [2, 1], [-4, 2], [-2, 3], [2, 4], [4, 5], [-2, 6], [2, 8], [-4, 9], [2, -10]], [[2, 0], [-2, 1], [4, 2], [2, 3], [-2, 4], [-4, 5], [2, 6], [-2, 8], [4, 9], [-2, -10]], [[2, 6], [2, -6]], [[-2, 3], [2, 4], [-4, 10], [-2, -10]], [[2, 3], [-2, 4], [4, 10], [2, -10]], [[2, 3], [2, -3]], [[4, 0], [2, 1], [-4, 2], [4, 3], [-4, 5], [2, 6], [4, 7], [-6, 8], [4, 10], [-4, -10]], [[-4, 0], [-2, 1], [4, 2], [-4, 3], [4, 5], [-2, 6], [-4, 7], [6, 8], [-4, 10], [4, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12719701
    {'center': '672.a1.a1', 'center_index': 672, 'center_order': 2, 'counter': 98, 'cyclotomic_n': 21, 'dim': 8, 'faithful': True, 'field': [1, -8, 8, 6, -6, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '1344.9508', 'image_order': 1344, 'indicator': -1, 'kernel': '1344.a1.a1', 'kernel_order': 1, 'label': '1344.9508.8c2', 'nt': [336, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[4, 9], [4, -9]], [[4, 3], [4, -3]], [[4, 6], [4, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 9], [-4, -9]], [[-4, 6], [-4, -6]], [[-4, 3], [-4, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 9], [-2, -9]], [[-2, 3], [-2, -3]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 9], [2, -9]], [[2, 0], [-2, 1], [4, 2], [2, 3], [-2, 4], [-4, 5], [2, 6], [-2, 8], [4, 9], [-2, -10]], [[-2, 0], [2, 1], [-4, 2], [-2, 3], [2, 4], [4, 5], [-2, 6], [2, 8], [-4, 9], [2, -10]], [[2, 6], [2, -6]], [[2, 3], [-2, 4], [4, 10], [2, -10]], [[-2, 3], [2, 4], [-4, 10], [-2, -10]], [[2, 3], [2, -3]], [[-4, 0], [-2, 1], [4, 2], [-4, 3], [4, 5], [-2, 6], [-4, 7], [6, 8], [-4, 10], [4, -10]], [[4, 0], [2, 1], [-4, 2], [4, 3], [-4, 5], [2, 6], [4, 7], [-6, 8], [4, 10], [-4, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12719702
    {'center': '672.a1.a1', 'center_index': 672, 'center_order': 2, 'counter': 99, 'cyclotomic_n': 21, 'dim': 8, 'faithful': True, 'field': [1, -8, 8, 6, -6, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '1344.9508', 'image_order': 1344, 'indicator': -1, 'kernel': '1344.a1.a1', 'kernel_order': 1, 'label': '1344.9508.8c3', 'nt': [336, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[4, 6], [4, -6]], [[4, 9], [4, -9]], [[4, 3], [4, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 6], [-4, -6]], [[-4, 3], [-4, -3]], [[-4, 9], [-4, -9]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 9], [-2, -9]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[-4, 0], [-2, 1], [4, 2], [-4, 3], [4, 5], [-2, 6], [-4, 7], [6, 8], [-4, 10], [4, -10]], [[4, 0], [2, 1], [-4, 2], [4, 3], [-4, 5], [2, 6], [4, 7], [-6, 8], [4, 10], [-4, -10]], [[2, 3], [2, -3]], [[2, 0], [-2, 1], [4, 2], [2, 3], [-2, 4], [-4, 5], [2, 6], [-2, 8], [4, 9], [-2, -10]], [[-2, 0], [2, 1], [-4, 2], [-2, 3], [2, 4], [4, 5], [-2, 6], [2, 8], [-4, 9], [2, -10]], [[2, 9], [2, -9]], [[2, 3], [-2, 4], [4, 10], [2, -10]], [[-2, 3], [2, 4], [-4, 10], [-2, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12719603
    {'center': '672.a1.a1', 'center_index': 672, 'center_order': 2, 'counter': 100, 'cyclotomic_n': 21, 'dim': 8, 'faithful': True, 'field': [1, -8, 8, 6, -6, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '1344.9508', 'image_order': 1344, 'indicator': -1, 'kernel': '1344.a1.a1', 'kernel_order': 1, 'label': '1344.9508.8c4', 'nt': [336, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[4, 6], [4, -6]], [[4, 9], [4, -9]], [[4, 3], [4, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 6], [-4, -6]], [[-4, 3], [-4, -3]], [[-4, 9], [-4, -9]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 9], [-2, -9]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[4, 0], [2, 1], [-4, 2], [4, 3], [-4, 5], [2, 6], [4, 7], [-6, 8], [4, 10], [-4, -10]], [[-4, 0], [-2, 1], [4, 2], [-4, 3], [4, 5], [-2, 6], [-4, 7], [6, 8], [-4, 10], [4, -10]], [[2, 3], [2, -3]], [[-2, 0], [2, 1], [-4, 2], [-2, 3], [2, 4], [4, 5], [-2, 6], [2, 8], [-4, 9], [2, -10]], [[2, 0], [-2, 1], [4, 2], [2, 3], [-2, 4], [-4, 5], [2, 6], [-2, 8], [4, 9], [-2, -10]], [[2, 9], [2, -9]], [[-2, 3], [2, 4], [-4, 10], [-2, -10]], [[2, 3], [-2, 4], [4, 10], [2, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12719604
    {'center': '672.a1.a1', 'center_index': 672, 'center_order': 2, 'counter': 101, 'cyclotomic_n': 21, 'dim': 8, 'faithful': True, 'field': [1, -8, 8, 6, -6, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '1344.9508', 'image_order': 1344, 'indicator': -1, 'kernel': '1344.a1.a1', 'kernel_order': 1, 'label': '1344.9508.8c5', 'nt': [336, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[4, 3], [4, -3]], [[4, 6], [4, -6]], [[4, 9], [4, -9]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 3], [-4, -3]], [[-4, 9], [-4, -9]], [[-4, 6], [-4, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[-2, 6], [-2, -6]], [[-2, 9], [-2, -9]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 3], [-2, 4], [4, 10], [2, -10]], [[-2, 3], [2, 4], [-4, 10], [-2, -10]], [[2, 9], [2, -9]], [[-4, 0], [-2, 1], [4, 2], [-4, 3], [4, 5], [-2, 6], [-4, 7], [6, 8], [-4, 10], [4, -10]], [[4, 0], [2, 1], [-4, 2], [4, 3], [-4, 5], [2, 6], [4, 7], [-6, 8], [4, 10], [-4, -10]], [[2, 6], [2, -6]], [[2, 0], [-2, 1], [4, 2], [2, 3], [-2, 4], [-4, 5], [2, 6], [-2, 8], [4, 9], [-2, -10]], [[-2, 0], [2, 1], [-4, 2], [-2, 3], [2, 4], [4, 5], [-2, 6], [2, 8], [-4, 9], [2, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12719605
    {'center': '672.a1.a1', 'center_index': 672, 'center_order': 2, 'counter': 102, 'cyclotomic_n': 21, 'dim': 8, 'faithful': True, 'field': [1, -8, 8, 6, -6, -1, 1], 'group': '1344.9508', 'group_counter': 9508, 'group_order': 1344, 'image': None, 'image_isoclass': '1344.9508', 'image_order': 1344, 'indicator': -1, 'kernel': '1344.a1.a1', 'kernel_order': 1, 'label': '1344.9508.8c6', 'nt': [336, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[4, 3], [4, -3]], [[4, 6], [4, -6]], [[4, 9], [4, -9]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 3], [-4, -3]], [[-4, 9], [-4, -9]], [[-4, 6], [-4, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[-2, 6], [-2, -6]], [[-2, 9], [-2, -9]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[-2, 3], [2, 4], [-4, 10], [-2, -10]], [[2, 3], [-2, 4], [4, 10], [2, -10]], [[2, 9], [2, -9]], [[4, 0], [2, 1], [-4, 2], [4, 3], [-4, 5], [2, 6], [4, 7], [-6, 8], [4, 10], [-4, -10]], [[-4, 0], [-2, 1], [4, 2], [-4, 3], [4, 5], [-2, 6], [-4, 7], [6, 8], [-4, 10], [4, -10]], [[2, 6], [2, -6]], [[-2, 0], [2, 1], [-4, 2], [-2, 3], [2, 4], [4, 5], [-2, 6], [2, 8], [-4, 9], [2, -10]], [[2, 0], [-2, 1], [4, 2], [2, 3], [-2, 4], [-4, 5], [2, 6], [-2, 8], [4, 9], [-2, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• gps_subgroup_search •

  Column	Type
  Agroup	boolean
  Zgroup	boolean
  abelian	boolean
  ambient	text
  ambient_counter	integer
  ambient_order	numeric
  ambient_tex	text
  central	boolean
  central_factor	boolean
  centralizer_order	numeric
  characteristic	boolean
  core_order	numeric
  counter	integer
  cyclic	boolean
  direct	boolean
  hall	numeric
  label	text
  maximal	boolean
  maximal_normal	boolean
  metabelian	boolean
  metacyclic	boolean
  minimal	boolean
  minimal_normal	boolean
  nilpotent	boolean
  normal	boolean
  old_label	text
  outer_equivalence	boolean
  perfect	boolean
  proper	boolean
  quotient	text
  quotient_Agroup	boolean
  quotient_abelian	boolean
  quotient_cyclic	boolean
  quotient_hash	bigint
  quotient_metabelian	boolean
  quotient_nilpotent	boolean
  quotient_order	numeric
  quotient_simple	boolean
  quotient_solvable	boolean
  quotient_supersolvable	boolean
  quotient_tex	text
  simple	boolean
  solvable	boolean
  special_labels	text[]
  split	boolean
  standard_generators	boolean
  stem	boolean
  subgroup	text
  subgroup_hash	bigint
  subgroup_order	numeric
  subgroup_tex	text
  supersolvable	boolean
  sylow	smallint

  
  
  • id: 74506416
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1344, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 42, 'label': '1344.9508.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1344.9508', 'subgroup_hash': 9508, 'subgroup_order': 1344, 'subgroup_tex': 'C_{84}.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 74506527
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': True, 'core_order': 672, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.911', 'subgroup_hash': 911, 'subgroup_order': 672, 'subgroup_tex': 'C_{84}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506638
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 672, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.1209', 'subgroup_hash': 1209, 'subgroup_order': 672, 'subgroup_tex': 'C_{84}.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 74506749
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 672, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.998', 'subgroup_hash': 998, 'subgroup_order': 672, 'subgroup_tex': 'C_{42}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506860
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 672, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.1130', 'subgroup_hash': 1130, 'subgroup_order': 672, 'subgroup_tex': 'D_{12}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506888
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 672, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.441', 'subgroup_hash': 441, 'subgroup_order': 672, 'subgroup_tex': 'C_{84}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506899
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 672, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.2.f1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.428', 'subgroup_hash': 428, 'subgroup_order': 672, 'subgroup_tex': 'C_{84}.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 74506910
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 672, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.2.g1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.457', 'subgroup_hash': 457, 'subgroup_order': 672, 'subgroup_tex': 'C_{12}.D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74506921
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 672, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.2.h1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.633', 'subgroup_hash': 633, 'subgroup_order': 672, 'subgroup_tex': 'D_{12}:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506417
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 672, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.2.h1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.633', 'subgroup_hash': 633, 'subgroup_order': 672, 'subgroup_tex': 'D_{12}:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506428
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 672, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.2.i1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.634', 'subgroup_hash': 634, 'subgroup_order': 672, 'subgroup_tex': 'D_{12}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506439
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 672, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.2.i1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.634', 'subgroup_hash': 634, 'subgroup_order': 672, 'subgroup_tex': 'D_{12}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506450
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 672, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.2.j1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.627', 'subgroup_hash': 627, 'subgroup_order': 672, 'subgroup_tex': 'D_{28}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74506461
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 672, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.2.j1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.627', 'subgroup_hash': 627, 'subgroup_order': 672, 'subgroup_tex': 'D_{28}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74506472
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 672, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.2.k1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.628', 'subgroup_hash': 628, 'subgroup_order': 672, 'subgroup_tex': 'C_{84}.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 74506483
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 672, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.2.k1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.628', 'subgroup_hash': 628, 'subgroup_order': 672, 'subgroup_tex': 'C_{84}.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 74506494
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 224, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 14, 'label': '1344.9508.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '448.1228', 'subgroup_hash': 1228, 'subgroup_order': 448, 'subgroup_tex': 'D_8:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506505
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': True, 'core_order': 336, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.205', 'subgroup_hash': 205, 'subgroup_order': 336, 'subgroup_tex': 'D_4\\times C_{42}', 'supersolvable': True, 'sylow': 0}
  • id: 74506516
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': True, 'core_order': 336, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.187', 'subgroup_hash': 187, 'subgroup_order': 336, 'subgroup_tex': 'D_{12}:C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506528
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 336, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.177', 'subgroup_hash': 177, 'subgroup_order': 336, 'subgroup_tex': 'D_{28}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74506539
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 336, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.177', 'subgroup_hash': 177, 'subgroup_order': 336, 'subgroup_tex': 'D_{28}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74506550
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 336, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.194', 'subgroup_hash': 194, 'subgroup_order': 336, 'subgroup_tex': 'C_{42}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506561
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': True, 'core_order': 336, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.80', 'subgroup_hash': 80, 'subgroup_order': 336, 'subgroup_tex': 'C_{12}.C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74506572
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 336, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.95', 'subgroup_hash': 95, 'subgroup_order': 336, 'subgroup_tex': 'C_{42}:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506583
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 336, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.85', 'subgroup_hash': 85, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506594
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 336, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.85', 'subgroup_hash': 85, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506605
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 336, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.178', 'subgroup_hash': 178, 'subgroup_order': 336, 'subgroup_tex': 'C_{12}:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506616
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 336, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.178', 'subgroup_hash': 178, 'subgroup_order': 336, 'subgroup_tex': 'C_{12}:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506627
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 336, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.179', 'subgroup_hash': 179, 'subgroup_order': 336, 'subgroup_tex': 'C_{12}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506639
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 336, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.179', 'subgroup_hash': 179, 'subgroup_order': 336, 'subgroup_tex': 'C_{12}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506650
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 336, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.86', 'subgroup_hash': 86, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506661
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 336, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.86', 'subgroup_hash': 86, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506672
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 336, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.102', 'subgroup_hash': 102, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506683
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 336, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.102', 'subgroup_hash': 102, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506694
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 336, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.102', 'subgroup_hash': 102, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506705
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 336, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.102', 'subgroup_hash': 102, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506716
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.145', 'subgroup_hash': 145, 'subgroup_order': 336, 'subgroup_tex': 'D_{12}:D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506727
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.145', 'subgroup_hash': 145, 'subgroup_order': 336, 'subgroup_tex': 'D_{12}:D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506738
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 336, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.29', 'subgroup_hash': 29, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506750
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 336, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.33', 'subgroup_hash': 33, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506761
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.137', 'subgroup_hash': 137, 'subgroup_order': 336, 'subgroup_tex': 'C_{12}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506772
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.137', 'subgroup_hash': 137, 'subgroup_order': 336, 'subgroup_tex': 'C_{12}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506783
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 336, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.23', 'subgroup_hash': 23, 'subgroup_order': 336, 'subgroup_tex': 'C_{12}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506794
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 336, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.23', 'subgroup_hash': 23, 'subgroup_order': 336, 'subgroup_tex': 'C_{12}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506805
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 336, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.26', 'subgroup_hash': 26, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506816
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 336, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.26', 'subgroup_hash': 26, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506827
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 336, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.32', 'subgroup_hash': 32, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506838
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.34', 'subgroup_hash': 34, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506849
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.34', 'subgroup_hash': 34, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506861
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 336, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.38', 'subgroup_hash': 38, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506872
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.39', 'subgroup_hash': 39, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506880
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.4.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.39', 'subgroup_hash': 39, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506881
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 168, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.4.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.183', 'subgroup_hash': 183, 'subgroup_order': 336, 'subgroup_tex': 'C_{42}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506882
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 168, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.4.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.x1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.183', 'subgroup_hash': 183, 'subgroup_order': 336, 'subgroup_tex': 'C_{42}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506883
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 168, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.4.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.153', 'subgroup_hash': 153, 'subgroup_order': 336, 'subgroup_tex': 'D_6.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506884
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 168, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.4.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.y1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.153', 'subgroup_hash': 153, 'subgroup_order': 336, 'subgroup_tex': 'D_6.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506885
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 168, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.4.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.178', 'subgroup_hash': 178, 'subgroup_order': 336, 'subgroup_tex': 'C_{12}:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506886
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 168, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.4.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.179', 'subgroup_hash': 179, 'subgroup_order': 336, 'subgroup_tex': 'C_{12}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506887
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 168, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.4.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.138', 'subgroup_hash': 138, 'subgroup_order': 336, 'subgroup_tex': 'D_{28}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74506889
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 168, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.4.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.140', 'subgroup_hash': 140, 'subgroup_order': 336, 'subgroup_tex': 'C_{12}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506890
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 224, 'counter': 61, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '224.180', 'subgroup_hash': 180, 'subgroup_order': 224, 'subgroup_tex': 'D_4:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506891
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 112, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '224.171', 'subgroup_hash': 171, 'subgroup_order': 224, 'subgroup_tex': 'D_8:C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506892
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '224.128', 'subgroup_hash': 128, 'subgroup_order': 224, 'subgroup_tex': 'C_{14}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506893
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 112, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '224.186', 'subgroup_hash': 186, 'subgroup_order': 224, 'subgroup_tex': 'D_4.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506894
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '224.145', 'subgroup_hash': 145, 'subgroup_order': 224, 'subgroup_tex': 'C_{28}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506895
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.6.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '224.102', 'subgroup_hash': 102, 'subgroup_order': 224, 'subgroup_tex': 'C_8.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506896
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 112, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.6.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '224.104', 'subgroup_hash': 104, 'subgroup_order': 224, 'subgroup_tex': 'C_4.D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74506897
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 112, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.6.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '224.106', 'subgroup_hash': 106, 'subgroup_order': 224, 'subgroup_tex': 'C_8:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506898
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 112, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.6.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '224.106', 'subgroup_hash': 106, 'subgroup_order': 224, 'subgroup_tex': 'C_8:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506900
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 112, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.6.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '224.107', 'subgroup_hash': 107, 'subgroup_order': 224, 'subgroup_tex': 'D_8:D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506901
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 112, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.6.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '224.107', 'subgroup_hash': 107, 'subgroup_order': 224, 'subgroup_tex': 'D_8:D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506902
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 112, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.6.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '224.108', 'subgroup_hash': 108, 'subgroup_order': 224, 'subgroup_tex': 'D_7\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506903
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 112, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.6.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '224.108', 'subgroup_hash': 108, 'subgroup_order': 224, 'subgroup_tex': 'D_7\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506904
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 112, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.6.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '224.110', 'subgroup_hash': 110, 'subgroup_order': 224, 'subgroup_tex': 'C_8.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506905
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 112, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.6.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '224.110', 'subgroup_hash': 110, 'subgroup_order': 224, 'subgroup_tex': 'C_8.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506906
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 96, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '1344.9508.7.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1395', 'subgroup_hash': 1395, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 74506907
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 168, 'counter': 77, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.28', 'subgroup_hash': 28, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506908
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 168, 'counter': 78, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.8.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.28', 'subgroup_hash': 28, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506909
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 168, 'counter': 79, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.39', 'subgroup_hash': 39, 'subgroup_order': 168, 'subgroup_tex': 'C_2\\times C_{84}', 'supersolvable': True, 'sylow': 0}
  • id: 74506911
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': False, 'core_order': 168, 'counter': 80, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.40', 'subgroup_hash': 40, 'subgroup_order': 168, 'subgroup_tex': 'D_4\\times C_{21}', 'supersolvable': True, 'sylow': 0}
  • id: 74506912
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': False, 'core_order': 168, 'counter': 81, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.8.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.40', 'subgroup_hash': 40, 'subgroup_order': 168, 'subgroup_tex': 'D_4\\times C_{21}', 'supersolvable': True, 'sylow': 0}
  • id: 74506913
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': True, 'core_order': 168, 'counter': 82, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.31', 'subgroup_hash': 31, 'subgroup_order': 168, 'subgroup_tex': 'C_7\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74506914
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 168, 'counter': 83, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.25', 'subgroup_hash': 25, 'subgroup_order': 168, 'subgroup_tex': 'C_{12}\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506915
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 168, 'counter': 84, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.8.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.25', 'subgroup_hash': 25, 'subgroup_order': 168, 'subgroup_tex': 'C_{12}\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506916
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 168, 'counter': 85, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.26', 'subgroup_hash': 26, 'subgroup_order': 168, 'subgroup_tex': 'C_3\\times D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74506917
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 168, 'counter': 86, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.26', 'subgroup_hash': 26, 'subgroup_order': 168, 'subgroup_tex': 'C_3\\times D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74506918
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': True, 'core_order': 168, 'counter': 87, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.29', 'subgroup_hash': 29, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506919
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 168, 'counter': 88, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.24', 'subgroup_hash': 24, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506920
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 89, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.34', 'subgroup_hash': 34, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506922
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 90, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.8.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.34', 'subgroup_hash': 34, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506923
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 168, 'counter': 91, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.8.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.3', 'subgroup_hash': 3, 'subgroup_order': 168, 'subgroup_tex': 'C_3:C_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 74506924
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 168, 'counter': 92, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.8.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.3', 'subgroup_hash': 3, 'subgroup_order': 168, 'subgroup_tex': 'C_3:C_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 74506925
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 168, 'counter': 93, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.8.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.5', 'subgroup_hash': 5, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506926
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 168, 'counter': 94, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.8.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.5', 'subgroup_hash': 5, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506927
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 168, 'counter': 95, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.8.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.24', 'subgroup_hash': 24, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506928
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 84, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.8.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.57', 'subgroup_hash': 57, 'subgroup_order': 168, 'subgroup_tex': 'C_2^2\\times C_{42}', 'supersolvable': True, 'sylow': 0}
  • id: 74506929
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 84, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.8.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.33', 'subgroup_hash': 33, 'subgroup_order': 168, 'subgroup_tex': 'D_6:C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506930
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 84, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.8.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.28', 'subgroup_hash': 28, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506931
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.8.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.37', 'subgroup_hash': 37, 'subgroup_order': 168, 'subgroup_tex': 'C_{42}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506418
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 84, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.8.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.54', 'subgroup_hash': 54, 'subgroup_order': 168, 'subgroup_tex': 'C_6\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506419
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 84, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.8.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.54', 'subgroup_hash': 54, 'subgroup_order': 168, 'subgroup_tex': 'C_6\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506420
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 84, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.8.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.28', 'subgroup_hash': 28, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506421
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 84, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.8.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.28', 'subgroup_hash': 28, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506422
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 84, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.8.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.28', 'subgroup_hash': 28, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506423
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 84, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.8.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.28', 'subgroup_hash': 28, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506424
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 84, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.8.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.27', 'subgroup_hash': 27, 'subgroup_order': 168, 'subgroup_tex': 'C_{14}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74506425
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 84, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.8.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.27', 'subgroup_hash': 27, 'subgroup_order': 168, 'subgroup_tex': 'C_{14}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74506426
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': False, 'core_order': 84, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.8.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.40', 'subgroup_hash': 40, 'subgroup_order': 168, 'subgroup_tex': 'D_4\\times C_{21}', 'supersolvable': True, 'sylow': 0}
  • id: 74506427
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 84, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.8.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.15', 'subgroup_hash': 15, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506429
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 84, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.8.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.x1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.15', 'subgroup_hash': 15, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506430
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 84, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.8.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.30', 'subgroup_hash': 30, 'subgroup_order': 168, 'subgroup_tex': 'S_3\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74506431
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 84, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.8.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.13', 'subgroup_hash': 13, 'subgroup_order': 168, 'subgroup_tex': 'C_6.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506432
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 84, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.8.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.z1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.13', 'subgroup_hash': 13, 'subgroup_order': 168, 'subgroup_tex': 'C_6.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506433
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 84, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.8.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.12', 'subgroup_hash': 12, 'subgroup_order': 168, 'subgroup_tex': 'C_6.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506434
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 84, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.8.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.ba1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.12', 'subgroup_hash': 12, 'subgroup_order': 168, 'subgroup_tex': 'C_6.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506435
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 84, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.8.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.25', 'subgroup_hash': 25, 'subgroup_order': 168, 'subgroup_tex': 'C_{12}\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506436
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.8.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.34', 'subgroup_hash': 34, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506437
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 84, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.8.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.18', 'subgroup_hash': 18, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506438
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 84, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.8.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.bd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.18', 'subgroup_hash': 18, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506440
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': True, 'core_order': 112, 'counter': 120, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '112.38', 'subgroup_hash': 38, 'subgroup_order': 112, 'subgroup_tex': 'D_4\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506441
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 112, 'counter': 121, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '112.30', 'subgroup_hash': 30, 'subgroup_order': 112, 'subgroup_tex': 'D_{28}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506442
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 112, 'counter': 122, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '112.30', 'subgroup_hash': 30, 'subgroup_order': 112, 'subgroup_tex': 'D_{28}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506443
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 112, 'counter': 123, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '112.31', 'subgroup_hash': 31, 'subgroup_order': 112, 'subgroup_tex': 'D_4\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506444
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 112, 'counter': 124, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.12.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '112.31', 'subgroup_hash': 31, 'subgroup_order': 112, 'subgroup_tex': 'D_4\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506445
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 112, 'counter': 125, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '112.32', 'subgroup_hash': 32, 'subgroup_order': 112, 'subgroup_tex': 'D_4:D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506446
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 112, 'counter': 126, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.12.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '112.32', 'subgroup_hash': 32, 'subgroup_order': 112, 'subgroup_tex': 'D_4:D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506447
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 56, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.36', 'subgroup_hash': 36, 'subgroup_order': 112, 'subgroup_tex': 'C_{14}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506448
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 56, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.36', 'subgroup_hash': 36, 'subgroup_order': 112, 'subgroup_tex': 'C_{14}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506449
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 56, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.32', 'subgroup_hash': 32, 'subgroup_order': 112, 'subgroup_tex': 'D_4:D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506451
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 56, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.32', 'subgroup_hash': 32, 'subgroup_order': 112, 'subgroup_tex': 'D_4:D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506452
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 56, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.40', 'subgroup_hash': 40, 'subgroup_order': 112, 'subgroup_tex': 'D_4:C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506453
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.27', 'subgroup_hash': 27, 'subgroup_order': 112, 'subgroup_tex': 'C_{14}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506454
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 56, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.23', 'subgroup_hash': 23, 'subgroup_order': 112, 'subgroup_tex': 'C_7\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506455
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 56, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.8', 'subgroup_hash': 8, 'subgroup_order': 112, 'subgroup_tex': 'C_{14}:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506456
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 56, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.24', 'subgroup_hash': 24, 'subgroup_order': 112, 'subgroup_tex': 'C_7\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506457
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 56, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.24', 'subgroup_hash': 24, 'subgroup_order': 112, 'subgroup_tex': 'C_7\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506458
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 56, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.31', 'subgroup_hash': 31, 'subgroup_order': 112, 'subgroup_tex': 'D_4\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506459
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 56, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.32', 'subgroup_hash': 32, 'subgroup_order': 112, 'subgroup_tex': 'D_4:D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506460
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 56, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.25', 'subgroup_hash': 25, 'subgroup_order': 112, 'subgroup_tex': 'C_7\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506462
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 56, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.25', 'subgroup_hash': 25, 'subgroup_order': 112, 'subgroup_tex': 'C_7\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506463
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.15', 'subgroup_hash': 15, 'subgroup_order': 112, 'subgroup_tex': 'C_7:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506464
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.15', 'subgroup_hash': 15, 'subgroup_order': 112, 'subgroup_tex': 'C_7:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506465
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.15', 'subgroup_hash': 15, 'subgroup_order': 112, 'subgroup_tex': 'C_7:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506466
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.15', 'subgroup_hash': 15, 'subgroup_order': 112, 'subgroup_tex': 'C_7:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506467
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.30', 'subgroup_hash': 30, 'subgroup_order': 112, 'subgroup_tex': 'D_{28}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506468
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.27', 'subgroup_hash': 27, 'subgroup_order': 112, 'subgroup_tex': 'C_{14}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506469
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 56, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.32', 'subgroup_hash': 32, 'subgroup_order': 112, 'subgroup_tex': 'D_4:D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506470
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 56, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.32', 'subgroup_hash': 32, 'subgroup_order': 112, 'subgroup_tex': 'D_4:D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506471
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.14', 'subgroup_hash': 14, 'subgroup_order': 112, 'subgroup_tex': 'C_7:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506473
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.15', 'subgroup_hash': 15, 'subgroup_order': 112, 'subgroup_tex': 'C_7:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506474
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 56, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.33', 'subgroup_hash': 33, 'subgroup_order': 112, 'subgroup_tex': 'Q_8\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506475
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 56, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.33', 'subgroup_hash': 33, 'subgroup_order': 112, 'subgroup_tex': 'Q_8\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506476
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 56, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.3', 'subgroup_hash': 3, 'subgroup_order': 112, 'subgroup_tex': 'C_8\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506477
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 56, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.x1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.3', 'subgroup_hash': 3, 'subgroup_order': 112, 'subgroup_tex': 'C_8\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506478
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.4', 'subgroup_hash': 4, 'subgroup_order': 112, 'subgroup_tex': 'C_{56}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506479
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.y1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.4', 'subgroup_hash': 4, 'subgroup_order': 112, 'subgroup_tex': 'C_{56}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506480
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.16', 'subgroup_hash': 16, 'subgroup_order': 112, 'subgroup_tex': 'Q_8:D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506481
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 56, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.5', 'subgroup_hash': 5, 'subgroup_order': 112, 'subgroup_tex': 'C_{56}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506482
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 56, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ba1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.5', 'subgroup_hash': 5, 'subgroup_order': 112, 'subgroup_tex': 'C_{56}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506484
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.17', 'subgroup_hash': 17, 'subgroup_order': 112, 'subgroup_tex': 'C_7:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506485
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 56, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.7', 'subgroup_hash': 7, 'subgroup_order': 112, 'subgroup_tex': 'C_7:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506486
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 56, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.12.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.7', 'subgroup_hash': 7, 'subgroup_order': 112, 'subgroup_tex': 'C_7:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506487
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': True, 'core_order': 96, 'counter': 163, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.14.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '14.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '14.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 14, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_7', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.139', 'subgroup_hash': 139, 'subgroup_order': 96, 'subgroup_tex': 'D_{12}:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 74506488
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 48, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.14.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.224', 'subgroup_hash': 224, 'subgroup_order': 96, 'subgroup_tex': 'C_6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 74506489
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.14.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.140', 'subgroup_hash': 140, 'subgroup_order': 96, 'subgroup_tex': 'C_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506490
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.14.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.217', 'subgroup_hash': 217, 'subgroup_order': 96, 'subgroup_tex': 'D_4.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74506491
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.14.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.157', 'subgroup_hash': 157, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506492
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.14.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.155', 'subgroup_hash': 155, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 74506493
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.14.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.158', 'subgroup_hash': 158, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506495
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.14.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.139', 'subgroup_hash': 139, 'subgroup_order': 96, 'subgroup_tex': 'D_{12}:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 74506496
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.14.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.139', 'subgroup_hash': 139, 'subgroup_order': 96, 'subgroup_tex': 'D_{12}:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 74506497
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.14.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.157', 'subgroup_hash': 157, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506498
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.14.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.157', 'subgroup_hash': 157, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506499
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.14.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.140', 'subgroup_hash': 140, 'subgroup_order': 96, 'subgroup_tex': 'C_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506500
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.14.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.140', 'subgroup_hash': 140, 'subgroup_order': 96, 'subgroup_tex': 'C_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506501
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.14.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.158', 'subgroup_hash': 158, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506502
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.14.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.158', 'subgroup_hash': 158, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506503
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 84, 'counter': 178, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.15', 'subgroup_hash': 15, 'subgroup_order': 84, 'subgroup_tex': 'C_2\\times C_{42}', 'supersolvable': True, 'sylow': 0}
  • id: 74506504
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 84, 'counter': 179, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.12', 'subgroup_hash': 12, 'subgroup_order': 84, 'subgroup_tex': 'C_3\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506506
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 84, 'counter': 180, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.16.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.12', 'subgroup_hash': 12, 'subgroup_order': 84, 'subgroup_tex': 'C_3\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506507
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 84, 'counter': 181, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.9508.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.6', 'subgroup_hash': 6, 'subgroup_order': 84, 'subgroup_tex': 'C_{84}', 'supersolvable': True, 'sylow': 0}
  • id: 74506508
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 84, 'counter': 182, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.9508.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.6', 'subgroup_hash': 6, 'subgroup_order': 84, 'subgroup_tex': 'C_{84}', 'supersolvable': True, 'sylow': 0}
  • id: 74506509
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 84, 'counter': 183, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.4', 'subgroup_hash': 4, 'subgroup_order': 84, 'subgroup_tex': 'C_7:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74506510
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 84, 'counter': 184, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.16.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.4', 'subgroup_hash': 4, 'subgroup_order': 84, 'subgroup_tex': 'C_7:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74506511
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 42, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.15', 'subgroup_hash': 15, 'subgroup_order': 84, 'subgroup_tex': 'C_2\\times C_{42}', 'supersolvable': True, 'sylow': 0}
  • id: 74506512
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 42, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.16.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.15', 'subgroup_hash': 15, 'subgroup_order': 84, 'subgroup_tex': 'C_2\\times C_{42}', 'supersolvable': True, 'sylow': 0}
  • id: 74506513
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 42, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.13', 'subgroup_hash': 13, 'subgroup_order': 84, 'subgroup_tex': 'S_3\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506514
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 42, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.16.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.12', 'subgroup_hash': 12, 'subgroup_order': 84, 'subgroup_tex': 'C_3\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506515
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 42, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.16.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.3', 'subgroup_hash': 3, 'subgroup_order': 84, 'subgroup_tex': 'C_3:C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74506517
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 42, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.16.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.4', 'subgroup_hash': 4, 'subgroup_order': 84, 'subgroup_tex': 'C_7:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74506518
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 42, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.16.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.5', 'subgroup_hash': 5, 'subgroup_order': 84, 'subgroup_tex': 'C_{21}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506519
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 42, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.16.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.5', 'subgroup_hash': 5, 'subgroup_order': 84, 'subgroup_tex': 'C_{21}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506520
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 21, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.16.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.15', 'subgroup_hash': 15, 'subgroup_order': 84, 'subgroup_tex': 'C_2\\times C_{42}', 'supersolvable': True, 'sylow': 0}
  • id: 74506521
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 21, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.16.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.12', 'subgroup_hash': 12, 'subgroup_order': 84, 'subgroup_tex': 'C_3\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506522
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 21, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.16.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.12', 'subgroup_hash': 12, 'subgroup_order': 84, 'subgroup_tex': 'C_3\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506523
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1344.9508.21.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '21.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 21, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.258', 'subgroup_hash': 258, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 2}
  • id: 74506524
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 56, 'counter': 197, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.7', 'subgroup_hash': 7, 'subgroup_order': 56, 'subgroup_tex': 'C_7:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506525
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 56, 'counter': 198, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.24.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.7', 'subgroup_hash': 7, 'subgroup_order': 56, 'subgroup_tex': 'C_7:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506526
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 56, 'counter': 199, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74506529
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': False, 'core_order': 56, 'counter': 200, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.9', 'subgroup_hash': 9, 'subgroup_order': 56, 'subgroup_tex': 'C_7\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506530
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': False, 'core_order': 56, 'counter': 201, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.24.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.9', 'subgroup_hash': 9, 'subgroup_order': 56, 'subgroup_tex': 'C_7\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506531
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 56, 'counter': 202, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.4', 'subgroup_hash': 4, 'subgroup_order': 56, 'subgroup_tex': 'C_4\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506532
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 56, 'counter': 203, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.24.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.4', 'subgroup_hash': 4, 'subgroup_order': 56, 'subgroup_tex': 'C_4\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506533
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 56, 'counter': 204, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.5', 'subgroup_hash': 5, 'subgroup_order': 56, 'subgroup_tex': 'D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74506534
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 56, 'counter': 205, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.5', 'subgroup_hash': 5, 'subgroup_order': 56, 'subgroup_tex': 'D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74506535
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 56, 'counter': 206, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.3', 'subgroup_hash': 3, 'subgroup_order': 56, 'subgroup_tex': 'C_7:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506536
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 56, 'counter': 207, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.3', 'subgroup_hash': 3, 'subgroup_order': 56, 'subgroup_tex': 'C_7:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506537
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 28, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.24.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.13', 'subgroup_hash': 13, 'subgroup_order': 56, 'subgroup_tex': 'C_2^2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506538
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 28, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.24.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.9', 'subgroup_hash': 9, 'subgroup_order': 56, 'subgroup_tex': 'C_7\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506540
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 28, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.24.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.7', 'subgroup_hash': 7, 'subgroup_order': 56, 'subgroup_tex': 'C_7:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506541
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 28, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.24.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.6', 'subgroup_hash': 6, 'subgroup_order': 56, 'subgroup_tex': 'C_{14}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506542
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 28, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.24.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.12', 'subgroup_hash': 12, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506543
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 28, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.24.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.12', 'subgroup_hash': 12, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506544
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 28, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.24.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.7', 'subgroup_hash': 7, 'subgroup_order': 56, 'subgroup_tex': 'C_7:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506545
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 28, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.24.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.7', 'subgroup_hash': 7, 'subgroup_order': 56, 'subgroup_tex': 'C_7:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506546
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 28, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.24.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.7', 'subgroup_hash': 7, 'subgroup_order': 56, 'subgroup_tex': 'C_7:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506547
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 28, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.24.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.7', 'subgroup_hash': 7, 'subgroup_order': 56, 'subgroup_tex': 'C_7:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506548
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 28, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.24.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.6', 'subgroup_hash': 6, 'subgroup_order': 56, 'subgroup_tex': 'C_{14}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506549
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 28, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.24.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.6', 'subgroup_hash': 6, 'subgroup_order': 56, 'subgroup_tex': 'C_{14}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506551
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': False, 'core_order': 28, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.24.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.9', 'subgroup_hash': 9, 'subgroup_order': 56, 'subgroup_tex': 'C_7\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506552
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 28, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.24.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.7', 'subgroup_hash': 7, 'subgroup_order': 56, 'subgroup_tex': 'C_7:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506553
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 28, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.24.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.7', 'subgroup_hash': 7, 'subgroup_order': 56, 'subgroup_tex': 'C_7:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506554
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 28, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.24.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74506555
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 28, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.24.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.6', 'subgroup_hash': 6, 'subgroup_order': 56, 'subgroup_tex': 'C_{14}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506556
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 28, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.24.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.6', 'subgroup_hash': 6, 'subgroup_order': 56, 'subgroup_tex': 'C_{14}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506557
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 28, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.24.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.9', 'subgroup_hash': 9, 'subgroup_order': 56, 'subgroup_tex': 'C_7\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506558
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 28, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.24.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.4', 'subgroup_hash': 4, 'subgroup_order': 56, 'subgroup_tex': 'C_4\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506559
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 28, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.24.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.4', 'subgroup_hash': 4, 'subgroup_order': 56, 'subgroup_tex': 'C_4\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506560
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 28, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.24.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.4', 'subgroup_hash': 4, 'subgroup_order': 56, 'subgroup_tex': 'C_4\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506562
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 28, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.24.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.10', 'subgroup_hash': 10, 'subgroup_order': 56, 'subgroup_tex': 'C_7\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506563
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 28, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.24.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.3', 'subgroup_hash': 3, 'subgroup_order': 56, 'subgroup_tex': 'C_7:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506564
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 28, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.24.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.y1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.3', 'subgroup_hash': 3, 'subgroup_order': 56, 'subgroup_tex': 'C_7:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506565
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 28, 'counter': 233, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.24.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.2', 'subgroup_hash': 2, 'subgroup_order': 56, 'subgroup_tex': 'C_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 74506566
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 28, 'counter': 234, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.24.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.z1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.2', 'subgroup_hash': 2, 'subgroup_order': 56, 'subgroup_tex': 'C_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 74506567
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 28, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.24.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.1', 'subgroup_hash': 1, 'subgroup_order': 56, 'subgroup_tex': 'C_7:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506568
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.24.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.1', 'subgroup_hash': 1, 'subgroup_order': 56, 'subgroup_tex': 'C_7:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506569
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.24.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.3', 'subgroup_hash': 3, 'subgroup_order': 56, 'subgroup_tex': 'C_7:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506570
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 28, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.24.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.3', 'subgroup_hash': 3, 'subgroup_order': 56, 'subgroup_tex': 'C_7:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506571
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 28, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.24.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.3', 'subgroup_hash': 3, 'subgroup_order': 56, 'subgroup_tex': 'C_7:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506573
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': True, 'core_order': 48, 'counter': 240, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.28.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '28.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506574
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': True, 'core_order': 48, 'counter': 241, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.28.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '28.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 74506575
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': True, 'core_order': 48, 'counter': 242, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.28.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '28.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.10', 'subgroup_hash': 10, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506576
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 48, 'counter': 243, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.28.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '28.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.15', 'subgroup_hash': 15, 'subgroup_order': 48, 'subgroup_tex': 'C_3:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506577
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 48, 'counter': 244, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.28.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '28.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.15', 'subgroup_hash': 15, 'subgroup_order': 48, 'subgroup_tex': 'C_3:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506578
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 48, 'counter': 245, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.28.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '28.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506579
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 48, 'counter': 246, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.28.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '28.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506580
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506581
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506582
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74506584
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74506585
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.47', 'subgroup_hash': 47, 'subgroup_order': 48, 'subgroup_tex': 'D_4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74506586
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.47', 'subgroup_hash': 47, 'subgroup_order': 48, 'subgroup_tex': 'D_4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74506587
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506588
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.9', 'subgroup_hash': 9, 'subgroup_order': 48, 'subgroup_tex': 'C_6:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506589
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506590
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506591
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.47', 'subgroup_hash': 47, 'subgroup_order': 48, 'subgroup_tex': 'D_4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74506592
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.47', 'subgroup_hash': 47, 'subgroup_order': 48, 'subgroup_tex': 'D_4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74506593
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506595
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.47', 'subgroup_hash': 47, 'subgroup_order': 48, 'subgroup_tex': 'D_4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74506596
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506597
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506598
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506599
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506600
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74506601
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506602
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.37', 'subgroup_hash': 37, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506603
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.37', 'subgroup_hash': 37, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506604
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.15', 'subgroup_hash': 15, 'subgroup_order': 48, 'subgroup_tex': 'C_3:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506606
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.17', 'subgroup_hash': 17, 'subgroup_order': 48, 'subgroup_tex': 'Q_8:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74506607
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506608
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506609
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.9', 'subgroup_hash': 9, 'subgroup_order': 48, 'subgroup_tex': 'C_6:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506610
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.x1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.9', 'subgroup_hash': 9, 'subgroup_order': 48, 'subgroup_tex': 'C_6:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506611
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.10', 'subgroup_hash': 10, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506612
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.y1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.10', 'subgroup_hash': 10, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506613
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506614
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506615
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.ba1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506617
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.18', 'subgroup_hash': 18, 'subgroup_order': 48, 'subgroup_tex': 'C_3:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506618
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.18', 'subgroup_hash': 18, 'subgroup_order': 48, 'subgroup_tex': 'C_3:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506619
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.28.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.bc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.18', 'subgroup_hash': 18, 'subgroup_order': 48, 'subgroup_tex': 'C_3:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506620
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 42, 'counter': 283, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.9508.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.46', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['S', 'L2', 'C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '42.6', 'subgroup_hash': 6, 'subgroup_order': 42, 'subgroup_tex': 'C_{42}', 'supersolvable': True, 'sylow': 0}
  • id: 74506621
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 21, 'counter': 284, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.6', 'subgroup_hash': 6, 'subgroup_order': 42, 'subgroup_tex': 'C_{42}', 'supersolvable': True, 'sylow': 0}
  • id: 74506622
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 21, 'counter': 285, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.6', 'subgroup_hash': 6, 'subgroup_order': 42, 'subgroup_tex': 'C_{42}', 'supersolvable': True, 'sylow': 0}
  • id: 74506623
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 21, 'counter': 286, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.32.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.6', 'subgroup_hash': 6, 'subgroup_order': 42, 'subgroup_tex': 'C_{42}', 'supersolvable': True, 'sylow': 0}
  • id: 74506624
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 21, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.32.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.3', 'subgroup_hash': 3, 'subgroup_order': 42, 'subgroup_tex': 'S_3\\times C_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506625
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 21, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.32.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.4', 'subgroup_hash': 4, 'subgroup_order': 42, 'subgroup_tex': 'C_3\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506626
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 21, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.32.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.4', 'subgroup_hash': 4, 'subgroup_order': 42, 'subgroup_tex': 'C_3\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506628
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 21, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.32.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.4', 'subgroup_hash': 4, 'subgroup_order': 42, 'subgroup_tex': 'C_3\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506629
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 16, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.42.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506630
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 16, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.42.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 74506631
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.42.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506632
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.42.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.50', 'subgroup_hash': 50, 'subgroup_order': 32, 'subgroup_tex': 'C_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 74506633
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.42.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506634
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.42.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.38', 'subgroup_hash': 38, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506635
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.42.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506636
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.42.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506637
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.42.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506640
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.42.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506641
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.42.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506642
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.42.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506643
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.42.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506644
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.42.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506645
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.42.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506646
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 28, 'counter': 306, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.43', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506647
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 28, 'counter': 307, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.43', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:D_4', 'simple': False, 'solvable': True, 'special_labels': [], '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: 74506648
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 28, 'counter': 308, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.48.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.43', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:D_4', 'simple': False, 'solvable': True, 'special_labels': [], '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: 74506649
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 28, 'counter': 309, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.9508.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.51', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 51, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74506651
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 28, 'counter': 310, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.9508.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.43', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:D_4', 'simple': False, 'solvable': True, 'special_labels': [], '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: 74506652
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 28, 'counter': 311, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.48.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.43', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:D_4', 'simple': False, 'solvable': True, 'special_labels': [], '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: 74506653
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 28, 'counter': 312, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.48.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.43', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:D_4', 'simple': False, 'solvable': True, 'special_labels': [], '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: 74506654
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 14, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.48.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506655
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 14, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.48.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506656
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 14, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.48.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506657
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 14, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.48.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506658
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 14, 'counter': 317, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.48.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74506659
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 14, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.48.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.1', 'subgroup_hash': 1, 'subgroup_order': 28, 'subgroup_tex': 'C_7:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506660
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.48.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.1', 'subgroup_hash': 1, 'subgroup_order': 28, 'subgroup_tex': 'C_7:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506662
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.48.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.1', 'subgroup_hash': 1, 'subgroup_order': 28, 'subgroup_tex': 'C_7:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506663
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 7, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.48.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506664
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 7, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.48.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506665
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 7, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.48.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506666
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 24, 'counter': 324, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.56.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '56.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74506667
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 24, 'counter': 325, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.56.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '56.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506668
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 24, 'counter': 326, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.56.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '56.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506669
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 24, 'counter': 327, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.56.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '56.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74506670
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 24, 'counter': 328, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.56.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '56.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506671
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 24, 'counter': 329, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.56.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '56.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506673
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 24, 'counter': 330, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.56.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '56.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506674
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 12, 'counter': 331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74506675
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 12, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506676
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506677
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506678
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506679
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506680
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74506681
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74506682
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506684
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506685
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506686
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506687
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74506688
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74506689
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 12, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506690
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506691
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506692
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 12, 'counter': 348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74506693
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74506695
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74506696
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74506697
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74506698
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506699
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506700
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506701
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74506702
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506703
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506704
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506706
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.y1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506707
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506708
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506709
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506710
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506711
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506712
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.56.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.bd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506713
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 21, 'counter': 367, 'cyclic': True, 'direct': False, 'hall': 21, 'label': '1344.9508.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.258', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 258, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8:C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['L3', 'C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '21.2', 'subgroup_hash': 2, 'subgroup_order': 21, 'subgroup_tex': 'C_{21}', 'supersolvable': True, 'sylow': 0}
  • id: 74506714
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': True, 'core_order': 16, 'counter': 368, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.84.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '84.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '84.8', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 84, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_7', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506715
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506717
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506718
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506719
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506720
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 8, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506721
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506722
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506723
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506724
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 8, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506725
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506726
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 8, 'counter': 379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506728
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 8, 'counter': 380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506729
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506730
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506731
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506732
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506733
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506734
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506735
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 8, 'counter': 387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506736
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 8, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506737
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506739
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506740
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506741
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506742
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506743
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506744
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506745
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506746
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506747
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506748
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506751
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506752
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506753
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.x1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506754
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506755
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.y1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506756
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506757
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506758
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.ba1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506759
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506760
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506762
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.84.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.bc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74506763
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 14, 'counter': 411, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.9508.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.219', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 219, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506764
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 7, 'counter': 412, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.96.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506765
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 7, 'counter': 413, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.96.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506766
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 7, 'counter': 414, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.96.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506767
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 7, 'counter': 415, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.96.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74506768
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 7, 'counter': 416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.96.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506769
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 7, 'counter': 417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.96.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506770
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 7, 'counter': 418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.96.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74506771
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 12, 'counter': 419, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.112.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '112.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '112.31', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 31, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4\\times D_7', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74506773
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 12, 'counter': 420, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.9508.112.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '112.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '112.42', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 42, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74506774
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 12, 'counter': 421, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.9508.112.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '112.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '112.31', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 31, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4\\times D_7', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74506775
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 6, 'counter': 422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.112.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74506776
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 6, 'counter': 423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.112.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74506777
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 6, 'counter': 424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.112.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74506778
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.112.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74506779
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.112.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74506780
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.112.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74506781
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 6, 'counter': 428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.112.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506782
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 429, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.112.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74506784
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 430, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.112.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74506785
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 431, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.112.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74506786
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.112.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506787
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.112.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506788
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 3, 'counter': 434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.112.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74506789
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.112.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74506790
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.112.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74506791
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 8, 'counter': 437, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.168.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '168.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '168.50', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 50, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 168, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': ['U1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506792
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 8, 'counter': 438, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.168.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '168.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '168.50', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 50, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 168, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506793
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 8, 'counter': 439, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.168.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '168.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '168.50', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 50, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 168, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506795
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 4, 'counter': 440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 74506796
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 4, 'counter': 441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506797
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506798
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506799
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506800
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506801
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 74506802
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 74506803
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506804
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506806
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506807
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506808
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506809
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506810
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 4, 'counter': 454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506811
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506812
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506813
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 4, 'counter': 457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506814
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506815
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506817
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 4, 'counter': 460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506818
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506819
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506820
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506821
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506822
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506823
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506824
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506825
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 4, 'counter': 468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506826
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506828
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506829
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.x1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506830
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 4, 'counter': 472, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.168.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506831
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 4, 'counter': 473, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.168.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.y1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506832
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 474, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.168.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506833
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 475, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.168.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506834
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506835
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506836
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506837
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.168.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.bd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74506839
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 7, 'counter': 480, 'cyclic': True, 'direct': False, 'hall': 7, 'label': '1344.9508.192.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '192.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '192.1395', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1395, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}.C_2^4', 'simple': True, 'solvable': True, 'special_labels': ['C7'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 7}
  • id: 74506840
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 6, 'counter': 481, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.9508.224.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '224.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '224.178', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 178, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 224, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4\\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: 74506841
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 3, 'counter': 482, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.224.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 224, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74506842
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 3, 'counter': 483, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.224.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 224, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74506843
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 3, 'counter': 484, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.224.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 224, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74506844
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 3, 'counter': 485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.224.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '224.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 224, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74506845
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 486, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.224.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 224, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74506846
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 487, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.224.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 224, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74506847
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 488, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.224.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 224, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74506848
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 4, 'counter': 489, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9508.336.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '336.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '336.161', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 161, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 336, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6:D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 74506850
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 4, 'counter': 490, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.9508.336.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '336.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '336.219', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 219, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 336, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': ['Phi'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506851
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 4, 'counter': 491, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.9508.336.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '336.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '336.161', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 161, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 336, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6:D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506852
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 2, 'counter': 492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.336.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 74506853
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 2, 'counter': 493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.336.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 74506854
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 2, 'counter': 494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.336.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 74506855
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.336.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 74506856
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.336.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 74506857
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.336.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 74506858
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 2, 'counter': 498, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.336.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506859
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 499, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.336.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506862
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 500, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.336.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506863
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 501, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.336.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506864
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 502, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.336.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506865
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 503, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.336.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74506866
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 1, 'counter': 504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.336.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 74506867
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.336.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 74506868
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.9508.336.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 74506869
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 3, 'counter': 507, 'cyclic': True, 'direct': False, 'hall': 3, 'label': '1344.9508.448.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '448.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '448.1228', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1228, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 448, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_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: 74506870
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': True, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': True, 'core_order': 2, 'counter': 508, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.9508.672.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '672.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '672.1175', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1175, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 672, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{42}:C_2^3', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'U2'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506871
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': False, 'core_order': 1, 'counter': 509, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.672.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506873
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 1, 'counter': 510, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.672.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506874
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 1, 'counter': 511, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.672.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506875
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 1, 'counter': 512, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.672.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506876
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 513, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.672.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506877
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 514, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.672.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506878
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 515, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.9508.672.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74506879
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9508', 'ambient_counter': 9508, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': True, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': True, 'core_order': 1, 'counter': 516, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1344.9508.1344.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1344.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '1344.9508', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 9508, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1344, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{84}.C_2^4', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U3', 'D2', 'C8'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 74506416
    {'ambient': '1344.9508', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['1344.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1', '2.h1.a1', '2.h1.b1', '2.i1.a1', '2.i1.b1', '2.j1.a1', '2.j1.b1', '2.k1.a1', '2.k1.b1', '3.a1.a1', '7.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7332, 4912, 7234, 4728, 6251, 4725, 5779, 5194], 'generators': [1, 8, 448, 4, 672, 192, 2, 336], 'label': '1344.9508.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1', '2.h1.b1', '2.h1.a1', '2.i1.b1', '2.i1.a1', '2.j1.b1', '2.j1.a1', '2.k1.b1', '2.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '672.1175'}
  • id: 74506417
    {'ambient': '1344.9508', 'aut_centralizer_order': 2, 'aut_label': '2.h1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '672.a1.a1', 'complements': ['672.b1.a1', '672.e1.a1', '672.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.h1.b1', '4.i1.b1', '4.m1.b1', '4.n1.b1', '4.o1.a1', '4.s1.b1', '4.u1.b1', '6.h1.b1', '14.h1.b1'], 'core': '2.h1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7561, 3774, 6768, 4441, 6251, 3555, 5695, 6618], 'generators': [337, 448, 4, 680, 722, 192, 672], 'label': '1344.9508.2.h1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.h1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.h1.b1', '4.i1.b1', '4.m1.b1', '4.n1.b1', '4.o1.a1', '4.s1.b1', '4.u1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.h1.b1', 'projective_image': '672.1175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.h1.b1', 'subgroup_fusion': None, 'weyl_group': '672.1175'}
  • id: 74506418
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '8.s1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '112.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.x1.a1', '4.z1.a1'], 'contains': ['16.b1.a1', '16.f1.a1', '16.h1.a1', '16.m1.a1', '24.m1.a1', '56.k1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [430, -1, 472, -1, 333, -1, 187, -1], 'generators': [1, 672, 448, 2, 192], 'label': '1344.9508.8.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.s1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.s1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506419
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '8.s1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '112.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.b1', '4.x1.b1', '4.z1.a1'], 'contains': ['16.b1.b1', '16.f1.b1', '16.h1.a1', '16.m1.b1', '24.m1.b1', '56.k1.b1'], 'core': '16.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [430, -1, 758, -1, 333, -1, 88, -1], 'generators': [337, 672, 448, 722, 192], 'label': '1344.9508.8.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.s1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.s1.b1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506420
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '8.t1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '112.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '4.x1.b1', '4.z1.a1'], 'contains': ['16.b1.b1', '16.f1.a1', '16.j1.a1', '24.n1.a1', '56.l1.a1'], 'core': '16.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [761, -1, 994, -1, 563, -1, 612, -1], 'generators': [1, 448, 672, 722, 192], 'label': '1344.9508.8.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.t1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.t1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506421
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '8.t1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '112.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.b1', '4.x1.a1', '4.z1.a1'], 'contains': ['16.b1.a1', '16.f1.b1', '16.j1.a1', '24.n1.b1', '56.l1.b1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [761, -1, 1077, -1, 563, -1, 870, -1], 'generators': [337, 448, 672, 2, 192], 'label': '1344.9508.8.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.t1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.t1.b1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506422
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '8.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '112.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.x1.b1', '4.ba1.a1'], 'contains': ['16.e1.a1', '16.f1.a1', '16.h1.a1', '24.o1.a1', '56.m1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [637, -1, 671, -1, 693, -1, 960, -1], 'generators': [1, 448, 672, 10, 192], 'label': '1344.9508.8.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.u1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.u1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506423
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '8.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '112.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.b1', '4.x1.a1', '4.ba1.a1'], 'contains': ['16.e1.b1', '16.f1.b1', '16.h1.a1', '24.o1.b1', '56.m1.b1'], 'core': '16.e1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [637, -1, 1265, -1, 693, -1, 1127, -1], 'generators': [337, 448, 672, 58, 192], 'label': '1344.9508.8.u1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.u1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.u1.b1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506424
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '8.v1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '112.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '4.x1.a1', '4.ba1.a1'], 'contains': ['16.e1.b1', '16.f1.a1', '16.j1.a1', '24.p1.a1', '56.n1.a1'], 'core': '16.e1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [983, -1, 2060, -1, 814, -1, 1254, -1], 'generators': [1, 448, 672, 58, 192], 'label': '1344.9508.8.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.v1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.v1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506425
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '8.v1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '112.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.b1', '4.x1.b1', '4.ba1.a1'], 'contains': ['16.e1.a1', '16.f1.b1', '16.j1.a1', '24.p1.b1', '56.n1.b1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [983, -1, 2283, -1, 814, -1, 1332, -1], 'generators': [337, 448, 672, 10, 192], 'label': '1344.9508.8.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.v1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.v1.b1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506426
    {'ambient': '1344.9508', 'aut_centralizer_order': 168, 'aut_label': '8.w1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.221', 'aut_weyl_index': 336, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.z1.a1', '4.ba1.a1'], 'contains': ['16.d1.a1', '16.f1.a1', '16.f1.b1', '24.q1.a1', '56.o1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [876, -1, 1341, -1, 1148, -1, 696, -1], 'generators': [1, 448, 192, 336, 672], 'label': '1344.9508.8.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.w1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.w1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506427
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '8.x1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 32, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1', '4.y1.a1', '4.bb1.a1'], 'contains': ['16.b1.a1', '16.g1.a1', '16.k1.a1', '24.r1.a1', '56.p1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3099, -1, 2968, -1, 1820, -1, 1734, -1], 'generators': [789, 672, 448, 2, 192], 'label': '1344.9508.8.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.x1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.x1.a1', 'subgroup_fusion': None, 'weyl_group': '336.219'}
  • id: 74506428
    {'ambient': '1344.9508', 'aut_centralizer_order': 2, 'aut_label': '2.i1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '672.a1.a1', 'complements': ['672.b1.a1', '672.e1.a1', '672.c1.b1', '672.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.h1.a1', '4.j1.a1', '4.l1.a1', '4.n1.b1', '4.p1.a1', '4.r1.b1', '4.w1.b1', '6.i1.a1', '14.i1.a1'], 'core': '2.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6411, 5817, 7885, 4728, 5971, 6361, 5540, 4462], 'generators': [1, 448, 124, 8, 722, 192, 672], 'label': '1344.9508.2.i1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.i1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.h1.a1', '4.j1.a1', '4.l1.a1', '4.n1.b1', '4.p1.a1', '4.r1.b1', '4.w1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.i1.a1', 'projective_image': '672.1175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.i1.a1', 'subgroup_fusion': None, 'weyl_group': '672.1175'}
  • id: 74506429
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '8.x1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 32, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.b1', '4.y1.b1', '4.bb1.a1'], 'contains': ['16.b1.b1', '16.g1.a1', '16.k1.b1', '24.r1.b1', '56.p1.b1'], 'core': '16.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3099, -1, 2867, -1, 1820, -1, 1945, -1], 'generators': [789, 672, 448, 722, 192], 'label': '1344.9508.8.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.x1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.x1.b1', 'subgroup_fusion': None, 'weyl_group': '336.219'}
  • id: 74506430
    {'ambient': '1344.9508', 'aut_centralizer_order': 112, 'aut_label': '8.y1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '144.195', 'aut_weyl_index': 224, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.bb1.a1', '4.bc1.a1'], 'contains': ['16.d1.a1', '16.g1.a1', '16.i1.a1', '24.s1.a1', '56.q1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3405, -1, 2546, -1, 2381, -1, 2011, -1], 'generators': [5, 192, 672, 336, 448], 'label': '1344.9508.8.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.y1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.y1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 74506431
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '8.z1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 32, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1', '4.y1.b1', '4.bc1.a1'], 'contains': ['16.e1.a1', '16.g1.a1', '16.k1.a1', '24.t1.a1', '56.r1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2227, -1, 2774, -1, 2028, -1, 2445, -1], 'generators': [789, 672, 448, 10, 192], 'label': '1344.9508.8.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.z1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.z1.a1', 'subgroup_fusion': None, 'weyl_group': '336.219'}
  • id: 74506432
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '8.z1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 32, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.b1', '4.y1.a1', '4.bc1.a1'], 'contains': ['16.e1.b1', '16.g1.a1', '16.k1.b1', '24.t1.b1', '56.r1.b1'], 'core': '16.e1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2227, -1, 2703, -1, 2028, -1, 2368, -1], 'generators': [789, 672, 448, 58, 192], 'label': '1344.9508.8.z1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.z1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.z1.b1', 'subgroup_fusion': None, 'weyl_group': '336.219'}
  • id: 74506433
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '8.ba1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 32, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '4.y1.a1', '4.bb1.a1'], 'contains': ['16.b1.a1', '16.i1.a1', '16.k1.b1', '24.v1.a1', '56.t1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2993, -1, 3062, -1, 2270, -1, 1801, -1], 'generators': [5, 672, 448, 2, 192], 'label': '1344.9508.8.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.ba1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '336.219'}
  • id: 74506434
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '8.ba1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 32, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.b1', '4.y1.b1', '4.bb1.a1'], 'contains': ['16.b1.b1', '16.i1.a1', '16.k1.a1', '24.v1.b1', '56.t1.b1'], 'core': '16.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2993, -1, 3183, -1, 2270, -1, 1879, -1], 'generators': [5, 672, 448, 722, 192], 'label': '1344.9508.8.ba1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.ba1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ba1.b1', 'subgroup_fusion': None, 'weyl_group': '336.219'}
  • id: 74506435
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '8.bb1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '112.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.z1.a1', '4.ba1.a1'], 'contains': ['16.d1.a1', '16.h1.a1', '16.j1.a1', '24.w1.a1', '56.v1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1208, -1, 1779, -1, 1259, -1, 1044, -1], 'generators': [3, 448, 672, 336, 192], 'label': '1344.9508.8.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bb1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506436
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '8.bc1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2016.eo', 'aut_weyl_index': 16, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.bb1.a1', '4.bc1.a1'], 'contains': ['16.d1.a1', '16.k1.a1', '16.k1.b1', '24.bc1.a1', '56.bc1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3314, -1, 3656, -1, 2619, -1, 2301, -1], 'generators': [7, 672, 448, 336, 192], 'label': '1344.9508.8.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.bc1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
  • id: 74506437
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '8.bd1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 32, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '4.y1.b1', '4.bc1.a1'], 'contains': ['16.e1.a1', '16.i1.a1', '16.k1.b1', '24.bd1.a1', '56.bd1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2000, -1, 2917, -1, 2476, -1, 2512, -1], 'generators': [5, 672, 448, 10, 192], 'label': '1344.9508.8.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.bd1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '336.219'}
  • id: 74506438
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '8.bd1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 32, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.b1', '4.y1.a1', '4.bc1.a1'], 'contains': ['16.e1.b1', '16.i1.a1', '16.k1.a1', '24.bd1.b1', '56.bd1.b1'], 'core': '16.e1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2000, -1, 3122, -1, 2476, -1, 2155, -1], 'generators': [5, 672, 448, 58, 192], 'label': '1344.9508.8.bd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.bd1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bd1.b1', 'subgroup_fusion': None, 'weyl_group': '336.219'}
  • id: 74506439
    {'ambient': '1344.9508', 'aut_centralizer_order': 2, 'aut_label': '2.i1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '672.a1.a1', 'complements': ['672.b1.a1', '672.e1.b1', '672.c1.a1', '672.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.h1.b1', '4.j1.b1', '4.l1.b1', '4.n1.a1', '4.p1.a1', '4.r1.a1', '4.w1.a1', '6.i1.b1', '14.i1.b1'], 'core': '2.i1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6411, 5817, 6569, 5410, 5971, 6361, 5615, 4203], 'generators': [337, 448, 4, 680, 2, 192, 672], 'label': '1344.9508.2.i1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.i1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.h1.b1', '4.j1.b1', '4.l1.b1', '4.n1.a1', '4.p1.a1', '4.r1.a1', '4.w1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.i1.b1', 'projective_image': '672.1175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.i1.b1', 'subgroup_fusion': None, 'weyl_group': '672.1175'}
  • id: 74506440
    {'ambient': '1344.9508', 'aut_centralizer_order': 168, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '192.1534', 'aut_weyl_index': 168, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.b1.a1', '6.c1.a1'], 'contains': ['24.b1.a1', '24.c1.a1', '24.c1.b1', '24.i1.a1', '24.q1.a1', '84.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6473, 6282, 3797, 8047, 5431, 3196, 3335, 5488], 'generators': [1, 336, 192, 8, 672], 'label': '1344.9508.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['24.b1.a1', '24.c1.b1', '24.c1.a1', '84.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506441
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 48, 'centralizer': '112.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.a1.a1', '6.d1.a1', '6.f1.a1'], 'contains': ['24.a1.a1', '24.a1.b1', '24.b1.a1', '24.d1.a1', '24.d1.b1', '24.e1.a1', '24.h1.a1', '84.e1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5885, 1381, 4034, 3854, 5248, 1204, 3264, 1487], 'generators': [2, 336, 672, 8, 192], 'label': '1344.9508.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.c1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '24.a1.b1', '24.b1.a1', '24.d1.a1', '24.d1.b1', '24.e1.a1', '24.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '112.42'}
  • id: 74506442
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '12.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 48, 'centralizer': '112.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.a1.a1', '6.e1.a1', '6.g1.a1'], 'contains': ['24.b1.a1', '24.f1.a1', '24.g1.a1', '24.k1.a1', '24.w1.a1', '84.f1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6742, 2766, 4534, 6423, 6607, 2241, 3406, 2590], 'generators': [3, 336, 672, 8, 192], 'label': '1344.9508.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.d1.a1', '6.a1.a1'], 'normal_contains': ['24.b1.a1', '24.f1.a1', '24.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
  • id: 74506443
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '12.d1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 48, 'centralizer': '224.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.a1.a1', '6.h1.a1', '6.j1.a1'], 'contains': ['24.c1.a1', '24.d1.a1', '24.f1.a1', '24.m1.a1', '24.o1.a1', '84.k1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6377, 3299, 3901, 7666, 5672, 1917, 3775, 3034], 'generators': [1, 8, 672, 2, 192], 'label': '1344.9508.12.d1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.d1.a1', 'normal_contained_in': ['4.i1.a1', '6.a1.a1'], 'normal_contains': ['24.c1.a1', '24.d1.a1', '24.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '224.178'}
  • id: 74506444
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '12.d1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 48, 'centralizer': '224.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.i1.b1', '6.a1.a1', '6.h1.b1', '6.j1.b1'], 'contains': ['24.c1.b1', '24.d1.b1', '24.f1.a1', '24.m1.b1', '24.o1.b1', '84.k1.b1'], 'core': '12.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6377, 3299, 4427, 7435, 5672, 1917, 3558, 2814], 'generators': [337, 8, 672, 722, 192], 'label': '1344.9508.12.d1.b1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.d1.b1', 'normal_contained_in': ['4.i1.b1', '6.a1.a1'], 'normal_contains': ['24.c1.b1', '24.d1.b1', '24.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.b1', 'subgroup_fusion': None, 'weyl_group': '224.178'}
  • id: 74506445
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '12.e1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 48, 'centralizer': '224.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '6.a1.a1', '6.i1.a1', '6.k1.a1'], 'contains': ['24.c1.a1', '24.d1.b1', '24.g1.a1', '24.n1.a1', '24.p1.a1', '84.l1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6893, 3584, 3852, 7243, 5594, 2513, 3461, 2402], 'generators': [1, 8, 672, 722, 192], 'label': '1344.9508.12.e1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.e1.a1', 'normal_contained_in': ['4.j1.a1', '6.a1.a1'], 'normal_contains': ['24.c1.a1', '24.d1.b1', '24.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '224.178'}
  • id: 74506446
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '12.e1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 48, 'centralizer': '224.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.j1.b1', '6.a1.a1', '6.i1.b1', '6.k1.b1'], 'contains': ['24.c1.b1', '24.d1.a1', '24.g1.a1', '24.n1.b1', '24.p1.b1', '84.l1.b1'], 'core': '12.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6893, 3584, 5065, 7086, 5594, 2513, 3504, 2253], 'generators': [337, 8, 672, 2, 192], 'label': '1344.9508.12.e1.b1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.e1.b1', 'normal_contained_in': ['4.j1.b1', '6.a1.a1'], 'normal_contains': ['24.c1.b1', '24.d1.a1', '24.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.e1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.b1', 'subgroup_fusion': None, 'weyl_group': '224.178'}
  • id: 74506447
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '112.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.x1.a1', '6.a1.a1'], 'contains': ['24.a1.a1', '24.i1.a1', '24.k1.a1', '24.m1.a1', '24.n1.b1', '24.o1.b1', '24.p1.a1', '84.b1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2894, -1, 1621, -1, 2878, -1, 522, -1], 'generators': [1, 344, 672, 2, 192], 'label': '1344.9508.12.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.f1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506448
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '112.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.x1.b1', '6.a1.a1'], 'contains': ['24.a1.b1', '24.i1.a1', '24.k1.a1', '24.m1.b1', '24.n1.a1', '24.o1.a1', '24.p1.b1', '84.b1.b1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2894, -1, 1911, -1, 2878, -1, 431, -1], 'generators': [1, 344, 672, 722, 192], 'label': '1344.9508.12.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.f1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.b1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506449
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.y1.a1', '6.d1.a1'], 'contains': ['24.a1.a1', '24.j1.a1', '24.l1.a1', '24.r1.a1', '24.t1.b1', '24.v1.a1', '24.bd1.b1', '84.c1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4258, -1, 6012, -1, 3129, -1, 2627, -1], 'generators': [5, 344, 672, 2, 192], 'label': '1344.9508.12.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.g1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': '112.42'}
  • id: 74506450
    {'ambient': '1344.9508', 'aut_centralizer_order': 2, 'aut_label': '2.j1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '672.a1.a1', 'complements': ['672.b1.a1', '672.e1.b1', '672.c1.b1', '672.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.i1.a1', '4.k1.a1', '4.l1.a1', '4.q1.a1', '4.r1.a1', '4.t1.a1', '4.u1.b1', '6.j1.a1', '14.j1.a1'], 'core': '2.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5900, 6332, 7797, 3255, 6761, 5879, 5880, 4794], 'generators': [1, 448, 4, 8, 2, 192, 672], 'label': '1344.9508.2.j1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.j1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.i1.a1', '4.k1.a1', '4.l1.a1', '4.q1.a1', '4.r1.a1', '4.t1.a1', '4.u1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.j1.a1', 'projective_image': '672.1175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.j1.a1', 'subgroup_fusion': None, 'weyl_group': '672.1175'}
  • id: 74506451
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.y1.b1', '6.d1.a1'], 'contains': ['24.a1.b1', '24.j1.a1', '24.l1.a1', '24.r1.b1', '24.t1.a1', '24.v1.b1', '24.bd1.a1', '84.c1.b1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [4258, -1, 6052, -1, 3129, -1, 2670, -1], 'generators': [5, 344, 672, 722, 192], 'label': '1344.9508.12.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.g1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.b1', 'subgroup_fusion': None, 'weyl_group': '112.42'}
  • id: 74506452
    {'ambient': '1344.9508', 'aut_centralizer_order': 112, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.221', 'aut_weyl_index': 336, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.b1.a1', '6.d1.a1', '6.e1.a1'], 'contains': ['24.b1.a1', '24.j1.a1', '24.s1.a1', '24.u1.a1', '24.x1.a1', '84.d1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7076, -1, 6282, -1, 6711, -1, 3704, -1], 'generators': [5, 336, 192, 8, 672], 'label': '1344.9508.12.h1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.h1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506453
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1344.11444', 'aut_weyl_index': 24, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.c1.a1', '6.d1.a1', '6.g1.a1'], 'contains': ['24.b1.a1', '24.l1.a1', '24.y1.a1', '24.y1.b1', '24.bc1.a1', '84.g1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7184, -1, 6795, -1, 5836, -1, 5061, -1], 'generators': [7, 336, 672, 8, 192], 'label': '1344.9508.12.i1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.i1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.a1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
  • id: 74506454
    {'ambient': '1344.9508', 'aut_centralizer_order': 112, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.221', 'aut_weyl_index': 336, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.b1.a1', '6.f1.a1', '6.g1.a1'], 'contains': ['24.b1.a1', '24.z1.a1', '24.z1.b1', '84.h1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8435, -1, 9566, -1, 9057, -1, 7176, -1], 'generators': [4, 192, 8, 336, 672], 'label': '1344.9508.12.j1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.j1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 74506455
    {'ambient': '1344.9508', 'aut_centralizer_order': 32, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.c1.a1', '6.e1.a1', '6.f1.a1'], 'contains': ['24.b1.a1', '24.ba1.a1', '24.bb1.a1', '84.i1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9962, -1, 9483, -1, 9950, -1, 7021, -1], 'generators': [6, 8, 672, 336, 192], 'label': '1344.9508.12.k1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.k1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506456
    {'ambient': '1344.9508', 'aut_centralizer_order': 56, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.221', 'aut_weyl_index': 336, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.b1.a1', '6.h1.a1', '6.i1.a1'], 'contains': ['24.c1.a1', '24.u1.a1', '24.z1.b1', '84.j1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9228, -1, 9261, -1, 8352, -1, 4585, -1], 'generators': [1, 192, 8, 124, 672], 'label': '1344.9508.12.l1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.l1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 74506457
    {'ambient': '1344.9508', 'aut_centralizer_order': 56, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.221', 'aut_weyl_index': 336, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.b1', '6.b1.a1', '6.h1.b1', '6.i1.b1'], 'contains': ['24.c1.b1', '24.u1.a1', '24.z1.a1', '84.j1.b1'], 'core': '24.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [9228, -1, 8388, -1, 8352, -1, 4444, -1], 'generators': [337, 192, 680, 4, 672], 'label': '1344.9508.12.l1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.l1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1.b1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 74506458
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 48, 'centralizer': '224.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.z1.a1', '6.a1.a1'], 'contains': ['24.e1.a1', '24.m1.a1', '24.m1.b1', '24.n1.a1', '24.n1.b1', '24.q1.a1', '24.w1.a1', '84.m1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3090, -1, 1799, -1, 2989, -1, 354, -1], 'generators': [1, 336, 672, 2, 192], 'label': '1344.9508.12.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.m1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1.a1', 'subgroup_fusion': None, 'weyl_group': '112.42'}
  • id: 74506459
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 48, 'centralizer': '224.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.ba1.a1', '6.a1.a1'], 'contains': ['24.h1.a1', '24.o1.a1', '24.o1.b1', '24.p1.a1', '24.p1.b1', '24.q1.a1', '24.w1.a1', '84.n1.a1'], 'core': '24.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3223, -1, 2673, -1, 3067, -1, 1194, -1], 'generators': [1, 336, 672, 10, 192], 'label': '1344.9508.12.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.n1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1.a1', 'subgroup_fusion': None, 'weyl_group': '112.42'}
  • id: 74506460
    {'ambient': '1344.9508', 'aut_centralizer_order': 56, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.221', 'aut_weyl_index': 336, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '6.b1.a1', '6.j1.a1', '6.k1.a1'], 'contains': ['24.c1.a1', '24.x1.a1', '24.z1.a1', '84.o1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7999, -1, 8184, -1, 9505, -1, 5345, -1], 'generators': [1, 192, 8, 4, 672], 'label': '1344.9508.12.o1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.o1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.o1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 74506461
    {'ambient': '1344.9508', 'aut_centralizer_order': 2, 'aut_label': '2.j1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '672.a1.a1', 'complements': ['672.b1.a1', '672.e1.a1', '672.c1.a1', '672.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.i1.b1', '4.k1.b1', '4.l1.b1', '4.q1.b1', '4.r1.b1', '4.t1.a1', '4.u1.a1', '6.j1.b1', '14.j1.b1'], 'core': '2.j1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5900, 6332, 7058, 6028, 6761, 5879, 6227, 3871], 'generators': [337, 448, 124, 680, 722, 192, 672], 'label': '1344.9508.2.j1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.j1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.i1.b1', '4.k1.b1', '4.l1.b1', '4.q1.b1', '4.r1.b1', '4.t1.a1', '4.u1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.j1.b1', 'projective_image': '672.1175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.j1.b1', 'subgroup_fusion': None, 'weyl_group': '672.1175'}
  • id: 74506462
    {'ambient': '1344.9508', 'aut_centralizer_order': 56, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.221', 'aut_weyl_index': 336, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.b1', '6.b1.a1', '6.j1.b1', '6.k1.b1'], 'contains': ['24.c1.b1', '24.x1.a1', '24.z1.b1', '84.o1.b1'], 'core': '24.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [7999, -1, 8295, -1, 9505, -1, 6131, -1], 'generators': [337, 192, 680, 124, 672], 'label': '1344.9508.12.o1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.k1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.o1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.o1.b1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 74506463
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '12.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 48, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '6.c1.a1', '6.i1.a1', '6.j1.a1'], 'contains': ['24.c1.a1', '24.y1.b1', '24.ba1.a1', '84.p1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9127, -1, 9120, -1, 9253, -1, 6223, -1], 'generators': [1, 8, 672, 6, 192], 'label': '1344.9508.12.p1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.p1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.p1.a1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
  • id: 74506464
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '12.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 48, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.b1', '6.c1.a1', '6.i1.b1', '6.j1.b1'], 'contains': ['24.c1.b1', '24.y1.a1', '24.ba1.a1', '84.p1.b1'], 'core': '24.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [9127, -1, 8784, -1, 9253, -1, 6498, -1], 'generators': [337, 8, 672, 6, 192], 'label': '1344.9508.12.p1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.p1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.p1.b1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
  • id: 74506465
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '12.q1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 48, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '6.c1.a1', '6.h1.a1', '6.k1.a1'], 'contains': ['24.c1.a1', '24.y1.a1', '24.bb1.a1', '84.q1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9719, -1, 9195, -1, 9371, -1, 6899, -1], 'generators': [1, 680, 672, 1174, 192], 'label': '1344.9508.12.q1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.q1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.q1.a1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
  • id: 74506466
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '12.q1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 48, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.b1', '6.c1.a1', '6.h1.b1', '6.k1.b1'], 'contains': ['24.c1.b1', '24.y1.b1', '24.bb1.a1', '84.q1.b1'], 'core': '24.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [9719, -1, 8970, -1, 9371, -1, 6305, -1], 'generators': [337, 680, 672, 1174, 192], 'label': '1344.9508.12.q1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.m1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.q1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.q1.b1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
  • id: 74506467
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '12.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 48, 'centralizer': '336.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bb1.a1', '6.d1.a1'], 'contains': ['24.e1.a1', '24.r1.a1', '24.r1.b1', '24.s1.a1', '24.v1.a1', '24.v1.b1', '24.bc1.a1', '84.r1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4558, -1, 5962, -1, 3208, -1, 2572, -1], 'generators': [5, 336, 672, 2, 192], 'label': '1344.9508.12.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.r1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.r1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506468
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '12.s1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 48, 'centralizer': '336.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bc1.a1', '6.d1.a1'], 'contains': ['24.h1.a1', '24.s1.a1', '24.t1.a1', '24.t1.b1', '24.bc1.a1', '24.bd1.a1', '24.bd1.b1', '84.s1.a1'], 'core': '24.h1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4443, -1, 5218, -1, 3311, -1, 2731, -1], 'generators': [5, 336, 672, 10, 192], 'label': '1344.9508.12.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.s1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.s1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506469
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '12.t1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 48, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1', '6.d1.a1', '6.h1.a1', '6.i1.b1'], 'contains': ['24.d1.a1', '24.r1.a1', '24.t1.a1', '24.u1.a1', '24.y1.a1', '84.t1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7646, -1, 6902, -1, 5749, -1, 4103, -1], 'generators': [789, 8, 672, 2, 192], 'label': '1344.9508.12.t1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.t1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.t1.a1', 'subgroup_fusion': None, 'weyl_group': '224.178'}
  • id: 74506470
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '12.t1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 48, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.b1', '6.d1.a1', '6.h1.b1', '6.i1.a1'], 'contains': ['24.d1.b1', '24.r1.b1', '24.t1.b1', '24.u1.a1', '24.y1.b1', '84.t1.b1'], 'core': '24.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [7646, -1, 6723, -1, 5749, -1, 4060, -1], 'generators': [789, 8, 672, 722, 192], 'label': '1344.9508.12.t1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.n1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.t1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.t1.b1', 'subgroup_fusion': None, 'weyl_group': '224.178'}
  • id: 74506471
    {'ambient': '1344.9508', 'aut_centralizer_order': 16, 'aut_label': '12.u1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 48, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.o1.a1', '6.e1.a1', '6.h1.a1', '6.h1.b1'], 'contains': ['24.f1.a1', '24.u1.a1', '24.bb1.a1', '84.u1.a1'], 'core': '24.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9854, -1, 8913, -1, 8548, -1, 4639, -1], 'generators': [789, 8, 672, 1174, 192], 'label': '1344.9508.12.u1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.u1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.u1.a1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
  • id: 74506472
    {'ambient': '1344.9508', 'aut_centralizer_order': 2, 'aut_label': '2.k1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '672.a1.a1', 'complements': ['672.b1.a1', '672.e1.a1', '672.c1.b1', '672.d1.a1', '672.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.j1.a1', '4.k1.a1', '4.m1.a1', '4.q1.b1', '4.s1.b1', '4.v1.a1', '4.w1.a1', '6.k1.a1', '14.k1.a1'], 'core': '2.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7423, 4302, 7683, 3673, 6929, 4725, 6110, 5588], 'generators': [1, 448, 4, 8, 722, 192, 672], 'label': '1344.9508.2.k1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.k1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.j1.a1', '4.k1.a1', '4.m1.a1', '4.q1.b1', '4.s1.b1', '4.v1.a1', '4.w1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.k1.a1', 'projective_image': '672.1175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.k1.a1', 'subgroup_fusion': None, 'weyl_group': '672.1175'}
  • id: 74506473
    {'ambient': '1344.9508', 'aut_centralizer_order': 16, 'aut_label': '12.v1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 48, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.p1.a1', '6.e1.a1', '6.i1.a1', '6.i1.b1'], 'contains': ['24.g1.a1', '24.u1.a1', '24.ba1.a1', '84.v1.a1'], 'core': '24.g1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9480, -1, 8521, -1, 8458, -1, 4371, -1], 'generators': [341, 8, 672, 6, 192], 'label': '1344.9508.12.v1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.v1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.v1.a1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
  • id: 74506474
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '12.w1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 48, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '6.d1.a1', '6.j1.a1', '6.k1.b1'], 'contains': ['24.d1.a1', '24.v1.a1', '24.x1.a1', '24.y1.b1', '24.bd1.a1', '84.w1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6979, -1, 6642, -1, 6813, -1, 4234, -1], 'generators': [5, 8, 672, 2, 192], 'label': '1344.9508.12.w1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.w1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.w1.a1', 'subgroup_fusion': None, 'weyl_group': '224.178'}
  • id: 74506475
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '12.w1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 48, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.b1', '6.d1.a1', '6.j1.b1', '6.k1.a1'], 'contains': ['24.d1.b1', '24.v1.b1', '24.x1.a1', '24.y1.a1', '24.bd1.b1', '84.w1.b1'], 'core': '24.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6979, -1, 6567, -1, 6813, -1, 4298, -1], 'generators': [5, 8, 672, 722, 192], 'label': '1344.9508.12.w1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.q1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.w1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.w1.b1', 'subgroup_fusion': None, 'weyl_group': '224.178'}
  • id: 74506476
    {'ambient': '1344.9508', 'aut_centralizer_order': 16, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '168.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.r1.a1', '6.f1.a1', '6.i1.b1', '6.j1.a1'], 'contains': ['24.d1.a1', '24.z1.a1', '24.ba1.a1', '84.x1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9026, -1, 9037, -1, 9768, -1, 6670, -1], 'generators': [2, 8, 672, 4, 192], 'label': '1344.9508.12.x1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.x1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506477
    {'ambient': '1344.9508', 'aut_centralizer_order': 16, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '168.y1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.r1.b1', '6.f1.a1', '6.i1.a1', '6.j1.b1'], 'contains': ['24.d1.b1', '24.z1.b1', '24.ba1.a1', '84.x1.b1'], 'core': '24.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [9026, -1, 9659, -1, 9768, -1, 7092, -1], 'generators': [722, 680, 672, 124, 192], 'label': '1344.9508.12.x1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.r1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.x1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1.b1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506478
    {'ambient': '1344.9508', 'aut_centralizer_order': 16, 'aut_label': '12.y1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '336.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.s1.a1', '6.f1.a1', '6.h1.a1', '6.k1.b1'], 'contains': ['24.d1.a1', '24.z1.b1', '24.bb1.a1', '84.y1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9599, -1, 9713, -1, 9854, -1, 7312, -1], 'generators': [2, 680, 672, 124, 192], 'label': '1344.9508.12.y1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.y1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.y1.a1', 'subgroup_fusion': None, 'weyl_group': '112.42'}
  • id: 74506479
    {'ambient': '1344.9508', 'aut_centralizer_order': 16, 'aut_label': '12.y1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '336.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.s1.b1', '6.f1.a1', '6.h1.b1', '6.k1.a1'], 'contains': ['24.d1.b1', '24.z1.a1', '24.bb1.a1', '84.y1.b1'], 'core': '24.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [9599, -1, 9316, -1, 9854, -1, 7256, -1], 'generators': [722, 8, 672, 4, 192], 'label': '1344.9508.12.y1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.s1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.y1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.y1.b1', 'subgroup_fusion': None, 'weyl_group': '112.42'}
  • id: 74506480
    {'ambient': '1344.9508', 'aut_centralizer_order': 16, 'aut_label': '12.z1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 48, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1', '6.e1.a1', '6.j1.a1', '6.j1.b1'], 'contains': ['24.f1.a1', '24.x1.a1', '24.ba1.a1', '84.z1.a1'], 'core': '24.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7744, -1, 8710, -1, 9610, -1, 5474, -1], 'generators': [5, 8, 672, 6, 192], 'label': '1344.9508.12.z1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.z1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.z1.a1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
  • id: 74506481
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '12.ba1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 48, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.u1.a1', '6.g1.a1', '6.h1.a1', '6.j1.b1'], 'contains': ['24.f1.a1', '24.y1.a1', '24.z1.b1', '84.ba1.a1'], 'core': '24.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8335, -1, 9377, -1, 9163, -1, 6961, -1], 'generators': [3, 680, 672, 124, 192], 'label': '1344.9508.12.ba1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.ba1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '224.178'}
  • id: 74506482
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '12.ba1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 48, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.u1.b1', '6.g1.a1', '6.h1.b1', '6.j1.a1'], 'contains': ['24.f1.a1', '24.y1.b1', '24.z1.a1', '84.ba1.b1'], 'core': '24.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8335, -1, 8842, -1, 9163, -1, 6561, -1], 'generators': [3, 8, 672, 4, 192], 'label': '1344.9508.12.ba1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.u1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.ba1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ba1.b1', 'subgroup_fusion': None, 'weyl_group': '224.178'}
  • id: 74506483
    {'ambient': '1344.9508', 'aut_centralizer_order': 2, 'aut_label': '2.k1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '672.a1.a1', 'complements': ['672.b1.a1', '672.e1.b1', '672.c1.a1', '672.d1.a1', '672.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.j1.b1', '4.k1.b1', '4.m1.b1', '4.q1.a1', '4.s1.a1', '4.v1.a1', '4.w1.b1', '6.k1.b1', '14.k1.b1'], 'core': '2.k1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7423, 4302, 7343, 4084, 6929, 4725, 5996, 5194], 'generators': [337, 448, 124, 680, 2, 192, 672], 'label': '1344.9508.2.k1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.k1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.j1.b1', '4.k1.b1', '4.m1.b1', '4.q1.a1', '4.s1.a1', '4.v1.a1', '4.w1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.k1.b1', 'projective_image': '672.1175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.k1.b1', 'subgroup_fusion': None, 'weyl_group': '672.1175'}
  • id: 74506484
    {'ambient': '1344.9508', 'aut_centralizer_order': 16, 'aut_label': '12.bb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 48, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.v1.a1', '6.e1.a1', '6.k1.a1', '6.k1.b1'], 'contains': ['24.g1.a1', '24.x1.a1', '24.bb1.a1', '84.bb1.a1'], 'core': '24.g1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9385, -1, 8458, -1, 9681, -1, 5425, -1], 'generators': [453, 8, 672, 1174, 192], 'label': '1344.9508.12.bb1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bb1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
  • id: 74506485
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '12.bc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 48, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.w1.a1', '6.g1.a1', '6.i1.b1', '6.k1.a1'], 'contains': ['24.g1.a1', '24.y1.a1', '24.z1.a1', '84.bc1.a1'], 'core': '24.g1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8944, -1, 8584, -1, 8854, -1, 6610, -1], 'generators': [51, 680, 672, 4, 192], 'label': '1344.9508.12.bc1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bc1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '224.178'}
  • id: 74506486
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '12.bc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 48, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.w1.b1', '6.g1.a1', '6.i1.a1', '6.k1.b1'], 'contains': ['24.g1.a1', '24.y1.b1', '24.z1.b1', '84.bc1.b1'], 'core': '24.g1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8944, -1, 9422, -1, 8854, -1, 6374, -1], 'generators': [51, 8, 672, 124, 192], 'label': '1344.9508.12.bc1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.w1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bc1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bc1.b1', 'subgroup_fusion': None, 'weyl_group': '224.178'}
  • id: 74506487
    {'ambient': '1344.9508', 'aut_centralizer_order': 84, 'aut_label': '14.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '384.19195', 'aut_weyl_index': 84, 'centralizer': '96.a1.a1', 'complements': ['96.e1.a1', '96.e1.b1', '96.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '7.a1.a1'], 'contains': ['28.a1.a1', '28.b1.a1', '28.c1.a1', '28.d1.a1', '28.d1.b1', '28.e1.a1', '28.e1.b1', '42.a1.a1'], 'core': '14.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4866, 7612, 7012, 7538, 5314, 9878, 7752, 9916], 'generators': [1, 448, 672, 4, 336, 8], 'label': '1344.9508.14.a1.a1', 'mobius_quo': 0, 'mobius_sub': 7, 'normal_closure': '14.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['28.a1.a1', '28.b1.a1', '28.c1.a1', '28.d1.b1', '28.d1.a1', '28.e1.b1', '28.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '14.a1.a1', 'projective_image': '672.1175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '7.1', 'quotient_action_kernel_order': 7, 'quotient_fusion': None, 'short_label': '14.a1.a1', 'subgroup_fusion': None, 'weyl_group': '96.219'}
  • id: 74506488
    {'ambient': '1344.9508', 'aut_centralizer_order': 36, 'aut_label': '14.b1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 252, 'centralizer': '224.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '7.a1.a1'], 'contains': ['28.a1.a1', '28.f1.a1', '28.f1.b1', '28.h1.a1', '28.i1.a1', '28.l1.a1', '28.l1.b1', '28.m1.a1', '28.m1.b1', '28.n1.a1', '28.o1.a1', '42.b1.a1'], 'core': '28.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [3508, -1, 3367, -1, 3628, -1, 4629, -1], 'generators': [1, 672, 448, 2, 8, 336], 'label': '1344.9508.14.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.b1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.b1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 74506489
    {'ambient': '1344.9508', 'aut_centralizer_order': 12, 'aut_label': '14.c1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '384.20143', 'aut_weyl_index': 84, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '7.a1.a1'], 'contains': ['28.a1.a1', '28.j1.a1', '28.k1.a1', '28.p1.a1', '28.p1.b1', '28.q1.a1', '28.q1.b1', '42.c1.a1'], 'core': '28.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8027, -1, 7434, -1, 5647, -1, 8781, -1], 'generators': [1, 448, 672, 6, 336, 8], 'label': '1344.9508.14.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.c1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.c1.a1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 74506490
    {'ambient': '1344.9508', 'aut_centralizer_order': 12, 'aut_label': '14.d1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '384.19195', 'aut_weyl_index': 84, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '7.a1.a1'], 'contains': ['28.b1.a1', '28.g1.a1', '28.g1.b1', '28.h1.a1', '28.j1.a1', '28.r1.a1', '28.s1.a1', '28.t1.a1', '28.t1.b1', '28.w1.a1', '28.w1.b1', '42.d1.a1'], 'core': '28.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [3750, -1, 4210, -1, 4151, -1, 4792, -1], 'generators': [5, 448, 672, 2, 8, 336], 'label': '1344.9508.14.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.d1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.d1.a1', 'subgroup_fusion': None, 'weyl_group': '96.219'}
  • id: 74506491
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '14.e1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 168, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '7.a1.a1'], 'contains': ['28.b1.a1', '28.i1.a1', '28.k1.a1', '28.u1.a1', '28.v1.a1', '28.z1.a1', '28.bb1.a1', '42.e1.a1'], 'core': '28.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7891, -1, 5781, -1, 5763, -1, 7802, -1], 'generators': [5, 448, 672, 6, 336, 8], 'label': '1344.9508.14.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.e1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.e1.a1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 74506492
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '14.f1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 168, 'centralizer': '336.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '7.a1.a1'], 'contains': ['28.c1.a1', '28.h1.a1', '28.k1.a1', '28.x1.a1', '28.x1.b1', '28.y1.a1', '28.y1.b1', '42.f1.a1'], 'core': '28.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8178, -1, 8910, -1, 6481, -1, 9517, -1], 'generators': [2, 448, 672, 4, 336, 8], 'label': '1344.9508.14.f1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.f1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.f1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 74506493
    {'ambient': '1344.9508', 'aut_centralizer_order': 12, 'aut_label': '14.g1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '384.19195', 'aut_weyl_index': 84, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '7.a1.a1'], 'contains': ['28.c1.a1', '28.i1.a1', '28.j1.a1', '28.ba1.a1', '28.ba1.b1', '28.bc1.a1', '28.bc1.b1', '42.g1.a1'], 'core': '28.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6003, -1, 7221, -1, 5449, -1, 9017, -1], 'generators': [3, 448, 672, 4, 336, 8], 'label': '1344.9508.14.g1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.g1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.g1.a1', 'subgroup_fusion': None, 'weyl_group': '96.219'}
  • id: 74506494
    {'ambient': '1344.9508', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.c1.a1', '6.d1.a1', '6.e1.a1', '6.f1.a1', '6.g1.a1', '6.h1.a1', '6.h1.b1', '6.i1.a1', '6.i1.b1', '6.j1.a1', '6.j1.b1', '6.k1.a1', '6.k1.b1', '21.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8615, -1, 8330, -1, 8230, -1, 5297, -1], 'generators': [1, 672, 4, 336, 2, 192, 8], 'label': '1344.9508.3.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '224.178'}
  • id: 74506495
    {'ambient': '1344.9508', 'aut_centralizer_order': 12, 'aut_label': '14.h1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 168, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.h1.a1', '7.a1.a1'], 'contains': ['28.d1.a1', '28.l1.a1', '28.q1.a1', '28.t1.a1', '28.u1.a1', '28.y1.a1', '28.ba1.a1', '42.h1.a1'], 'core': '28.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7392, -1, 7783, -1, 5522, -1, 8049, -1], 'generators': [1, 448, 672, 2, 124, 8], 'label': '1344.9508.14.h1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.h1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.h1.a1', 'subgroup_fusion': None, 'weyl_group': '96.219'}
  • id: 74506496
    {'ambient': '1344.9508', 'aut_centralizer_order': 12, 'aut_label': '14.h1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 168, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.h1.b1', '7.a1.a1'], 'contains': ['28.d1.b1', '28.l1.b1', '28.q1.b1', '28.t1.b1', '28.u1.a1', '28.y1.b1', '28.ba1.b1', '42.h1.b1'], 'core': '28.d1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [7392, -1, 5735, -1, 5522, -1, 7992, -1], 'generators': [337, 448, 672, 722, 4, 680], 'label': '1344.9508.14.h1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.h1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.h1.b1', 'subgroup_fusion': None, 'weyl_group': '96.219'}
  • id: 74506497
    {'ambient': '1344.9508', 'aut_centralizer_order': 12, 'aut_label': '14.i1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 168, 'centralizer': '336.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.i1.a1', '7.a1.a1'], 'contains': ['28.d1.a1', '28.m1.a1', '28.p1.a1', '28.t1.b1', '28.v1.a1', '28.x1.b1', '28.bc1.b1', '42.i1.a1'], 'core': '28.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6319, -1, 8183, -1, 5386, -1, 7898, -1], 'generators': [1, 448, 672, 722, 124, 8], 'label': '1344.9508.14.i1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.i1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.i1.a1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 74506498
    {'ambient': '1344.9508', 'aut_centralizer_order': 12, 'aut_label': '14.i1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 168, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.i1.b1', '7.a1.a1'], 'contains': ['28.d1.b1', '28.m1.b1', '28.p1.b1', '28.t1.a1', '28.v1.a1', '28.x1.a1', '28.bc1.a1', '42.i1.b1'], 'core': '28.d1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [6319, -1, 5458, -1, 5386, -1, 7942, -1], 'generators': [337, 448, 672, 2, 4, 680], 'label': '1344.9508.14.i1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.i1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.i1.b1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 74506499
    {'ambient': '1344.9508', 'aut_centralizer_order': 12, 'aut_label': '14.j1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 168, 'centralizer': '336.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.j1.a1', '7.a1.a1'], 'contains': ['28.e1.a1', '28.l1.a1', '28.p1.a1', '28.w1.a1', '28.x1.a1', '28.z1.a1', '28.ba1.b1', '42.j1.a1'], 'core': '28.e1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5892, -1, 7890, -1, 6152, -1, 8156, -1], 'generators': [1, 448, 672, 2, 4, 8], 'label': '1344.9508.14.j1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.j1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.j1.a1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 74506500
    {'ambient': '1344.9508', 'aut_centralizer_order': 12, 'aut_label': '14.j1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 168, 'centralizer': '336.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.j1.b1', '7.a1.a1'], 'contains': ['28.e1.b1', '28.l1.b1', '28.p1.b1', '28.w1.b1', '28.x1.b1', '28.z1.a1', '28.ba1.a1', '42.j1.b1'], 'core': '28.e1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [5892, -1, 6518, -1, 6152, -1, 8515, -1], 'generators': [337, 448, 672, 722, 124, 680], 'label': '1344.9508.14.j1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.j1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.j1.b1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 74506501
    {'ambient': '1344.9508', 'aut_centralizer_order': 12, 'aut_label': '14.k1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 168, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.k1.a1', '7.a1.a1'], 'contains': ['28.e1.a1', '28.m1.a1', '28.q1.a1', '28.w1.b1', '28.y1.b1', '28.bb1.a1', '28.bc1.a1', '42.k1.a1'], 'core': '28.e1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7297, -1, 8296, -1, 6267, -1, 8294, -1], 'generators': [1, 448, 672, 722, 4, 8], 'label': '1344.9508.14.k1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.k1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.k1.a1', 'subgroup_fusion': None, 'weyl_group': '96.219'}
  • id: 74506502
    {'ambient': '1344.9508', 'aut_centralizer_order': 12, 'aut_label': '14.k1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 168, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.k1.b1', '7.a1.a1'], 'contains': ['28.e1.b1', '28.m1.b1', '28.q1.b1', '28.w1.a1', '28.y1.a1', '28.bb1.a1', '28.bc1.b1', '42.k1.b1'], 'core': '28.e1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [7297, -1, 7260, -1, 6267, -1, 8246, -1], 'generators': [337, 448, 672, 2, 124, 680], 'label': '1344.9508.14.k1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.k1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.k1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.k1.b1', 'subgroup_fusion': None, 'weyl_group': '96.219'}
  • id: 74506503
    {'ambient': '1344.9508', 'aut_centralizer_order': 1344, 'aut_label': '16.a1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '24.15', 'aut_weyl_index': 1344, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.a1.b1', '8.b1.a1', '8.o1.a1', '8.p1.a1', '8.q1.a1', '8.r1.a1'], 'contains': ['32.a1.a1', '32.b1.a1', '48.a1.a1', '112.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1653, 2353, 1253, 2557, 1456, 2665, 1453, 3400], 'generators': [344, 448, 192, 672], 'label': '1344.9508.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.a1.b1', '8.b1.a1'], 'normal_contains': ['32.a1.a1', '48.a1.a1', '112.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506504
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '16.b1', 'aut_quo_index': 16, 'aut_stab_index': 2, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '56.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.e1.a1', '8.f1.a1', '8.s1.a1', '8.t1.b1', '8.x1.a1', '8.ba1.a1'], 'contains': ['32.a1.a1', '32.e1.a1', '48.b1.a1', '112.f1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1327, 1384, 952, 2240, 1355, 905, 1320, 2309], 'generators': [2, 448, 192, 672], 'label': '1344.9508.16.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1', '8.e1.a1', '8.f1.a1'], 'normal_contains': ['32.a1.a1', '48.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506505
    {'ambient': '1344.9508', 'aut_centralizer_order': 84, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '384.20157', 'aut_weyl_index': 84, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.b1.a1', '8.c1.a1', '8.c1.b1', '8.o1.a1', '8.w1.a1', '12.a1.a1', '28.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3793, 9756, 4000, 9835, 4055, 4219, 3675, 7625], 'generators': [1, 672, 336, 448, 8, 192], 'label': '1344.9508.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.b1.a1', '8.c1.b1', '8.c1.a1', '12.a1.a1', '28.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506506
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '16.b1', 'aut_quo_index': 16, 'aut_stab_index': 2, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '56.b1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '8.e1.b1', '8.f1.a1', '8.s1.b1', '8.t1.a1', '8.x1.b1', '8.ba1.b1'], 'contains': ['32.a1.a1', '32.e1.b1', '48.b1.b1', '112.f1.b1'], 'core': '16.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1327, 1384, 1189, 2010, 1355, 905, 1384, 1146], 'generators': [722, 448, 192, 672], 'label': '1344.9508.16.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.b1', 'normal_contained_in': ['8.a1.b1', '8.e1.b1', '8.f1.a1'], 'normal_contains': ['32.a1.a1', '48.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.b1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506507
    {'ambient': '1344.9508', 'aut_centralizer_order': 1344, 'aut_label': '16.c1', 'aut_quo_index': 10080, 'aut_stab_index': 1, 'aut_weyl_group': '24.15', 'aut_weyl_index': 1344, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.c1.a1', '8.c1.b1', '8.d1.a1', '8.e1.a1', '8.e1.b1', '8.g1.a1', '8.h1.a1', '8.i1.a1', '8.j1.a1', '8.j1.b1', '8.k1.a1', '8.k1.b1', '8.l1.a1', '8.m1.a1'], 'contains': ['32.a1.a1', '48.c1.a1', '112.b1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5106, 4332, 4768, 4900, 5657, 4429, 5588, 4955], 'generators': [8, 192, 672, 448], 'label': '1344.9508.16.c1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.b1.a1', '8.c1.b1', '8.c1.a1', '8.d1.a1', '8.e1.a1', '8.e1.b1', '8.g1.a1', '8.h1.a1', '8.i1.a1', '8.j1.a1', '8.j1.b1', '8.k1.a1', '8.k1.b1', '8.l1.a1', '8.m1.a1'], 'normal_contains': ['32.a1.a1', '48.c1.a1', '112.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.a1', 'projective_image': '672.1175', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506508
    {'ambient': '1344.9508', 'aut_centralizer_order': 1344, 'aut_label': '16.d1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '24.15', 'aut_weyl_index': 1344, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.f1.a1', '8.n1.a1', '8.w1.a1', '8.y1.a1', '8.bb1.a1', '8.bc1.a1'], 'contains': ['32.a1.a1', '48.d1.a1', '112.c1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1572, 2041, 2234, 3960, 1745, 2371, 1512, 3198], 'generators': [336, 192, 672, 448], 'label': '1344.9508.16.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': ['8.b1.a1', '8.f1.a1', '8.n1.a1'], 'normal_contains': ['32.a1.a1', '48.d1.a1', '112.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.d1.a1', 'projective_image': '672.1175', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506509
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '16.e1', 'aut_quo_index': 16, 'aut_stab_index': 2, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '56.b1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '8.e1.a1', '8.n1.a1', '8.u1.a1', '8.v1.b1', '8.z1.a1', '8.bd1.a1'], 'contains': ['32.a1.a1', '48.e1.a1', '112.i1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1223, 529, 2303, 2898, 1567, 1754, 1747, 1874], 'generators': [10, 672, 192, 448], 'label': '1344.9508.16.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': ['8.a1.b1', '8.e1.a1', '8.n1.a1'], 'normal_contains': ['32.a1.a1', '48.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.e1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506510
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '16.e1', 'aut_quo_index': 16, 'aut_stab_index': 2, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '56.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.e1.b1', '8.n1.a1', '8.u1.b1', '8.v1.a1', '8.z1.b1', '8.bd1.b1'], 'contains': ['32.a1.a1', '48.e1.b1', '112.i1.b1'], 'core': '16.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1223, 529, 2165, 3177, 1567, 1754, 1613, 2994], 'generators': [58, 672, 192, 448], 'label': '1344.9508.16.e1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.e1.b1', 'normal_contained_in': ['8.a1.a1', '8.e1.b1', '8.n1.a1'], 'normal_contains': ['32.a1.a1', '48.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.e1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1.b1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506511
    {'ambient': '1344.9508', 'aut_centralizer_order': 336, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.15', 'aut_weyl_index': 1344, 'centralizer': '8.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.o1.a1', '8.s1.a1', '8.t1.a1', '8.u1.a1', '8.v1.a1', '8.w1.a1'], 'contains': ['32.a1.a1', '32.c1.a1', '48.f1.a1', '112.d1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [504, -1, 505, -1, 462, -1, 527, -1], 'generators': [1, 448, 192, 672], 'label': '1344.9508.16.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.f1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506512
    {'ambient': '1344.9508', 'aut_centralizer_order': 336, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.15', 'aut_weyl_index': 1344, 'centralizer': '8.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.b1', '8.o1.a1', '8.s1.b1', '8.t1.b1', '8.u1.b1', '8.v1.b1', '8.w1.a1'], 'contains': ['32.a1.a1', '32.c1.b1', '48.f1.b1', '112.d1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [504, -1, 855, -1, 462, -1, 666, -1], 'generators': [337, 448, 192, 672], 'label': '1344.9508.16.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.f1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506513
    {'ambient': '1344.9508', 'aut_centralizer_order': 224, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '72.48', 'aut_weyl_index': 448, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.p1.a1', '8.x1.a1', '8.x1.b1', '8.y1.a1', '8.z1.a1', '8.z1.b1'], 'contains': ['32.a1.a1', '32.d1.a1', '48.g1.a1', '112.e1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2382, -1, 2542, -1, 2014, -1, 1922, -1], 'generators': [789, 192, 448, 672], 'label': '1344.9508.16.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.g1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 74506514
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '56.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.q1.a1', '8.s1.a1', '8.s1.b1', '8.u1.a1', '8.u1.b1', '8.bb1.a1'], 'contains': ['32.a1.a1', '32.f1.a1', '48.h1.a1', '112.g1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [693, -1, 655, -1, 655, -1, 597, -1], 'generators': [3, 448, 192, 672], 'label': '1344.9508.16.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.h1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 74506515
    {'ambient': '1344.9508', 'aut_centralizer_order': 224, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '72.48', 'aut_weyl_index': 448, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.p1.a1', '8.y1.a1', '8.ba1.a1', '8.ba1.b1', '8.bd1.a1', '8.bd1.b1'], 'contains': ['32.a1.a1', '48.i1.a1', '112.h1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2151, -1, 2914, -1, 2205, -1, 1999, -1], 'generators': [5, 672, 448, 192], 'label': '1344.9508.16.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.i1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 74506516
    {'ambient': '1344.9508', 'aut_centralizer_order': 56, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '576.8609', 'aut_weyl_index': 56, 'centralizer': '48.d1.a1', 'complements': ['336.m1.a1', '336.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.b1.a1', '8.d1.a1', '8.h1.a1', '8.p1.a1', '8.y1.a1', '12.h1.a1', '28.b1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4442, 7433, 4742, 7216, 4869, 8925, 4173, 7913], 'generators': [5, 448, 336, 192, 8, 672], 'label': '1344.9508.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.b1.a1', '8.d1.a1', '8.h1.a1', '28.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 74506517
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '56.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.q1.a1', '8.t1.a1', '8.t1.b1', '8.v1.a1', '8.v1.b1', '8.bb1.a1'], 'contains': ['32.a1.a1', '48.j1.a1', '112.j1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [993, -1, 1331, -1, 1051, -1, 1249, -1], 'generators': [51, 672, 192, 448], 'label': '1344.9508.16.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.j1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 74506518
    {'ambient': '1344.9508', 'aut_centralizer_order': 16, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '504.162', 'aut_weyl_index': 64, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.r1.a1', '8.x1.a1', '8.z1.a1', '8.ba1.b1', '8.bc1.a1', '8.bd1.b1'], 'contains': ['32.a1.a1', '48.k1.a1', '112.k1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2292, -1, 3576, -1, 2109, -1, 2066, -1], 'generators': [1175, 448, 192, 672], 'label': '1344.9508.16.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.k1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1.a1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
  • id: 74506519
    {'ambient': '1344.9508', 'aut_centralizer_order': 16, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '504.162', 'aut_weyl_index': 64, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.b1', '8.r1.a1', '8.x1.b1', '8.z1.b1', '8.ba1.a1', '8.bc1.a1', '8.bd1.a1'], 'contains': ['32.a1.a1', '48.k1.b1', '112.k1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2292, -1, 3525, -1, 2109, -1, 2121, -1], 'generators': [7, 448, 192, 672], 'label': '1344.9508.16.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.k1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1.b1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
  • id: 74506520
    {'ambient': '1344.9508', 'aut_centralizer_order': 168, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.15', 'aut_weyl_index': 1344, 'centralizer': '8.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1'], 'contains': ['32.b1.a1', '32.c1.a1', '32.c1.b1', '48.l1.a1', '112.l1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [790, -1, 199, -1, 141, -1, 162, -1], 'generators': [1, 448, 192, 344], 'label': '1344.9508.16.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.o1.a1', 'old_label': '16.l1.a1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 74506521
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '84.7', 'aut_weyl_index': 384, 'centralizer': '112.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.a1'], 'contains': ['32.c1.a1', '32.e1.a1', '32.f1.a1', '48.m1.a1', '112.m1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [168, -1, 26, -1, 40, -1, 92, -1], 'generators': [1, 448, 192, 2], 'label': '1344.9508.16.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.s1.a1', 'old_label': '16.m1.a1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
  • id: 74506522
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '84.7', 'aut_weyl_index': 384, 'centralizer': '112.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.b1'], 'contains': ['32.c1.b1', '32.e1.b1', '32.f1.a1', '48.m1.b1', '112.m1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [168, -1, 279, -1, 40, -1, 28, -1], 'generators': [337, 448, 192, 722], 'label': '1344.9508.16.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.s1.b1', 'old_label': '16.m1.b1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1.b1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
  • id: 74506523
    {'ambient': '1344.9508', 'aut_centralizer_order': 12, 'aut_label': '21.a1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 252, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '7.a1.a1'], 'contains': ['42.a1.a1', '42.b1.a1', '42.c1.a1', '42.d1.a1', '42.e1.a1', '42.f1.a1', '42.g1.a1', '42.h1.a1', '42.h1.b1', '42.i1.a1', '42.i1.b1', '42.j1.a1', '42.j1.b1', '42.k1.a1', '42.k1.b1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [8789, -1, 9566, -1, 7905, -1, 7850, -1], 'generators': [1, 2, 4, 336], 'label': '1344.9508.21.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '21.a1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '21.a1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 74506524
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '56.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.b1.a1', '12.f1.a1', '12.g1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.e1.b1', '168.e1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3604, 671, 2139, 4025, 3970, 1204, 1680, 2104], 'generators': [2, 672, 192, 344], 'label': '1344.9508.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.b1.a1'], 'normal_contains': ['48.a1.a1', '48.b1.a1', '48.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506525
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '56.b1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '12.b1.a1', '12.f1.b1', '12.g1.b1'], 'contains': ['48.a1.a1', '48.b1.b1', '48.e1.a1', '168.e1.b1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3604, 671, 3244, 3602, 3970, 1204, 1813, 1352], 'generators': [722, 672, 192, 344], 'label': '1344.9508.24.a1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': ['8.a1.b1', '12.b1.a1'], 'normal_contains': ['48.a1.a1', '48.b1.b1', '48.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.b1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506526
    {'ambient': '1344.9508', 'aut_centralizer_order': 1344, 'aut_label': '24.b1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '24.15', 'aut_weyl_index': 1344, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1', '12.h1.a1', '12.i1.a1', '12.j1.a1', '12.k1.a1'], 'contains': ['48.a1.a1', '48.c1.a1', '48.d1.a1', '168.a1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6763, 3013, 5043, 5893, 6329, 3252, 5125, 3811], 'generators': [8, 192, 672, 336], 'label': '1344.9508.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.b1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1'], 'normal_contains': ['48.a1.a1', '48.c1.a1', '48.d1.a1', '168.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '672.1175', 'quotient_action_image': '8.5', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506541
    {'ambient': '1344.9508', 'aut_centralizer_order': 16, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '336.125', 'aut_weyl_index': 96, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.r1.a1', '12.g1.a1', '12.g1.b1', '12.i1.a1'], 'contains': ['48.a1.a1', '48.k1.a1', '48.k1.b1', '168.g1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3911, -1, 6050, -1, 4281, -1, 2426, -1], 'generators': [7, 672, 192, 344], 'label': '1344.9508.24.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.l1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506527
    {'ambient': '1344.9508', 'aut_centralizer_order': 14, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 14, 'centralizer': '96.a1.a1', 'complements': ['672.e1.a1', '672.e1.b1', '672.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.f1.a1', '4.h1.a1', '4.h1.b1', '4.k1.a1', '4.k1.b1', '6.b1.a1', '14.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5388, 8721, 6850, 8864, 5850, 8505, 5381, 8674], 'generators': [1, 672, 336, 192, 4, 448, 8], 'label': '1344.9508.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.f1.a1', '4.h1.b1', '4.h1.a1', '4.k1.b1', '4.k1.a1', '14.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '672.1175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '96.219'}
  • id: 74506528
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '1344.11434', 'aut_weyl_index': 24, 'centralizer': '112.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'contains': ['8.a1.a1', '8.a1.b1', '8.b1.a1', '8.e1.a1', '8.e1.b1', '8.f1.a1', '8.n1.a1', '12.b1.a1', '28.h1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3312, 244, 2554, 165, 3927, 230, 3586, 158], 'generators': [2, 192, 336, 448, 8, 672], 'label': '1344.9508.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'normal_contains': ['8.a1.a1', '8.a1.b1', '8.b1.a1', '8.e1.a1', '8.e1.b1', '8.f1.a1', '8.n1.a1', '12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '112.42'}
  • id: 74506529
    {'ambient': '1344.9508', 'aut_centralizer_order': 336, 'aut_label': '24.c1', 'aut_quo_index': 24, 'aut_stab_index': 2, 'aut_weyl_group': '48.45', 'aut_weyl_index': 672, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.a1.a1', '12.d1.a1', '12.e1.a1', '12.l1.a1', '12.o1.a1', '12.p1.a1', '12.q1.a1'], 'contains': ['48.c1.a1', '48.f1.a1', '168.b1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7445, 5066, 3912, 7989, 7132, 3818, 5494, 4687], 'generators': [1, 192, 672, 8], 'label': '1344.9508.24.c1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.c1.a1', 'normal_contained_in': ['8.c1.a1', '12.a1.a1', '12.d1.a1', '12.e1.a1'], 'normal_contains': ['48.c1.a1', '168.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506530
    {'ambient': '1344.9508', 'aut_centralizer_order': 336, 'aut_label': '24.c1', 'aut_quo_index': 24, 'aut_stab_index': 2, 'aut_weyl_group': '48.45', 'aut_weyl_index': 672, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.b1', '12.a1.a1', '12.d1.b1', '12.e1.b1', '12.l1.b1', '12.o1.b1', '12.p1.b1', '12.q1.b1'], 'contains': ['48.c1.a1', '48.f1.b1', '168.b1.b1'], 'core': '24.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7445, 5066, 6340, 7759, 7132, 3818, 5430, 4261], 'generators': [337, 192, 672, 8], 'label': '1344.9508.24.c1.b1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.c1.b1', 'normal_contained_in': ['8.c1.b1', '12.a1.a1', '12.d1.b1', '12.e1.b1'], 'normal_contains': ['48.c1.a1', '168.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506531
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '24.d1', 'aut_quo_index': 24, 'aut_stab_index': 2, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '56.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.b1.a1', '12.d1.a1', '12.e1.b1', '12.t1.a1', '12.w1.a1', '12.x1.a1', '12.y1.a1'], 'contains': ['48.b1.a1', '48.c1.a1', '48.e1.a1', '168.q1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6945, 1313, 6454, 4644, 6228, 2108, 5302, 2529], 'generators': [2, 672, 192, 8], 'label': '1344.9508.24.d1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.d1.a1', 'normal_contained_in': ['8.e1.a1', '12.b1.a1', '12.d1.a1', '12.e1.b1'], 'normal_contains': ['48.b1.a1', '48.c1.a1', '48.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.d1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506532
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '24.d1', 'aut_quo_index': 24, 'aut_stab_index': 2, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '56.e1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.e1.b1', '12.b1.a1', '12.d1.b1', '12.e1.a1', '12.t1.b1', '12.w1.b1', '12.x1.b1', '12.y1.b1'], 'contains': ['48.b1.b1', '48.c1.a1', '48.e1.b1', '168.q1.b1'], 'core': '24.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6945, 1313, 4434, 4875, 6228, 2108, 5238, 2749], 'generators': [722, 672, 192, 8], 'label': '1344.9508.24.d1.b1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.d1.b1', 'normal_contained_in': ['8.e1.b1', '12.b1.a1', '12.d1.b1', '12.e1.a1'], 'normal_contains': ['48.b1.b1', '48.c1.a1', '48.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.d1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.b1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506533
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '24.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '336.125', 'aut_weyl_index': 96, 'centralizer': '56.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.b1.a1', '12.m1.a1', '12.r1.a1'], 'contains': ['48.b1.a1', '48.b1.b1', '48.d1.a1', '168.s1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4222, 1868, 2903, 3363, 4040, 642, 1554, 1519], 'generators': [2, 672, 192, 336], 'label': '1344.9508.24.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': ['8.f1.a1', '12.b1.a1'], 'normal_contains': ['48.b1.a1', '48.b1.b1', '48.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.e1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506534
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '24.f1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '336.125', 'aut_weyl_index': 96, 'centralizer': '112.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '12.c1.a1', '12.d1.a1', '12.d1.b1', '12.u1.a1', '12.z1.a1', '12.ba1.a1', '12.ba1.b1'], 'contains': ['48.c1.a1', '48.h1.a1', '168.u1.a1'], 'core': '24.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7372, 3326, 4741, 6764, 7319, 2959, 5546, 4014], 'generators': [3, 672, 192, 8], 'label': '1344.9508.24.f1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.f1.a1', 'normal_contained_in': ['8.g1.a1', '12.c1.a1', '12.d1.b1', '12.d1.a1'], 'normal_contains': ['48.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.f1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
  • id: 74506535
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '24.g1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '336.125', 'aut_weyl_index': 96, 'centralizer': '112.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '12.c1.a1', '12.e1.a1', '12.e1.b1', '12.v1.a1', '12.bb1.a1', '12.bc1.a1', '12.bc1.b1'], 'contains': ['48.c1.a1', '48.j1.a1', '168.w1.a1'], 'core': '24.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8537, 3646, 6405, 6445, 7209, 3551, 5185, 3606], 'generators': [51, 672, 192, 8], 'label': '1344.9508.24.g1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.g1.a1', 'normal_contained_in': ['8.i1.a1', '12.c1.a1', '12.e1.b1', '12.e1.a1'], 'normal_contains': ['48.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.g1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.a1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
  • id: 74506536
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '24.h1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '336.125', 'aut_weyl_index': 96, 'centralizer': '56.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '12.b1.a1', '12.n1.a1', '12.s1.a1'], 'contains': ['48.d1.a1', '48.e1.a1', '48.e1.b1', '168.bb1.a1'], 'core': '24.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4164, 1029, 3641, 4204, 4101, 1451, 1863, 1665], 'generators': [10, 672, 192, 336], 'label': '1344.9508.24.h1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.h1.a1', 'normal_contained_in': ['8.n1.a1', '12.b1.a1'], 'normal_contains': ['48.d1.a1', '48.e1.a1', '48.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.h1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506537
    {'ambient': '1344.9508', 'aut_centralizer_order': 336, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.45', 'aut_weyl_index': 672, 'centralizer': '8.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '12.a1.a1', '12.f1.a1', '12.f1.b1'], 'contains': ['48.a1.a1', '48.f1.a1', '48.f1.b1', '48.l1.a1', '168.c1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2354, -1, 1339, -1, 2978, -1, 390, -1], 'generators': [1, 672, 192, 344], 'label': '1344.9508.24.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.i1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506538
    {'ambient': '1344.9508', 'aut_centralizer_order': 224, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.15', 'aut_weyl_index': 1344, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '12.g1.a1', '12.g1.b1', '12.h1.a1'], 'contains': ['48.a1.a1', '48.g1.a1', '48.i1.a1', '168.d1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4349, -1, 5692, -1, 4178, -1, 2617, -1], 'generators': [5, 192, 672, 344], 'label': '1344.9508.24.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.j1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506539
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '1344.11434', 'aut_weyl_index': 24, 'centralizer': '112.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.g1.a1', '8.i1.a1', '8.q1.a1', '8.bb1.a1', '12.c1.a1', '28.i1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4574, 874, 4281, 6672, 4520, 1702, 3764, 1373], 'generators': [3, 192, 336, 448, 8, 672], 'label': '1344.9508.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1', '8.g1.a1', '8.i1.a1', '12.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
  • id: 74506540
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '56.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '12.c1.a1', '12.f1.a1', '12.f1.b1'], 'contains': ['48.a1.a1', '48.h1.a1', '48.j1.a1', '168.f1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2689, -1, 1950, -1, 3643, -1, 732, -1], 'generators': [3, 672, 192, 344], 'label': '1344.9508.24.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.k1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 74506542
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '112.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.a1', '12.d1.a1', '12.f1.a1', '12.m1.a1'], 'contains': ['48.b1.a1', '48.f1.a1', '48.h1.a1', '48.m1.a1', '168.h1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2574, -1, 597, -1, 3093, -1, 310, -1], 'generators': [1, 672, 192, 2], 'label': '1344.9508.24.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.m1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506543
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '112.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.b1', '12.d1.b1', '12.f1.b1', '12.m1.a1'], 'contains': ['48.b1.b1', '48.f1.b1', '48.h1.a1', '48.m1.b1', '168.h1.b1'], 'core': '48.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2574, -1, 1560, -1, 3093, -1, 237, -1], 'generators': [337, 672, 192, 722], 'label': '1344.9508.24.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.m1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.b1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506544
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '112.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.t1.a1', '12.e1.a1', '12.f1.b1', '12.m1.a1'], 'contains': ['48.b1.b1', '48.f1.a1', '48.j1.a1', '168.i1.a1'], 'core': '48.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2842, -1, 2023, -1, 3278, -1, 461, -1], 'generators': [1, 672, 192, 722], 'label': '1344.9508.24.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.n1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506545
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '112.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.t1.b1', '12.e1.b1', '12.f1.a1', '12.m1.a1'], 'contains': ['48.b1.a1', '48.f1.b1', '48.j1.a1', '168.i1.b1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2842, -1, 1636, -1, 3278, -1, 788, -1], 'generators': [337, 672, 192, 2], 'label': '1344.9508.24.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.n1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1.b1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506546
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '112.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.u1.a1', '12.d1.a1', '12.f1.b1', '12.n1.a1'], 'contains': ['48.e1.a1', '48.f1.a1', '48.h1.a1', '168.j1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2765, -1, 1469, -1, 3359, -1, 907, -1], 'generators': [1, 672, 192, 10], 'label': '1344.9508.24.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.o1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506547
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '112.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.u1.b1', '12.d1.b1', '12.f1.a1', '12.n1.a1'], 'contains': ['48.e1.b1', '48.f1.b1', '48.h1.a1', '168.j1.b1'], 'core': '48.e1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2765, -1, 1735, -1, 3359, -1, 1026, -1], 'generators': [337, 672, 192, 58], 'label': '1344.9508.24.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.o1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.b1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506548
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '112.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1.a1', '12.e1.a1', '12.f1.a1', '12.n1.a1'], 'contains': ['48.e1.b1', '48.f1.a1', '48.j1.a1', '168.k1.a1'], 'core': '48.e1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2958, -1, 2350, -1, 3455, -1, 1093, -1], 'generators': [1, 672, 192, 58], 'label': '1344.9508.24.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.p1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506549
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '112.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1.b1', '12.e1.b1', '12.f1.b1', '12.n1.a1'], 'contains': ['48.e1.a1', '48.f1.b1', '48.j1.a1', '168.k1.b1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2958, -1, 2698, -1, 3455, -1, 1171, -1], 'generators': [337, 672, 192, 10], 'label': '1344.9508.24.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.p1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.b1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506550
    {'ambient': '1344.9508', 'aut_centralizer_order': 4, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '336.a1.a1', 'complements': ['336.m1.a1', '336.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.j1.a1', '8.j1.b1', '8.r1.a1', '8.bc1.a1', '12.i1.a1', '28.j1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4814, 2326, 5106, 2616, 4739, 2180, 4718, 3116], 'generators': [7, 192, 336, 672, 8, 448], 'label': '1344.9508.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1', '8.j1.a1', '8.j1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '336.161'}
  • id: 74506551
    {'ambient': '1344.9508', 'aut_centralizer_order': 336, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.45', 'aut_weyl_index': 672, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.w1.a1', '12.a1.a1', '12.m1.a1', '12.n1.a1'], 'contains': ['48.d1.a1', '48.f1.a1', '48.f1.b1', '168.l1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3129, -1, 1895, -1, 3729, -1, 847, -1], 'generators': [1, 192, 672, 336], 'label': '1344.9508.24.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.q1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.q1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506552
    {'ambient': '1344.9508', 'aut_centralizer_order': 16, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '336.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.x1.a1', '12.g1.a1', '12.r1.a1', '12.t1.a1'], 'contains': ['48.b1.a1', '48.g1.a1', '48.k1.a1', '168.m1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4744, -1, 6595, -1, 4377, -1, 2177, -1], 'generators': [789, 672, 192, 2], 'label': '1344.9508.24.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.r1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506553
    {'ambient': '1344.9508', 'aut_centralizer_order': 16, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '336.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.x1.b1', '12.g1.b1', '12.r1.a1', '12.t1.b1'], 'contains': ['48.b1.b1', '48.g1.a1', '48.k1.b1', '168.m1.b1'], 'core': '48.b1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [4744, -1, 5766, -1, 4377, -1, 2360, -1], 'generators': [789, 672, 192, 722], 'label': '1344.9508.24.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.r1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1.b1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506554
    {'ambient': '1344.9508', 'aut_centralizer_order': 224, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.15', 'aut_weyl_index': 1344, 'centralizer': '24.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.y1.a1', '12.h1.a1', '12.r1.a1', '12.s1.a1'], 'contains': ['48.d1.a1', '48.g1.a1', '48.i1.a1', '168.n1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4949, -1, 4956, -1, 4676, -1, 2547, -1], 'generators': [5, 192, 672, 336], 'label': '1344.9508.24.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.s1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.s1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506555
    {'ambient': '1344.9508', 'aut_centralizer_order': 16, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '336.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.z1.a1', '12.g1.b1', '12.s1.a1', '12.t1.a1'], 'contains': ['48.e1.a1', '48.g1.a1', '48.k1.a1', '168.o1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4628, -1, 6535, -1, 4473, -1, 2809, -1], 'generators': [789, 672, 192, 10], 'label': '1344.9508.24.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.t1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.t1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506556
    {'ambient': '1344.9508', 'aut_centralizer_order': 16, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '336.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.z1.b1', '12.g1.a1', '12.s1.a1', '12.t1.b1'], 'contains': ['48.e1.b1', '48.g1.a1', '48.k1.b1', '168.o1.b1'], 'core': '48.e1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [4628, -1, 5826, -1, 4473, -1, 2731, -1], 'generators': [789, 672, 192, 58], 'label': '1344.9508.24.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.t1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.t1.b1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506557
    {'ambient': '1344.9508', 'aut_centralizer_order': 224, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.45', 'aut_weyl_index': 672, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.h1.a1', '12.l1.a1', '12.l1.b1', '12.t1.a1', '12.t1.b1', '12.u1.a1', '12.v1.a1'], 'contains': ['48.c1.a1', '48.g1.a1', '168.p1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9442, -1, 7431, -1, 6881, -1, 5366, -1], 'generators': [789, 192, 672, 8], 'label': '1344.9508.24.u1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.u1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.u1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506558
    {'ambient': '1344.9508', 'aut_centralizer_order': 16, 'aut_label': '24.v1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '336.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ba1.a1', '12.g1.a1', '12.r1.a1', '12.w1.a1'], 'contains': ['48.b1.a1', '48.i1.a1', '48.k1.b1', '168.r1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4826, -1, 5560, -1, 4575, -1, 2236, -1], 'generators': [5, 672, 192, 2], 'label': '1344.9508.24.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.v1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.v1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506559
    {'ambient': '1344.9508', 'aut_centralizer_order': 16, 'aut_label': '24.v1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '336.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ba1.b1', '12.g1.b1', '12.r1.a1', '12.w1.b1'], 'contains': ['48.b1.b1', '48.i1.a1', '48.k1.a1', '168.r1.b1'], 'core': '48.b1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [4826, -1, 5931, -1, 4575, -1, 2300, -1], 'generators': [5, 672, 192, 722], 'label': '1344.9508.24.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.v1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.v1.b1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506560
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '24.w1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '112.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bb1.a1', '12.c1.a1', '12.m1.a1', '12.n1.a1'], 'contains': ['48.d1.a1', '48.h1.a1', '48.j1.a1', '168.t1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3218, -1, 2419, -1, 3821, -1, 967, -1], 'generators': [3, 672, 192, 336], 'label': '1344.9508.24.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.w1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.w1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506561
    {'ambient': '1344.9508', 'aut_centralizer_order': 56, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '576.8609', 'aut_weyl_index': 56, 'centralizer': '48.c1.a1', 'complements': ['336.m1.a1', '336.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.k1.a1', '8.k1.b1', '12.j1.a1', '28.c1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5976, 6877, 8637, 5455, 6639, 7226, 7246, 8674], 'generators': [4, 448, 192, 8, 336, 672], 'label': '1344.9508.4.f1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1', '8.k1.a1', '8.k1.b1', '28.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 74506562
    {'ambient': '1344.9508', 'aut_centralizer_order': 224, 'aut_label': '24.x1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.45', 'aut_weyl_index': 672, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.h1.a1', '12.o1.a1', '12.o1.b1', '12.w1.a1', '12.w1.b1', '12.z1.a1', '12.bb1.a1'], 'contains': ['48.c1.a1', '48.i1.a1', '168.v1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7558, -1, 7140, -1, 7783, -1, 5683, -1], 'generators': [5, 192, 672, 8], 'label': '1344.9508.24.x1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.x1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.x1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506563
    {'ambient': '1344.9508', 'aut_centralizer_order': 16, 'aut_label': '24.y1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '336.125', 'aut_weyl_index': 96, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '12.i1.a1', '12.p1.b1', '12.q1.a1', '12.t1.a1', '12.w1.b1', '12.ba1.a1', '12.bc1.a1'], 'contains': ['48.c1.a1', '48.k1.a1', '168.x1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9057, -1, 7479, -1, 7380, -1, 6233, -1], 'generators': [1175, 672, 192, 8], 'label': '1344.9508.24.y1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.y1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.y1.a1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
  • id: 74506564
    {'ambient': '1344.9508', 'aut_centralizer_order': 16, 'aut_label': '24.y1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '336.125', 'aut_weyl_index': 96, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.b1', '12.i1.a1', '12.p1.a1', '12.q1.b1', '12.t1.b1', '12.w1.a1', '12.ba1.b1', '12.bc1.b1'], 'contains': ['48.c1.a1', '48.k1.b1', '168.x1.b1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9057, -1, 7662, -1, 7380, -1, 5737, -1], 'generators': [7, 672, 192, 8], 'label': '1344.9508.24.y1.b1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.y1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.y1.b1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
  • id: 74506565
    {'ambient': '1344.9508', 'aut_centralizer_order': 224, 'aut_label': '24.z1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.15', 'aut_weyl_index': 1344, 'centralizer': '24.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '12.j1.a1', '12.l1.b1', '12.o1.a1', '12.x1.a1', '12.y1.b1', '12.ba1.b1', '12.bc1.a1'], 'contains': ['48.c1.a1', '168.y1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9217, -1, 8781, -1, 8911, -1, 6532, -1], 'generators': [4, 8, 672, 192], 'label': '1344.9508.24.z1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.z1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.z1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506566
    {'ambient': '1344.9508', 'aut_centralizer_order': 224, 'aut_label': '24.z1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.15', 'aut_weyl_index': 1344, 'centralizer': '24.z1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.b1', '12.j1.a1', '12.l1.a1', '12.o1.b1', '12.x1.b1', '12.y1.a1', '12.ba1.a1', '12.bc1.b1'], 'contains': ['48.c1.a1', '168.y1.b1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9217, -1, 9231, -1, 8911, -1, 6756, -1], 'generators': [124, 680, 672, 192], 'label': '1344.9508.24.z1.b1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.k1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.z1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.z1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506567
    {'ambient': '1344.9508', 'aut_centralizer_order': 64, 'aut_label': '24.ba1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '84.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '12.k1.a1', '12.p1.a1', '12.p1.b1', '12.v1.a1', '12.x1.a1', '12.x1.b1', '12.z1.a1'], 'contains': ['48.c1.a1', '168.z1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9345, -1, 9120, -1, 9140, -1, 6490, -1], 'generators': [6, 672, 192, 8], 'label': '1344.9508.24.ba1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.ba1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 74506568
    {'ambient': '1344.9508', 'aut_centralizer_order': 64, 'aut_label': '24.bb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '12.k1.a1', '12.q1.a1', '12.q1.b1', '12.u1.a1', '12.y1.a1', '12.y1.b1', '12.bb1.a1'], 'contains': ['48.c1.a1', '168.ba1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9865, -1, 9175, -1, 9315, -1, 6574, -1], 'generators': [1174, 672, 192, 680], 'label': '1344.9508.24.bb1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bb1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506569
    {'ambient': '1344.9508', 'aut_centralizer_order': 16, 'aut_label': '24.bc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '336.125', 'aut_weyl_index': 96, 'centralizer': '168.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bc1.a1', '12.i1.a1', '12.r1.a1', '12.s1.a1'], 'contains': ['48.d1.a1', '48.k1.a1', '48.k1.b1', '168.bc1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5128, -1, 5881, -1, 4886, -1, 2487, -1], 'generators': [7, 672, 192, 336], 'label': '1344.9508.24.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.bc1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 74506570
    {'ambient': '1344.9508', 'aut_centralizer_order': 16, 'aut_label': '24.bd1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '336.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.a1', '12.g1.b1', '12.s1.a1', '12.w1.a1'], 'contains': ['48.e1.a1', '48.i1.a1', '48.k1.b1', '168.bd1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4447, -1, 4702, -1, 4762, -1, 2869, -1], 'generators': [5, 672, 192, 10], 'label': '1344.9508.24.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.bd1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506571
    {'ambient': '1344.9508', 'aut_centralizer_order': 16, 'aut_label': '24.bd1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '336.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.b1', '12.g1.a1', '12.s1.a1', '12.w1.b1'], 'contains': ['48.e1.b1', '48.i1.a1', '48.k1.a1', '168.bd1.b1'], 'core': '48.e1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [4447, -1, 5609, -1, 4762, -1, 2670, -1], 'generators': [5, 672, 192, 58], 'label': '1344.9508.24.bd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.bd1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bd1.b1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506572
    {'ambient': '1344.9508', 'aut_centralizer_order': 16, 'aut_label': '4.g1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 16, 'centralizer': '168.a1.a1', 'complements': ['336.m1.a1', '336.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'contains': ['8.b1.a1', '8.l1.a1', '8.m1.a1', '12.k1.a1', '28.k1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8865, 5609, 8152, 777, 7677, 5942, 7064, 7337], 'generators': [6, 192, 8, 672, 336, 448], 'label': '1344.9508.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'normal_contains': ['8.b1.a1', '8.l1.a1', '8.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
  • id: 74506573
    {'ambient': '1344.9508', 'aut_centralizer_order': 504, 'aut_label': '28.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '64.264', 'aut_weyl_index': 504, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '14.a1.a1', '14.b1.a1', '14.c1.a1'], 'contains': ['56.a1.a1', '56.b1.a1', '56.b1.b1', '56.f1.a1', '56.o1.a1', '84.a1.a1'], 'core': '28.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3309, 8220, 3964, 8066, 3526, 7079, 5132, 7328], 'generators': [1, 672, 8, 336, 448], 'label': '1344.9508.28.a1.a1', 'mobius_quo': 0, 'mobius_sub': -14, 'normal_closure': '28.a1.a1', 'normal_contained_in': ['4.a1.a1', '14.a1.a1'], 'normal_contains': ['56.a1.a1', '56.b1.b1', '56.b1.a1', '84.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '28.a1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506574
    {'ambient': '1344.9508', 'aut_centralizer_order': 336, 'aut_label': '28.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '96.209', 'aut_weyl_index': 336, 'centralizer': '48.d1.a1', 'complements': ['48.m1.a1', '48.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '14.a1.a1', '14.d1.a1', '14.e1.a1'], 'contains': ['56.a1.a1', '56.c1.a1', '56.d1.a1', '56.g1.a1', '56.q1.a1', '84.d1.a1'], 'core': '28.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3939, 6952, 4840, 6534, 4342, 8009, 5799, 7533], 'generators': [5, 448, 8, 336, 672], 'label': '1344.9508.28.b1.a1', 'mobius_quo': 0, 'mobius_sub': -14, 'normal_closure': '28.b1.a1', 'normal_contained_in': ['4.b1.a1', '14.a1.a1'], 'normal_contains': ['56.a1.a1', '56.c1.a1', '56.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '28.b1.a1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '7.1', 'quotient_action_kernel_order': 7, 'quotient_fusion': None, 'short_label': '28.b1.a1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 74506575
    {'ambient': '1344.9508', 'aut_centralizer_order': 336, 'aut_label': '28.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '96.209', 'aut_weyl_index': 336, 'centralizer': '48.c1.a1', 'complements': ['48.m1.a1', '48.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '14.a1.a1', '14.f1.a1', '14.g1.a1'], 'contains': ['56.a1.a1', '56.e1.a1', '56.e1.b1', '84.h1.a1'], 'core': '28.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5963, 6582, 8272, 5724, 6033, 7447, 9797, 8055], 'generators': [4, 448, 336, 8, 672], 'label': '1344.9508.28.c1.a1', 'mobius_quo': 0, 'mobius_sub': -14, 'normal_closure': '28.c1.a1', 'normal_contained_in': ['4.f1.a1', '14.a1.a1'], 'normal_contains': ['56.a1.a1', '56.e1.a1', '56.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '28.c1.a1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '7.1', 'quotient_action_kernel_order': 7, 'quotient_fusion': None, 'short_label': '28.c1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 74506576
    {'ambient': '1344.9508', 'aut_centralizer_order': 168, 'aut_label': '28.d1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '96.209', 'aut_weyl_index': 336, 'centralizer': '48.e1.b1', 'complements': ['48.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '14.a1.a1', '14.h1.a1', '14.i1.a1'], 'contains': ['56.b1.a1', '56.c1.a1', '56.e1.b1', '84.j1.a1'], 'core': '28.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6338, 7215, 7509, 7800, 4413, 7762, 8001, 8272], 'generators': [1, 448, 124, 8, 672], 'label': '1344.9508.28.d1.a1', 'mobius_quo': 0, 'mobius_sub': -14, 'normal_closure': '28.d1.a1', 'normal_contained_in': ['4.h1.a1', '14.a1.a1'], 'normal_contains': ['56.b1.a1', '56.c1.a1', '56.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '28.d1.a1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '7.1', 'quotient_action_kernel_order': 7, 'quotient_fusion': None, 'short_label': '28.d1.a1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 74506577
    {'ambient': '1344.9508', 'aut_centralizer_order': 168, 'aut_label': '28.d1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '96.209', 'aut_weyl_index': 336, 'centralizer': '48.e1.a1', 'complements': ['48.m1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.h1.b1', '14.a1.a1', '14.h1.b1', '14.i1.b1'], 'contains': ['56.b1.b1', '56.c1.a1', '56.e1.a1', '84.j1.b1'], 'core': '28.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6338, 7215, 5781, 7645, 4413, 7762, 7905, 8420], 'generators': [337, 448, 4, 680, 672], 'label': '1344.9508.28.d1.b1', 'mobius_quo': 0, 'mobius_sub': -14, 'normal_closure': '28.d1.b1', 'normal_contained_in': ['4.h1.b1', '14.a1.a1'], 'normal_contains': ['56.b1.b1', '56.c1.a1', '56.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '28.d1.b1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '7.1', 'quotient_action_kernel_order': 7, 'quotient_fusion': None, 'short_label': '28.d1.b1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 74506578
    {'ambient': '1344.9508', 'aut_centralizer_order': 168, 'aut_label': '28.e1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '96.209', 'aut_weyl_index': 336, 'centralizer': '48.b1.a1', 'complements': ['48.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '14.a1.a1', '14.j1.a1', '14.k1.a1'], 'contains': ['56.b1.a1', '56.d1.a1', '56.e1.a1', '84.o1.a1'], 'core': '28.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5824, 7641, 7566, 6286, 6919, 8354, 8330, 8635], 'generators': [1, 448, 4, 8, 672], 'label': '1344.9508.28.e1.a1', 'mobius_quo': 0, 'mobius_sub': -14, 'normal_closure': '28.e1.a1', 'normal_contained_in': ['4.k1.a1', '14.a1.a1'], 'normal_contains': ['56.b1.a1', '56.d1.a1', '56.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '28.e1.a1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '7.1', 'quotient_action_kernel_order': 7, 'quotient_fusion': None, 'short_label': '28.e1.a1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 74506579
    {'ambient': '1344.9508', 'aut_centralizer_order': 168, 'aut_label': '28.e1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '96.209', 'aut_weyl_index': 336, 'centralizer': '48.b1.b1', 'complements': ['48.m1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.k1.b1', '14.a1.a1', '14.j1.b1', '14.k1.b1'], 'contains': ['56.b1.b1', '56.d1.a1', '56.e1.b1', '84.o1.b1'], 'core': '28.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5824, 7641, 6272, 7420, 6919, 8354, 8653, 7771], 'generators': [337, 448, 124, 680, 672], 'label': '1344.9508.28.e1.b1', 'mobius_quo': 0, 'mobius_sub': -14, 'normal_closure': '28.e1.b1', 'normal_contained_in': ['4.k1.b1', '14.a1.a1'], 'normal_contains': ['56.b1.b1', '56.d1.a1', '56.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '28.e1.b1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '7.1', 'quotient_action_kernel_order': 7, 'quotient_fusion': None, 'short_label': '28.e1.b1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 74506580
    {'ambient': '1344.9508', 'aut_centralizer_order': 72, 'aut_label': '28.f1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2016, 'centralizer': '112.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.x1.a1', '14.b1.a1'], 'contains': ['56.f1.a1', '56.h1.a1', '56.i1.a1', '56.k1.a1', '56.l1.b1', '56.m1.b1', '56.n1.a1', '84.b1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [556, -1, 1411, -1, 451, -1, 2930, -1], 'generators': [1, 672, 2, 344, 448], 'label': '1344.9508.28.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '28.f1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506581
    {'ambient': '1344.9508', 'aut_centralizer_order': 72, 'aut_label': '28.f1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2016, 'centralizer': '112.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.x1.b1', '14.b1.a1'], 'contains': ['56.f1.a1', '56.h1.b1', '56.i1.a1', '56.k1.b1', '56.l1.a1', '56.m1.a1', '56.n1.b1', '84.b1.b1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [556, -1, 1337, -1, 451, -1, 2866, -1], 'generators': [1, 672, 722, 344, 448], 'label': '1344.9508.28.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '28.f1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.f1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506582
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '28.g1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '48.51', 'aut_weyl_index': 672, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.y1.a1', '14.d1.a1'], 'contains': ['56.g1.a1', '56.h1.a1', '56.j1.a1', '56.p1.a1', '56.r1.b1', '56.t1.a1', '56.bd1.b1', '84.c1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [1840, -1, 3506, -1, 2547, -1, 3104, -1], 'generators': [5, 448, 2, 344, 672], 'label': '1344.9508.28.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '28.g1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.g1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 74506583
    {'ambient': '1344.9508', 'aut_centralizer_order': 28, 'aut_label': '4.h1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '576.8609', 'aut_weyl_index': 56, 'centralizer': '96.a1.a1', 'complements': ['336.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.h1.a1', '2.i1.a1'], 'contains': ['8.c1.a1', '8.d1.a1', '8.k1.b1', '12.l1.a1', '28.d1.a1'], 'core': '4.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6136, 8721, 7752, 9495, 5850, 8505, 5389, 9011], 'generators': [1, 448, 192, 8, 124, 672], 'label': '1344.9508.4.h1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.h1.a1', 'normal_contained_in': ['2.a1.a1', '2.h1.a1', '2.i1.a1'], 'normal_contains': ['8.c1.a1', '8.d1.a1', '8.k1.b1', '28.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.h1.a1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.h1.a1', 'subgroup_fusion': None, 'weyl_group': '96.219'}
  • id: 74506584
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '28.g1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '48.51', 'aut_weyl_index': 672, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.y1.b1', '14.d1.a1'], 'contains': ['56.g1.a1', '56.h1.b1', '56.j1.a1', '56.p1.b1', '56.r1.a1', '56.t1.b1', '56.bd1.a1', '84.c1.b1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [1840, -1, 3297, -1, 2547, -1, 3147, -1], 'generators': [5, 448, 722, 344, 672], 'label': '1344.9508.28.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '28.g1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.g1.b1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 74506585
    {'ambient': '1344.9508', 'aut_centralizer_order': 144, 'aut_label': '28.h1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1008, 'centralizer': '112.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '14.b1.a1', '14.d1.a1', '14.f1.a1'], 'contains': ['56.a1.a1', '56.h1.a1', '56.h1.b1', '56.s1.a1', '56.s1.b1', '56.u1.a1', '56.bb1.a1', '84.e1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [2337, -1, 3040, -1, 3424, -1, 4905, -1], 'generators': [2, 672, 8, 336, 448], 'label': '1344.9508.28.h1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.h1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.h1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 74506586
    {'ambient': '1344.9508', 'aut_centralizer_order': 144, 'aut_label': '28.i1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1008, 'centralizer': '112.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '14.b1.a1', '14.e1.a1', '14.g1.a1'], 'contains': ['56.a1.a1', '56.i1.a1', '56.v1.a1', '56.w1.a1', '56.x1.a1', '84.f1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5510, -1, 4481, -1, 3833, -1, 5202, -1], 'generators': [3, 672, 8, 336, 448], 'label': '1344.9508.28.i1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.i1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.i1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506587
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '28.j1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '192.1524', 'aut_weyl_index': 168, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '14.c1.a1', '14.d1.a1', '14.g1.a1'], 'contains': ['56.a1.a1', '56.j1.a1', '56.y1.a1', '56.y1.b1', '56.bc1.a1', '84.g1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [4120, -1, 5235, -1, 4246, -1, 6819, -1], 'generators': [7, 448, 8, 336, 672], 'label': '1344.9508.28.j1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.j1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.j1.a1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 74506588
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '28.k1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '48.51', 'aut_weyl_index': 672, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '14.c1.a1', '14.e1.a1', '14.f1.a1'], 'contains': ['56.a1.a1', '56.z1.a1', '56.ba1.a1', '84.i1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8367, -1, 8183, -1, 7385, -1, 9638, -1], 'generators': [6, 448, 336, 8, 672], 'label': '1344.9508.28.k1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.k1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.k1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 74506589
    {'ambient': '1344.9508', 'aut_centralizer_order': 72, 'aut_label': '28.l1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1008, 'centralizer': '112.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '14.b1.a1', '14.h1.a1', '14.j1.a1'], 'contains': ['56.b1.a1', '56.k1.a1', '56.m1.a1', '56.s1.a1', '56.w1.a1', '84.k1.a1'], 'core': '56.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [4021, -1, 4352, -1, 3731, -1, 5858, -1], 'generators': [1, 672, 2, 8, 448], 'label': '1344.9508.28.l1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.l1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.l1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506590
    {'ambient': '1344.9508', 'aut_centralizer_order': 72, 'aut_label': '28.l1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1008, 'centralizer': '112.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.b1', '14.b1.a1', '14.h1.b1', '14.j1.b1'], 'contains': ['56.b1.b1', '56.k1.b1', '56.m1.b1', '56.s1.b1', '56.w1.a1', '84.k1.b1'], 'core': '56.b1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [4021, -1, 4633, -1, 3731, -1, 5739, -1], 'generators': [337, 672, 722, 8, 448], 'label': '1344.9508.28.l1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.l1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.l1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506591
    {'ambient': '1344.9508', 'aut_centralizer_order': 72, 'aut_label': '28.m1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1008, 'centralizer': '112.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '14.b1.a1', '14.i1.a1', '14.k1.a1'], 'contains': ['56.b1.a1', '56.l1.a1', '56.n1.a1', '56.s1.b1', '56.x1.a1', '84.l1.a1'], 'core': '56.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5714, -1, 4045, -1, 3628, -1, 5668, -1], 'generators': [1, 672, 722, 8, 448], 'label': '1344.9508.28.m1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.m1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.m1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506592
    {'ambient': '1344.9508', 'aut_centralizer_order': 72, 'aut_label': '28.m1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1008, 'centralizer': '112.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.b1', '14.b1.a1', '14.i1.b1', '14.k1.b1'], 'contains': ['56.b1.b1', '56.l1.b1', '56.n1.b1', '56.s1.a1', '56.x1.a1', '84.l1.b1'], 'core': '56.b1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [5714, -1, 4777, -1, 3628, -1, 5590, -1], 'generators': [337, 672, 2, 8, 448], 'label': '1344.9508.28.m1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.m1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.m1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506593
    {'ambient': '1344.9508', 'aut_centralizer_order': 72, 'aut_label': '28.n1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1008, 'centralizer': '112.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.z1.a1', '14.b1.a1'], 'contains': ['56.k1.a1', '56.k1.b1', '56.l1.a1', '56.l1.b1', '56.o1.a1', '56.u1.a1', '56.v1.a1', '84.m1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [791, -1, 1470, -1, 916, -1, 2802, -1], 'generators': [1, 672, 2, 336, 448], 'label': '1344.9508.28.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '28.n1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.n1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506594
    {'ambient': '1344.9508', 'aut_centralizer_order': 28, 'aut_label': '4.h1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '576.8609', 'aut_weyl_index': 56, 'centralizer': '96.a1.a1', 'complements': ['336.m1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.h1.b1', '2.i1.b1'], 'contains': ['8.c1.b1', '8.d1.a1', '8.k1.a1', '12.l1.b1', '28.d1.b1'], 'core': '4.h1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6136, 8721, 6579, 9214, 5850, 8505, 5268, 9280], 'generators': [337, 448, 192, 680, 4, 672], 'label': '1344.9508.4.h1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.h1.b1', 'normal_contained_in': ['2.a1.a1', '2.h1.b1', '2.i1.b1'], 'normal_contains': ['8.c1.b1', '8.d1.a1', '8.k1.a1', '28.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.h1.b1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.h1.b1', 'subgroup_fusion': None, 'weyl_group': '96.219'}
  • id: 74506595
    {'ambient': '1344.9508', 'aut_centralizer_order': 72, 'aut_label': '28.o1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1008, 'centralizer': '112.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.ba1.a1', '14.b1.a1'], 'contains': ['56.m1.a1', '56.m1.b1', '56.n1.a1', '56.n1.b1', '56.o1.a1', '56.v1.a1', '56.bb1.a1', '84.n1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [1433, -1, 1825, -1, 1370, -1, 3000, -1], 'generators': [1, 672, 10, 336, 448], 'label': '1344.9508.28.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '28.o1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.o1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506596
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '28.p1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '96.209', 'aut_weyl_index': 336, 'centralizer': '168.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '14.c1.a1', '14.i1.a1', '14.j1.a1'], 'contains': ['56.b1.a1', '56.y1.b1', '56.z1.a1', '84.p1.a1'], 'core': '56.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6868, -1, 7866, -1, 6270, -1, 8735, -1], 'generators': [1, 448, 6, 8, 672], 'label': '1344.9508.28.p1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.p1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.p1.a1', 'subgroup_fusion': None, 'weyl_group': '24.8'}
  • id: 74506597
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '28.p1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '96.209', 'aut_weyl_index': 336, 'centralizer': '168.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.b1', '14.c1.a1', '14.i1.b1', '14.j1.b1'], 'contains': ['56.b1.b1', '56.y1.a1', '56.z1.a1', '84.p1.b1'], 'core': '56.b1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [6868, -1, 6398, -1, 6270, -1, 9118, -1], 'generators': [337, 448, 6, 8, 672], 'label': '1344.9508.28.p1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.p1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.p1.b1', 'subgroup_fusion': None, 'weyl_group': '24.8'}
  • id: 74506598
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '28.q1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '96.209', 'aut_weyl_index': 336, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '14.c1.a1', '14.h1.a1', '14.k1.a1'], 'contains': ['56.b1.a1', '56.y1.a1', '56.ba1.a1', '84.q1.a1'], 'core': '56.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8016, -1, 7792, -1, 6388, -1, 9476, -1], 'generators': [1, 448, 1174, 680, 672], 'label': '1344.9508.28.q1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.q1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.q1.a1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 74506599
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '28.q1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '96.209', 'aut_weyl_index': 336, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.b1', '14.c1.a1', '14.h1.b1', '14.k1.b1'], 'contains': ['56.b1.b1', '56.y1.b1', '56.ba1.a1', '84.q1.b1'], 'core': '56.b1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [8016, -1, 7035, -1, 6388, -1, 8920, -1], 'generators': [337, 448, 1174, 680, 672], 'label': '1344.9508.28.q1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.m1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.q1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.q1.b1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 74506600
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '28.r1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '96.209', 'aut_weyl_index': 336, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bb1.a1', '14.d1.a1'], 'contains': ['56.p1.a1', '56.p1.b1', '56.q1.a1', '56.t1.a1', '56.t1.b1', '56.u1.a1', '56.bc1.a1', '84.r1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2909, -1, 3425, -1, 2690, -1, 3061, -1], 'generators': [5, 448, 2, 336, 672], 'label': '1344.9508.28.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '28.r1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.r1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 74506601
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '28.s1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '96.209', 'aut_weyl_index': 336, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bc1.a1', '14.d1.a1'], 'contains': ['56.q1.a1', '56.r1.a1', '56.r1.b1', '56.bb1.a1', '56.bc1.a1', '56.bd1.a1', '56.bd1.b1', '84.s1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [1959, -1, 3105, -1, 2767, -1, 3200, -1], 'generators': [5, 448, 10, 336, 672], 'label': '1344.9508.28.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '28.s1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.s1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 74506602
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '28.t1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '96.209', 'aut_weyl_index': 336, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1', '14.d1.a1', '14.h1.a1', '14.i1.b1'], 'contains': ['56.c1.a1', '56.p1.a1', '56.r1.a1', '56.s1.a1', '56.y1.a1', '84.t1.a1'], 'core': '56.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6083, -1, 4907, -1, 4150, -1, 5973, -1], 'generators': [789, 448, 2, 8, 672], 'label': '1344.9508.28.t1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.t1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.t1.a1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 74506603
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '28.t1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '96.209', 'aut_weyl_index': 336, 'centralizer': '336.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.b1', '14.d1.a1', '14.h1.b1', '14.i1.a1'], 'contains': ['56.c1.a1', '56.p1.b1', '56.r1.b1', '56.s1.b1', '56.y1.b1', '84.t1.b1'], 'core': '56.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6083, -1, 5009, -1, 4150, -1, 5918, -1], 'generators': [789, 448, 722, 8, 672], 'label': '1344.9508.28.t1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.n1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.t1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.t1.b1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 74506604
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '28.u1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '96.209', 'aut_weyl_index': 336, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.o1.a1', '14.e1.a1', '14.h1.a1', '14.h1.b1'], 'contains': ['56.c1.a1', '56.w1.a1', '56.ba1.a1', '84.u1.a1'], 'core': '56.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7881, -1, 5860, -1, 4984, -1, 8044, -1], 'generators': [789, 448, 1174, 8, 672], 'label': '1344.9508.28.u1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.u1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.u1.a1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 74506605
    {'ambient': '1344.9508', 'aut_centralizer_order': 12, 'aut_label': '4.i1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '1344.11434', 'aut_weyl_index': 24, 'centralizer': '224.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.h1.a1', '2.j1.a1'], 'contains': ['8.c1.a1', '8.e1.a1', '8.g1.a1', '8.s1.a1', '8.u1.a1', '12.d1.a1', '28.l1.a1'], 'core': '4.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4312, 1406, 4089, 8476, 4376, 1204, 4267, 2057], 'generators': [1, 192, 8, 448, 2, 672], 'label': '1344.9508.4.i1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.i1.a1', 'normal_contained_in': ['2.b1.a1', '2.h1.a1', '2.j1.a1'], 'normal_contains': ['8.c1.a1', '8.e1.a1', '8.g1.a1', '12.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.i1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1.a1', 'subgroup_fusion': None, 'weyl_group': '224.178'}
  • id: 74506606
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '28.v1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '96.209', 'aut_weyl_index': 336, 'centralizer': '168.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.p1.a1', '14.e1.a1', '14.i1.a1', '14.i1.b1'], 'contains': ['56.c1.a1', '56.x1.a1', '56.z1.a1', '84.v1.a1'], 'core': '56.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7187, -1, 5821, -1, 4809, -1, 7809, -1], 'generators': [789, 448, 6, 680, 672], 'label': '1344.9508.28.v1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.v1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.v1.a1', 'subgroup_fusion': None, 'weyl_group': '24.8'}
  • id: 74506607
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '28.w1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '96.209', 'aut_weyl_index': 336, 'centralizer': '336.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '14.d1.a1', '14.j1.a1', '14.k1.b1'], 'contains': ['56.d1.a1', '56.s1.a1', '56.t1.a1', '56.y1.b1', '56.bd1.a1', '84.w1.a1'], 'core': '56.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [3847, -1, 5451, -1, 4721, -1, 6040, -1], 'generators': [5, 448, 2, 8, 672], 'label': '1344.9508.28.w1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.w1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.w1.a1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 74506608
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '28.w1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '96.209', 'aut_weyl_index': 336, 'centralizer': '336.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.b1', '14.d1.a1', '14.j1.b1', '14.k1.a1'], 'contains': ['56.d1.a1', '56.s1.b1', '56.t1.b1', '56.y1.a1', '56.bd1.b1', '84.w1.b1'], 'core': '56.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [3847, -1, 5164, -1, 4721, -1, 6741, -1], 'generators': [5, 448, 722, 8, 672], 'label': '1344.9508.28.w1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.q1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.w1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.w1.b1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 74506609
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '28.x1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '48.51', 'aut_weyl_index': 672, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.r1.a1', '14.f1.a1', '14.i1.b1', '14.j1.a1'], 'contains': ['56.e1.a1', '56.s1.a1', '56.z1.a1', '84.x1.a1'], 'core': '56.e1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6469, -1, 8020, -1, 7152, -1, 9396, -1], 'generators': [2, 448, 4, 8, 672], 'label': '1344.9508.28.x1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.x1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.x1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 74506610
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '28.x1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '48.51', 'aut_weyl_index': 672, 'centralizer': '168.q1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.r1.b1', '14.f1.a1', '14.i1.a1', '14.j1.b1'], 'contains': ['56.e1.b1', '56.s1.b1', '56.z1.a1', '84.x1.b1'], 'core': '56.e1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [6469, -1, 8346, -1, 7152, -1, 9716, -1], 'generators': [722, 448, 124, 680, 672], 'label': '1344.9508.28.x1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.r1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.x1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.x1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 74506611
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '28.y1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '48.51', 'aut_weyl_index': 672, 'centralizer': '336.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.s1.a1', '14.f1.a1', '14.h1.a1', '14.k1.b1'], 'contains': ['56.e1.b1', '56.s1.a1', '56.ba1.a1', '84.y1.a1'], 'core': '56.e1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [8207, -1, 8451, -1, 7268, -1, 9962, -1], 'generators': [2, 448, 124, 680, 672], 'label': '1344.9508.28.y1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.y1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.y1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 74506612
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '28.y1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '48.51', 'aut_weyl_index': 672, 'centralizer': '336.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.s1.b1', '14.f1.a1', '14.h1.b1', '14.k1.a1'], 'contains': ['56.e1.a1', '56.s1.b1', '56.ba1.a1', '84.y1.b1'], 'core': '56.e1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8207, -1, 8094, -1, 7268, -1, 9879, -1], 'generators': [722, 448, 4, 8, 672], 'label': '1344.9508.28.y1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.s1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.y1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.y1.b1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 74506613
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '28.z1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '96.209', 'aut_weyl_index': 336, 'centralizer': '168.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1', '14.e1.a1', '14.j1.a1', '14.j1.b1'], 'contains': ['56.d1.a1', '56.w1.a1', '56.z1.a1', '84.z1.a1'], 'core': '56.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6705, -1, 6885, -1, 7037, -1, 8468, -1], 'generators': [5, 448, 6, 8, 672], 'label': '1344.9508.28.z1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.z1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.z1.a1', 'subgroup_fusion': None, 'weyl_group': '24.8'}
  • id: 74506614
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '28.ba1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '96.209', 'aut_weyl_index': 336, 'centralizer': '336.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.u1.a1', '14.g1.a1', '14.h1.a1', '14.j1.b1'], 'contains': ['56.e1.b1', '56.w1.a1', '56.y1.a1', '84.ba1.a1'], 'core': '56.e1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [6203, -1, 7435, -1, 6152, -1, 9558, -1], 'generators': [3, 448, 124, 680, 672], 'label': '1344.9508.28.ba1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.ba1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 74506615
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '28.ba1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '96.209', 'aut_weyl_index': 336, 'centralizer': '336.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.u1.b1', '14.g1.a1', '14.h1.b1', '14.j1.a1'], 'contains': ['56.e1.a1', '56.w1.a1', '56.y1.b1', '84.ba1.b1'], 'core': '56.e1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6203, -1, 6960, -1, 6152, -1, 9200, -1], 'generators': [3, 448, 4, 8, 672], 'label': '1344.9508.28.ba1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.u1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.ba1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.ba1.b1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 74506616
    {'ambient': '1344.9508', 'aut_centralizer_order': 12, 'aut_label': '4.i1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '1344.11434', 'aut_weyl_index': 24, 'centralizer': '224.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.h1.b1', '2.j1.b1'], 'contains': ['8.c1.b1', '8.e1.b1', '8.g1.a1', '8.s1.b1', '8.u1.b1', '12.d1.b1', '28.l1.b1'], 'core': '4.i1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4312, 1406, 4400, 8120, 4376, 1204, 4078, 1716], 'generators': [337, 192, 8, 448, 722, 672], 'label': '1344.9508.4.i1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.i1.b1', 'normal_contained_in': ['2.b1.a1', '2.h1.b1', '2.j1.b1'], 'normal_contains': ['8.c1.b1', '8.e1.b1', '8.g1.a1', '12.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.i1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1.b1', 'subgroup_fusion': None, 'weyl_group': '224.178'}
  • id: 74506617
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '28.bb1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '96.209', 'aut_weyl_index': 336, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.v1.a1', '14.e1.a1', '14.k1.a1', '14.k1.b1'], 'contains': ['56.d1.a1', '56.x1.a1', '56.ba1.a1', '84.bb1.a1'], 'core': '56.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8111, -1, 7629, -1, 7481, -1, 8399, -1], 'generators': [5, 448, 1174, 680, 672], 'label': '1344.9508.28.bb1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.bb1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 74506618
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '28.bc1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '96.209', 'aut_weyl_index': 336, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.w1.a1', '14.g1.a1', '14.i1.b1', '14.k1.a1'], 'contains': ['56.e1.a1', '56.x1.a1', '56.y1.a1', '84.bc1.a1'], 'core': '56.e1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6562, -1, 6335, -1, 5933, -1, 9269, -1], 'generators': [51, 448, 4, 680, 672], 'label': '1344.9508.28.bc1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.bc1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 74506619
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '28.bc1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '96.209', 'aut_weyl_index': 336, 'centralizer': '336.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.w1.b1', '14.g1.a1', '14.i1.a1', '14.k1.b1'], 'contains': ['56.e1.b1', '56.x1.a1', '56.y1.b1', '84.bc1.b1'], 'core': '56.e1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [6562, -1, 7728, -1, 5933, -1, 8989, -1], 'generators': [51, 448, 124, 8, 672], 'label': '1344.9508.28.bc1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.w1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.bc1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.bc1.b1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 74506620
    {'ambient': '1344.9508', 'aut_centralizer_order': 2688, 'aut_label': '32.a1', 'aut_quo_index': 384, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 2688, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.b1.b1', '16.c1.a1', '16.d1.a1', '16.e1.a1', '16.e1.b1', '16.f1.a1', '16.f1.b1', '16.g1.a1', '16.h1.a1', '16.i1.a1', '16.j1.a1', '16.k1.a1', '16.k1.b1'], 'contains': ['64.a1.a1', '96.a1.a1', '224.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1150, 1870, 834, 2911, 1708, 2644, 1563, 3198], 'generators': [672, 192, 448], 'label': '1344.9508.32.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1', '16.b1.a1', '16.b1.b1', '16.c1.a1', '16.d1.a1', '16.e1.a1', '16.e1.b1'], 'normal_contains': ['64.a1.a1', '96.a1.a1', '224.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506621
    {'ambient': '1344.9508', 'aut_centralizer_order': 1344, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.5', 'aut_weyl_index': 2688, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.l1.a1'], 'contains': ['64.a1.a1', '96.b1.a1', '224.b1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [824, -1, 268, -1, 1296, -1, 844, -1], 'generators': [344, 192, 448], 'label': '1344.9508.32.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.b1.a1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506622
    {'ambient': '1344.9508', 'aut_centralizer_order': 336, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.5', 'aut_weyl_index': 2688, 'centralizer': '8.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '16.l1.a1', '16.m1.a1'], 'contains': ['64.a1.a1', '96.c1.a1', '224.c1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [112, -1, 28, -1, 1085, -1, 739, -1], 'generators': [1, 192, 448], 'label': '1344.9508.32.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.x1.a1', 'old_label': '32.c1.a1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506623
    {'ambient': '1344.9508', 'aut_centralizer_order': 336, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.5', 'aut_weyl_index': 2688, 'centralizer': '8.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.b1', '16.l1.a1', '16.m1.b1'], 'contains': ['64.a1.a1', '96.c1.b1', '224.c1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [112, -1, 215, -1, 1085, -1, 621, -1], 'generators': [337, 192, 448], 'label': '1344.9508.32.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.x1.b1', 'old_label': '32.c1.b1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506624
    {'ambient': '1344.9508', 'aut_centralizer_order': 224, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.12', 'aut_weyl_index': 896, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1'], 'contains': ['64.a1.a1', '96.d1.a1', '224.d1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1588, -1, 2288, -1, 2203, -1, 1922, -1], 'generators': [789, 448, 192], 'label': '1344.9508.32.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bc1.a1', 'old_label': '32.d1.a1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 74506625
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '84.7', 'aut_weyl_index': 384, 'centralizer': '56.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.m1.a1'], 'contains': ['64.a1.a1', '96.e1.a1', '224.e1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [214, -1, 92, -1, 917, -1, 791, -1], 'generators': [2, 192, 448], 'label': '1344.9508.32.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.j1.a1', 'old_label': '32.e1.a1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 74506626
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '84.7', 'aut_weyl_index': 384, 'centralizer': '56.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.b1', '16.m1.b1'], 'contains': ['64.a1.a1', '96.e1.b1', '224.e1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [214, -1, 510, -1, 917, -1, 569, -1], 'generators': [722, 192, 448], 'label': '1344.9508.32.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.j1.b1', 'old_label': '32.e1.b1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1.b1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 74506627
    {'ambient': '1344.9508', 'aut_centralizer_order': 12, 'aut_label': '4.j1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '1344.11434', 'aut_weyl_index': 24, 'centralizer': '224.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.i1.a1', '2.k1.a1'], 'contains': ['8.c1.a1', '8.e1.b1', '8.i1.a1', '8.t1.a1', '8.v1.a1', '12.e1.a1', '28.m1.a1'], 'core': '4.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4955, 1877, 4174, 7801, 4248, 2602, 3853, 1064], 'generators': [1, 192, 8, 448, 722, 672], 'label': '1344.9508.4.j1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.j1.a1', 'normal_contained_in': ['2.b1.a1', '2.i1.a1', '2.k1.a1'], 'normal_contains': ['8.c1.a1', '8.e1.b1', '8.i1.a1', '12.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.j1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1.a1', 'subgroup_fusion': None, 'weyl_group': '224.178'}
  • id: 74506628
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '84.7', 'aut_weyl_index': 384, 'centralizer': '56.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.m1.a1', '16.m1.b1'], 'contains': ['64.a1.a1', '96.f1.a1', '224.f1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [38, -1, 151, -1, 1009, -1, 505, -1], 'generators': [3, 192, 448], 'label': '1344.9508.32.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.z1.a1', 'old_label': '32.f1.a1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.f1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
  • id: 74506629
    {'ambient': '1344.9508', 'aut_centralizer_order': 168, 'aut_label': '42.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.226', 'aut_weyl_index': 504, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '14.a1.a1', '21.a1.a1'], 'contains': ['84.a1.a1', '84.d1.a1', '84.h1.a1', '84.j1.a1', '84.j1.b1', '84.o1.a1', '84.o1.b1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7885, -1, 8149, -1, 7831, -1, 7632, -1], 'generators': [1, 4, 336], 'label': '1344.9508.42.a1.a1', 'mobius_quo': None, 'mobius_sub': -7, 'normal_closure': '14.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '42.a1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.a1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 74506630
    {'ambient': '1344.9508', 'aut_centralizer_order': 72, 'aut_label': '42.b1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '64.226', 'aut_weyl_index': 504, 'centralizer': '224.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '14.b1.a1', '21.a1.a1'], 'contains': ['84.a1.a1', '84.b1.a1', '84.b1.b1', '84.e1.a1', '84.f1.a1', '84.k1.a1', '84.k1.b1', '84.l1.a1', '84.l1.b1', '84.m1.a1', '84.n1.a1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5981, -1, 3862, -1, 5163, -1, 4840, -1], 'generators': [1, 2, 8, 336], 'label': '1344.9508.42.b1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '42.b1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.b1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 74506631
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '42.c1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '64.264', 'aut_weyl_index': 504, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '14.c1.a1', '21.a1.a1'], 'contains': ['84.a1.a1', '84.g1.a1', '84.i1.a1', '84.p1.a1', '84.p1.b1', '84.q1.a1', '84.q1.b1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [8962, -1, 8975, -1, 8169, -1, 8827, -1], 'generators': [1, 6, 336], 'label': '1344.9508.42.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.c1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506632
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '42.d1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '64.226', 'aut_weyl_index': 504, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '14.d1.a1', '21.a1.a1'], 'contains': ['84.c1.a1', '84.c1.b1', '84.d1.a1', '84.e1.a1', '84.g1.a1', '84.r1.a1', '84.s1.a1', '84.t1.a1', '84.t1.b1', '84.w1.a1', '84.w1.b1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [7404, -1, 7161, -1, 5525, -1, 5268, -1], 'generators': [5, 2, 8, 336], 'label': '1344.9508.42.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.d1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.d1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 74506633
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '42.e1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1008, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '14.e1.a1', '21.a1.a1'], 'contains': ['84.d1.a1', '84.f1.a1', '84.i1.a1', '84.u1.a1', '84.v1.a1', '84.z1.a1', '84.bb1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [9482, -1, 8462, -1, 8275, -1, 7680, -1], 'generators': [5, 6, 336], 'label': '1344.9508.42.e1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.e1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.e1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506634
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '42.f1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1008, 'centralizer': '168.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '14.f1.a1', '21.a1.a1'], 'contains': ['84.e1.a1', '84.h1.a1', '84.i1.a1', '84.x1.a1', '84.x1.b1', '84.y1.a1', '84.y1.b1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [9075, -1, 9874, -1, 8938, -1, 9327, -1], 'generators': [2, 4, 336], 'label': '1344.9508.42.f1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.f1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506635
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '42.g1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '64.226', 'aut_weyl_index': 504, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '14.g1.a1', '21.a1.a1'], 'contains': ['84.f1.a1', '84.g1.a1', '84.h1.a1', '84.ba1.a1', '84.ba1.b1', '84.bc1.a1', '84.bc1.b1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [8642, -1, 9049, -1, 7975, -1, 9046, -1], 'generators': [3, 4, 336], 'label': '1344.9508.42.g1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.g1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.g1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 74506636
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '42.h1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1008, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '14.h1.a1', '21.a1.a1'], 'contains': ['84.j1.a1', '84.k1.a1', '84.q1.a1', '84.t1.a1', '84.u1.a1', '84.y1.a1', '84.ba1.a1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [8855, -1, 9741, -1, 8057, -1, 7953, -1], 'generators': [1, 2, 124], 'label': '1344.9508.42.h1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.h1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.h1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 74506637
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '42.h1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1008, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.b1', '14.h1.b1', '21.a1.a1'], 'contains': ['84.j1.b1', '84.k1.b1', '84.q1.b1', '84.t1.b1', '84.u1.a1', '84.y1.b1', '84.ba1.b1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 21, 'diagramx': [8855, -1, 9264, -1, 8057, -1, 7857, -1], 'generators': [337, 722, 4], 'label': '1344.9508.42.h1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.h1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.h1.b1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 74506638
    {'ambient': '1344.9508', 'aut_centralizer_order': 6, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '224.a1.a1', 'complements': ['672.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '4.d1.a1', '4.i1.a1', '4.i1.b1', '4.j1.a1', '4.j1.b1', '4.x1.a1', '4.x1.b1', '4.z1.a1', '4.ba1.a1', '6.a1.a1', '14.b1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3631, 1406, 3883, 7801, 4055, 1702, 3719, 1373], 'generators': [1, 672, 8, 336, 2, 192, 448], 'label': '1344.9508.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.c1.a1', '4.d1.a1', '4.i1.b1', '4.i1.a1', '4.j1.b1', '4.j1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '672.1175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '224.178'}
  • id: 74506639
    {'ambient': '1344.9508', 'aut_centralizer_order': 12, 'aut_label': '4.j1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '1344.11434', 'aut_weyl_index': 24, 'centralizer': '224.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.i1.b1', '2.k1.b1'], 'contains': ['8.c1.b1', '8.e1.a1', '8.i1.a1', '8.t1.b1', '8.v1.b1', '12.e1.b1', '28.m1.b1'], 'core': '4.j1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4955, 1877, 4555, 7519, 4248, 2602, 3932, 794], 'generators': [337, 192, 8, 448, 2, 672], 'label': '1344.9508.4.j1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.j1.b1', 'normal_contained_in': ['2.b1.a1', '2.i1.b1', '2.k1.b1'], 'normal_contains': ['8.c1.b1', '8.e1.a1', '8.i1.a1', '12.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.j1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1.b1', 'subgroup_fusion': None, 'weyl_group': '224.178'}
  • id: 74506640
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '42.i1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1008, 'centralizer': '336.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '14.i1.a1', '21.a1.a1'], 'contains': ['84.j1.a1', '84.l1.a1', '84.p1.a1', '84.t1.b1', '84.v1.a1', '84.x1.b1', '84.bc1.b1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [9147, -1, 9363, -1, 7901, -1, 7723, -1], 'generators': [1, 722, 124], 'label': '1344.9508.42.i1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.i1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.i1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506641
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '42.i1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1008, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.b1', '14.i1.b1', '21.a1.a1'], 'contains': ['84.j1.b1', '84.l1.b1', '84.p1.b1', '84.t1.a1', '84.v1.a1', '84.x1.a1', '84.bc1.a1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 21, 'diagramx': [9147, -1, 9468, -1, 7901, -1, 7766, -1], 'generators': [337, 2, 4], 'label': '1344.9508.42.i1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.i1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.i1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506642
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '42.j1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1008, 'centralizer': '336.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1.a1', '14.j1.a1', '21.a1.a1'], 'contains': ['84.k1.a1', '84.o1.a1', '84.p1.a1', '84.w1.a1', '84.x1.a1', '84.z1.a1', '84.ba1.b1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [7752, -1, 8545, -1, 8653, -1, 8117, -1], 'generators': [1, 2, 4], 'label': '1344.9508.42.j1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.j1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.j1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506643
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '42.j1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1008, 'centralizer': '336.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1.b1', '14.j1.b1', '21.a1.a1'], 'contains': ['84.k1.b1', '84.o1.b1', '84.p1.b1', '84.w1.b1', '84.x1.b1', '84.z1.a1', '84.ba1.a1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 21, 'diagramx': [7752, -1, 8736, -1, 8653, -1, 8561, -1], 'generators': [337, 722, 124], 'label': '1344.9508.42.j1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.j1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.j1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506644
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '42.k1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1008, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1.a1', '14.k1.a1', '21.a1.a1'], 'contains': ['84.l1.a1', '84.o1.a1', '84.q1.a1', '84.w1.b1', '84.y1.b1', '84.bb1.a1', '84.bc1.a1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [8774, -1, 8414, -1, 8771, -1, 8259, -1], 'generators': [1, 722, 4], 'label': '1344.9508.42.k1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.k1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.k1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 74506645
    {'ambient': '1344.9508', 'aut_centralizer_order': 24, 'aut_label': '42.k1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1008, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1.b1', '14.k1.b1', '21.a1.a1'], 'contains': ['84.l1.b1', '84.o1.b1', '84.q1.b1', '84.w1.a1', '84.y1.a1', '84.bb1.a1', '84.bc1.b1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 21, 'diagramx': [8774, -1, 8358, -1, 8771, -1, 8199, -1], 'generators': [337, 2, 124], 'label': '1344.9508.42.k1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.k1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.k1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.k1.b1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 74506646
    {'ambient': '1344.9508', 'aut_centralizer_order': 2688, 'aut_label': '48.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 2688, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.a1.b1', '24.b1.a1', '24.i1.a1', '24.j1.a1', '24.k1.a1', '24.l1.a1'], 'contains': ['96.a1.a1', '96.b1.a1', '336.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3251, 2512, 2142, 3702, 3802, 2938, 1768, 3400], 'generators': [344, 192, 672], 'label': '1344.9508.48.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1', '24.a1.b1', '24.b1.a1'], 'normal_contains': ['96.a1.a1', '336.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '12.5', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506647
    {'ambient': '1344.9508', 'aut_centralizer_order': 192, 'aut_label': '48.b1', 'aut_quo_index': 8, 'aut_stab_index': 2, 'aut_weyl_group': '84.7', 'aut_weyl_index': 384, 'centralizer': '28.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.a1.a1', '24.d1.a1', '24.e1.a1', '24.m1.a1', '24.n1.b1', '24.r1.a1', '24.v1.a1'], 'contains': ['96.a1.a1', '96.e1.a1', '336.f1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3863, 1430, 837, 3479, 3887, 1204, 1668, 2309], 'generators': [2, 192, 672], 'label': '1344.9508.48.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': ['16.b1.a1', '24.a1.a1', '24.d1.a1', '24.e1.a1'], 'normal_contains': ['96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 74506648
    {'ambient': '1344.9508', 'aut_centralizer_order': 192, 'aut_label': '48.b1', 'aut_quo_index': 8, 'aut_stab_index': 2, 'aut_weyl_group': '84.7', 'aut_weyl_index': 384, 'centralizer': '28.e1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.b1', '24.a1.b1', '24.d1.b1', '24.e1.a1', '24.m1.b1', '24.n1.a1', '24.r1.b1', '24.v1.b1'], 'contains': ['96.a1.a1', '96.e1.b1', '336.f1.b1'], 'core': '48.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3863, 1430, 2584, 3330, 3887, 1204, 1709, 1519], 'generators': [722, 192, 672], 'label': '1344.9508.48.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.b1.b1', 'normal_contained_in': ['16.b1.b1', '24.a1.b1', '24.d1.b1', '24.e1.a1'], 'normal_contains': ['96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1.b1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 74506649
    {'ambient': '1344.9508', 'aut_centralizer_order': 2688, 'aut_label': '48.c1', 'aut_quo_index': 672, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 2688, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.b1.a1', '24.c1.a1', '24.c1.b1', '24.d1.a1', '24.d1.b1', '24.f1.a1', '24.g1.a1', '24.u1.a1', '24.x1.a1', '24.y1.a1', '24.y1.b1', '24.z1.a1', '24.z1.b1', '24.ba1.a1', '24.bb1.a1'], 'contains': ['96.a1.a1', '336.b1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8105, 3448, 6584, 6371, 7132, 3231, 5567, 3671], 'generators': [8, 672, 192], 'label': '1344.9508.48.c1.a1', 'mobius_quo': 0, 'mobius_sub': -192, 'normal_closure': '48.c1.a1', 'normal_contained_in': ['16.c1.a1', '24.b1.a1', '24.c1.b1', '24.c1.a1', '24.d1.a1', '24.d1.b1', '24.f1.a1', '24.g1.a1'], 'normal_contains': ['96.a1.a1', '336.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.c1.a1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '12.4', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506650
    {'ambient': '1344.9508', 'aut_centralizer_order': 28, 'aut_label': '4.k1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '576.8609', 'aut_weyl_index': 56, 'centralizer': '96.a1.a1', 'complements': ['336.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.j1.a1', '2.k1.a1'], 'contains': ['8.c1.a1', '8.h1.a1', '8.k1.a1', '12.o1.a1', '28.e1.a1'], 'core': '4.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5177, 9240, 7580, 5878, 7051, 9442, 5766, 9615], 'generators': [1, 448, 192, 8, 4, 672], 'label': '1344.9508.4.k1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.k1.a1', 'normal_contained_in': ['2.a1.a1', '2.j1.a1', '2.k1.a1'], 'normal_contains': ['8.c1.a1', '8.h1.a1', '8.k1.a1', '28.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.k1.a1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.k1.a1', 'subgroup_fusion': None, 'weyl_group': '96.219'}
  • id: 74506651
    {'ambient': '1344.9508', 'aut_centralizer_order': 2688, 'aut_label': '48.d1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 2688, 'centralizer': '4.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.b1.a1', '24.e1.a1', '24.h1.a1', '24.q1.a1', '24.s1.a1', '24.w1.a1', '24.bc1.a1'], 'contains': ['96.a1.a1', '336.c1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4520, 2200, 4220, 4433, 4057, 2395, 1827, 3056], 'generators': [336, 672, 192], 'label': '1344.9508.48.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.d1.a1', 'normal_contained_in': ['16.d1.a1', '24.b1.a1', '24.e1.a1', '24.h1.a1'], 'normal_contains': ['96.a1.a1', '336.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.d1.a1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '12.4', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '48.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506652
    {'ambient': '1344.9508', 'aut_centralizer_order': 192, 'aut_label': '48.e1', 'aut_quo_index': 8, 'aut_stab_index': 2, 'aut_weyl_group': '84.7', 'aut_weyl_index': 384, 'centralizer': '28.d1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '24.a1.b1', '24.d1.a1', '24.h1.a1', '24.o1.a1', '24.p1.b1', '24.t1.a1', '24.bd1.a1'], 'contains': ['96.a1.a1', '336.i1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3804, 959, 4261, 3916, 3997, 1754, 1975, 1874], 'generators': [10, 192, 672], 'label': '1344.9508.48.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.e1.a1', 'normal_contained_in': ['16.e1.a1', '24.a1.b1', '24.d1.a1', '24.h1.a1'], 'normal_contains': ['96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.e1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 74506653
    {'ambient': '1344.9508', 'aut_centralizer_order': 192, 'aut_label': '48.e1', 'aut_quo_index': 8, 'aut_stab_index': 2, 'aut_weyl_group': '84.7', 'aut_weyl_index': 384, 'centralizer': '28.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.e1.b1', '24.a1.a1', '24.d1.b1', '24.h1.a1', '24.o1.b1', '24.p1.a1', '24.t1.b1', '24.bd1.b1'], 'contains': ['96.a1.a1', '336.i1.b1'], 'core': '48.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3804, 959, 2651, 4282, 3997, 1754, 1869, 2749], 'generators': [58, 192, 672], 'label': '1344.9508.48.e1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.e1.b1', 'normal_contained_in': ['16.e1.b1', '24.a1.a1', '24.d1.b1', '24.h1.a1'], 'normal_contains': ['96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.e1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.b1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 74506654
    {'ambient': '1344.9508', 'aut_centralizer_order': 672, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.5', 'aut_weyl_index': 2688, 'centralizer': '8.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '24.c1.a1', '24.i1.a1', '24.m1.a1', '24.n1.a1', '24.o1.a1', '24.p1.a1', '24.q1.a1'], 'contains': ['96.a1.a1', '96.c1.a1', '336.d1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2632, -1, 450, -1, 3193, -1, 1093, -1], 'generators': [1, 192, 672], 'label': '1344.9508.48.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.f1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506655
    {'ambient': '1344.9508', 'aut_centralizer_order': 672, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.5', 'aut_weyl_index': 2688, 'centralizer': '8.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.b1', '24.c1.b1', '24.i1.a1', '24.m1.b1', '24.n1.b1', '24.o1.b1', '24.p1.b1', '24.q1.a1'], 'contains': ['96.a1.a1', '96.c1.b1', '336.d1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2632, -1, 1625, -1, 3193, -1, 1211, -1], 'generators': [337, 192, 672], 'label': '1344.9508.48.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.f1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506656
    {'ambient': '1344.9508', 'aut_centralizer_order': 448, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.5', 'aut_weyl_index': 2688, 'centralizer': '24.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '24.j1.a1', '24.r1.a1', '24.r1.b1', '24.s1.a1', '24.t1.a1', '24.t1.b1', '24.u1.a1'], 'contains': ['96.a1.a1', '96.d1.a1', '336.e1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4915, -1, 6087, -1, 4239, -1, 2486, -1], 'generators': [789, 192, 672], 'label': '1344.9508.48.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.g1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506657
    {'ambient': '1344.9508', 'aut_centralizer_order': 192, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '84.7', 'aut_weyl_index': 384, 'centralizer': '56.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '24.f1.a1', '24.k1.a1', '24.m1.a1', '24.m1.b1', '24.o1.a1', '24.o1.b1', '24.w1.a1'], 'contains': ['96.a1.a1', '96.f1.a1', '336.g1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2510, -1, 875, -1, 3327, -1, 1152, -1], 'generators': [3, 192, 672], 'label': '1344.9508.48.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.h1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 74506658
    {'ambient': '1344.9508', 'aut_centralizer_order': 448, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.5', 'aut_weyl_index': 2688, 'centralizer': '24.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '24.j1.a1', '24.s1.a1', '24.v1.a1', '24.v1.b1', '24.x1.a1', '24.bd1.a1', '24.bd1.b1'], 'contains': ['96.a1.a1', '336.h1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5108, -1, 5411, -1, 4372, -1, 2602, -1], 'generators': [5, 672, 192], 'label': '1344.9508.48.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.i1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506659
    {'ambient': '1344.9508', 'aut_centralizer_order': 192, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '84.7', 'aut_weyl_index': 384, 'centralizer': '56.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '24.g1.a1', '24.k1.a1', '24.n1.a1', '24.n1.b1', '24.p1.a1', '24.p1.b1', '24.w1.a1'], 'contains': ['96.a1.a1', '336.j1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2807, -1, 2401, -1, 3576, -1, 1270, -1], 'generators': [51, 192, 672], 'label': '1344.9508.48.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.j1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 74506660
    {'ambient': '1344.9508', 'aut_centralizer_order': 32, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '84.7', 'aut_weyl_index': 384, 'centralizer': '168.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '24.l1.a1', '24.r1.a1', '24.t1.a1', '24.v1.b1', '24.y1.a1', '24.bc1.a1', '24.bd1.b1'], 'contains': ['96.a1.a1', '336.k1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4833, -1, 6231, -1, 4524, -1, 2426, -1], 'generators': [1175, 192, 672], 'label': '1344.9508.48.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.k1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 74506661
    {'ambient': '1344.9508', 'aut_centralizer_order': 28, 'aut_label': '4.k1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '576.8609', 'aut_weyl_index': 56, 'centralizer': '96.a1.a1', 'complements': ['336.m1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.j1.b1', '2.k1.b1'], 'contains': ['8.c1.b1', '8.h1.a1', '8.k1.b1', '12.o1.b1', '28.e1.b1'], 'core': '4.k1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5177, 9240, 6846, 8864, 7051, 9442, 6164, 8269], 'generators': [337, 448, 192, 680, 124, 672], 'label': '1344.9508.4.k1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.k1.b1', 'normal_contained_in': ['2.a1.a1', '2.j1.b1', '2.k1.b1'], 'normal_contains': ['8.c1.b1', '8.h1.a1', '8.k1.b1', '28.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.k1.b1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.k1.b1', 'subgroup_fusion': None, 'weyl_group': '96.219'}
  • id: 74506662
    {'ambient': '1344.9508', 'aut_centralizer_order': 32, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '84.7', 'aut_weyl_index': 384, 'centralizer': '168.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.b1', '24.l1.a1', '24.r1.b1', '24.t1.b1', '24.v1.a1', '24.y1.b1', '24.bc1.a1', '24.bd1.a1'], 'contains': ['96.a1.a1', '336.k1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4833, -1, 5875, -1, 4524, -1, 2546, -1], 'generators': [7, 192, 672], 'label': '1344.9508.48.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.k1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1.b1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 74506663
    {'ambient': '1344.9508', 'aut_centralizer_order': 336, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.5', 'aut_weyl_index': 2688, 'centralizer': '8.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '24.i1.a1'], 'contains': ['96.b1.a1', '96.c1.a1', '96.c1.b1', '336.l1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1166, -1, 298, -1, 1381, -1, 680, -1], 'generators': [1, 192, 344], 'label': '1344.9508.48.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.o1.a1', 'old_label': '48.l1.a1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 74506664
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '42.1', 'aut_weyl_index': 768, 'centralizer': '112.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.a1', '24.m1.a1'], 'contains': ['96.c1.a1', '96.e1.a1', '96.f1.a1', '336.m1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1060, -1, 87, -1, 1145, -1, 452, -1], 'generators': [1, 192, 2], 'label': '1344.9508.48.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.s1.a1', 'old_label': '48.m1.a1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
  • id: 74506665
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '42.1', 'aut_weyl_index': 768, 'centralizer': '112.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.b1', '24.m1.b1'], 'contains': ['96.c1.b1', '96.e1.b1', '96.f1.a1', '336.m1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1060, -1, 930, -1, 1145, -1, 411, -1], 'generators': [337, 192, 722], 'label': '1344.9508.48.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.s1.b1', 'old_label': '48.m1.b1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1.b1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
  • id: 74506666
    {'ambient': '1344.9508', 'aut_centralizer_order': 4032, 'aut_label': '56.a1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '28.a1.a1', '28.b1.a1', '28.c1.a1', '28.h1.a1', '28.i1.a1', '28.j1.a1', '28.k1.a1'], 'contains': ['112.a1.a1', '112.b1.a1', '112.c1.a1', '168.a1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3729, 4153, 4623, 5660, 5236, 5981, 6054, 5225], 'generators': [8, 336, 448, 672], 'label': '1344.9508.56.a1.a1', 'mobius_quo': 0, 'mobius_sub': 56, 'normal_closure': '56.a1.a1', 'normal_contained_in': ['8.b1.a1', '28.a1.a1', '28.b1.a1', '28.c1.a1'], 'normal_contains': ['112.a1.a1', '112.b1.a1', '112.c1.a1', '168.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '56.a1.a1', 'projective_image': '672.1175', 'quotient_action_image': '8.5', 'quotient_action_kernel': '7.1', 'quotient_action_kernel_order': 7, 'quotient_fusion': None, 'short_label': '56.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506667
    {'ambient': '1344.9508', 'aut_centralizer_order': 1008, 'aut_label': '56.b1', 'aut_quo_index': 24, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '8.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '28.a1.a1', '28.d1.a1', '28.e1.a1', '28.l1.a1', '28.m1.a1', '28.p1.a1', '28.q1.a1'], 'contains': ['112.b1.a1', '112.d1.a1', '168.b1.a1'], 'core': '56.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6067, 7728, 3393, 8006, 5337, 6804, 7126, 7337], 'generators': [1, 8, 448, 672], 'label': '1344.9508.56.b1.a1', 'mobius_quo': 0, 'mobius_sub': 56, 'normal_closure': '56.b1.a1', 'normal_contained_in': ['8.c1.a1', '28.a1.a1', '28.d1.a1', '28.e1.a1'], 'normal_contains': ['112.b1.a1', '168.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '56.b1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 74506668
    {'ambient': '1344.9508', 'aut_centralizer_order': 1008, 'aut_label': '56.b1', 'aut_quo_index': 24, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '8.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.b1', '28.a1.a1', '28.d1.b1', '28.e1.b1', '28.l1.b1', '28.m1.b1', '28.p1.b1', '28.q1.b1'], 'contains': ['112.b1.a1', '112.d1.b1', '168.b1.b1'], 'core': '56.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6067, 7728, 5181, 7719, 5337, 6804, 6994, 7117], 'generators': [337, 8, 448, 672], 'label': '1344.9508.56.b1.b1', 'mobius_quo': 0, 'mobius_sub': 56, 'normal_closure': '56.b1.b1', 'normal_contained_in': ['8.c1.b1', '28.a1.a1', '28.d1.b1', '28.e1.b1'], 'normal_contains': ['112.b1.a1', '168.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '56.b1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.b1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 74506669
    {'ambient': '1344.9508', 'aut_centralizer_order': 672, 'aut_label': '56.c1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '48.38', 'aut_weyl_index': 672, 'centralizer': '24.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '28.b1.a1', '28.d1.a1', '28.d1.b1', '28.t1.a1', '28.t1.b1', '28.u1.a1', '28.v1.a1'], 'contains': ['112.b1.a1', '112.e1.a1', '168.p1.a1'], 'core': '56.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6378, 6400, 5059, 7369, 5413, 7710, 6844, 7869], 'generators': [789, 8, 672, 448], 'label': '1344.9508.56.c1.a1', 'mobius_quo': 0, 'mobius_sub': 56, 'normal_closure': '56.c1.a1', 'normal_contained_in': ['8.d1.a1', '28.b1.a1', '28.d1.b1', '28.d1.a1'], 'normal_contains': ['112.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '56.c1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.8'}
  • id: 74506670
    {'ambient': '1344.9508', 'aut_centralizer_order': 672, 'aut_label': '56.d1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '48.38', 'aut_weyl_index': 672, 'centralizer': '24.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '28.b1.a1', '28.e1.a1', '28.e1.b1', '28.w1.a1', '28.w1.b1', '28.z1.a1', '28.bb1.a1'], 'contains': ['112.b1.a1', '112.h1.a1', '168.v1.a1'], 'core': '56.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5261, 7207, 5394, 5874, 5841, 7964, 7331, 7533], 'generators': [5, 8, 672, 448], 'label': '1344.9508.56.d1.a1', 'mobius_quo': 0, 'mobius_sub': 56, 'normal_closure': '56.d1.a1', 'normal_contained_in': ['8.h1.a1', '28.b1.a1', '28.e1.b1', '28.e1.a1'], 'normal_contains': ['112.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '56.d1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.8'}
  • id: 74506671
    {'ambient': '1344.9508', 'aut_centralizer_order': 672, 'aut_label': '56.e1', 'aut_quo_index': 24, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1344, 'centralizer': '24.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '28.c1.a1', '28.d1.b1', '28.e1.a1', '28.x1.a1', '28.y1.b1', '28.ba1.b1', '28.bc1.a1'], 'contains': ['112.b1.a1', '168.y1.a1'], 'core': '56.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6670, 6811, 7452, 5445, 6631, 7447, 8687, 8055], 'generators': [4, 8, 672, 448], 'label': '1344.9508.56.e1.a1', 'mobius_quo': 0, 'mobius_sub': 56, 'normal_closure': '56.e1.a1', 'normal_contained_in': ['8.k1.a1', '28.c1.a1', '28.d1.b1', '28.e1.a1'], 'normal_contains': ['112.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '56.e1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.e1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 74506672
    {'ambient': '1344.9508', 'aut_centralizer_order': 4, 'aut_label': '4.l1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '336.a1.a1', 'complements': ['336.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.i1.a1', '2.j1.a1'], 'contains': ['8.c1.a1', '8.j1.b1', '8.l1.a1', '12.p1.a1', '28.p1.a1'], 'core': '4.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6650, 8363, 7914, 2879, 6845, 5296, 6368, 5732], 'generators': [1, 192, 8, 672, 6, 448], 'label': '1344.9508.4.l1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.l1.a1', 'normal_contained_in': ['2.c1.a1', '2.i1.a1', '2.j1.a1'], 'normal_contains': ['8.c1.a1', '8.j1.b1', '8.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.l1.a1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.l1.a1', 'subgroup_fusion': None, 'weyl_group': '336.161'}
  • id: 74506673
    {'ambient': '1344.9508', 'aut_centralizer_order': 672, 'aut_label': '56.e1', 'aut_quo_index': 24, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1344, 'centralizer': '24.d1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.k1.b1', '28.c1.a1', '28.d1.a1', '28.e1.b1', '28.x1.b1', '28.y1.a1', '28.ba1.a1', '28.bc1.b1'], 'contains': ['112.b1.a1', '168.y1.b1'], 'core': '56.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6670, 6811, 7832, 7049, 6631, 7447, 8815, 7723], 'generators': [124, 680, 672, 448], 'label': '1344.9508.56.e1.b1', 'mobius_quo': 0, 'mobius_sub': 56, 'normal_closure': '56.e1.b1', 'normal_contained_in': ['8.k1.b1', '28.c1.a1', '28.d1.a1', '28.e1.b1'], 'normal_contains': ['112.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '56.e1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.e1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 74506674
    {'ambient': '1344.9508', 'aut_centralizer_order': 1008, 'aut_label': '56.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '8.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '28.a1.a1', '28.f1.a1', '28.f1.b1'], 'contains': ['112.a1.a1', '112.d1.a1', '112.d1.b1', '112.l1.a1', '168.c1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [447, -1, 999, -1, 249, -1, 3138, -1], 'generators': [1, 344, 672, 448], 'label': '1344.9508.56.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '28.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '56.f1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506675
    {'ambient': '1344.9508', 'aut_centralizer_order': 672, 'aut_label': '56.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1344, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '28.b1.a1', '28.g1.a1', '28.g1.b1'], 'contains': ['112.a1.a1', '112.e1.a1', '112.h1.a1', '168.d1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1895, -1, 3134, -1, 2354, -1, 4661, -1], 'generators': [5, 344, 672, 448], 'label': '1344.9508.56.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '28.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '56.g1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.g1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 74506676
    {'ambient': '1344.9508', 'aut_centralizer_order': 288, 'aut_label': '56.h1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '56.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '28.f1.a1', '28.g1.a1', '28.h1.a1'], 'contains': ['112.a1.a1', '112.f1.a1', '112.i1.b1', '168.e1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [946, -1, 2247, -1, 1669, -1, 4053, -1], 'generators': [2, 344, 448, 672], 'label': '1344.9508.56.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.h1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.h1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506677
    {'ambient': '1344.9508', 'aut_centralizer_order': 288, 'aut_label': '56.h1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '56.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '28.f1.b1', '28.g1.b1', '28.h1.a1'], 'contains': ['112.a1.a1', '112.f1.b1', '112.i1.a1', '168.e1.b1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [946, -1, 2364, -1, 1669, -1, 4116, -1], 'generators': [722, 344, 448, 672], 'label': '1344.9508.56.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.h1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.h1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506678
    {'ambient': '1344.9508', 'aut_centralizer_order': 288, 'aut_label': '56.i1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '56.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '28.f1.a1', '28.f1.b1', '28.i1.a1'], 'contains': ['112.a1.a1', '112.g1.a1', '112.j1.a1', '168.f1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [1449, -1, 1358, -1, 949, -1, 3398, -1], 'generators': [3, 344, 448, 672], 'label': '1344.9508.56.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.i1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506679
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '56.j1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '48.38', 'aut_weyl_index': 672, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.r1.a1', '28.g1.a1', '28.g1.b1', '28.j1.a1'], 'contains': ['112.a1.a1', '112.k1.a1', '112.k1.b1', '168.g1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2502, -1, 3792, -1, 2533, -1, 4494, -1], 'generators': [7, 344, 672, 448], 'label': '1344.9508.56.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '56.j1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.j1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 74506680
    {'ambient': '1344.9508', 'aut_centralizer_order': 144, 'aut_label': '56.k1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '56.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.a1', '28.f1.a1', '28.l1.a1', '28.n1.a1'], 'contains': ['112.d1.a1', '112.f1.a1', '112.g1.a1', '112.m1.a1', '168.h1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [346, -1, 872, -1, 354, -1, 3001, -1], 'generators': [1, 2, 672, 448], 'label': '1344.9508.56.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.k1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506681
    {'ambient': '1344.9508', 'aut_centralizer_order': 144, 'aut_label': '56.k1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '56.k1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.b1', '28.f1.b1', '28.l1.b1', '28.n1.a1'], 'contains': ['112.d1.b1', '112.f1.b1', '112.g1.a1', '112.m1.b1', '168.h1.b1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [346, -1, 1124, -1, 354, -1, 2928, -1], 'generators': [337, 722, 672, 448], 'label': '1344.9508.56.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.k1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.k1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506682
    {'ambient': '1344.9508', 'aut_centralizer_order': 144, 'aut_label': '56.l1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '56.m1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.t1.a1', '28.f1.b1', '28.m1.a1', '28.n1.a1'], 'contains': ['112.d1.a1', '112.f1.b1', '112.j1.a1', '168.i1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [654, -1, 1300, -1, 563, -1, 3334, -1], 'generators': [1, 722, 448, 672], 'label': '1344.9508.56.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.l1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506683
    {'ambient': '1344.9508', 'aut_centralizer_order': 4, 'aut_label': '4.l1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '336.a1.a1', 'complements': ['336.m1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.i1.b1', '2.j1.b1'], 'contains': ['8.c1.b1', '8.j1.a1', '8.l1.a1', '12.p1.b1', '28.p1.b1'], 'core': '4.l1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6650, 8363, 6993, 4775, 6845, 5296, 6610, 5079], 'generators': [337, 192, 8, 672, 6, 448], 'label': '1344.9508.4.l1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.l1.b1', 'normal_contained_in': ['2.c1.a1', '2.i1.b1', '2.j1.b1'], 'normal_contains': ['8.c1.b1', '8.j1.a1', '8.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.l1.b1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.l1.b1', 'subgroup_fusion': None, 'weyl_group': '336.161'}
  • id: 74506684
    {'ambient': '1344.9508', 'aut_centralizer_order': 144, 'aut_label': '56.l1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '56.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.t1.b1', '28.f1.a1', '28.m1.b1', '28.n1.a1'], 'contains': ['112.d1.b1', '112.f1.a1', '112.j1.a1', '168.i1.b1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [654, -1, 1417, -1, 563, -1, 3526, -1], 'generators': [337, 2, 448, 672], 'label': '1344.9508.56.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.l1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.l1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506685
    {'ambient': '1344.9508', 'aut_centralizer_order': 144, 'aut_label': '56.m1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '56.l1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.u1.a1', '28.f1.b1', '28.l1.a1', '28.o1.a1'], 'contains': ['112.d1.a1', '112.g1.a1', '112.i1.a1', '168.j1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [541, -1, 1061, -1, 747, -1, 3590, -1], 'generators': [1, 10, 448, 672], 'label': '1344.9508.56.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.m1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.m1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506686
    {'ambient': '1344.9508', 'aut_centralizer_order': 144, 'aut_label': '56.m1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '56.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.u1.b1', '28.f1.a1', '28.l1.b1', '28.o1.a1'], 'contains': ['112.d1.b1', '112.g1.a1', '112.i1.b1', '168.j1.b1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [541, -1, 1491, -1, 747, -1, 3729, -1], 'generators': [337, 58, 448, 672], 'label': '1344.9508.56.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.m1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.m1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506687
    {'ambient': '1344.9508', 'aut_centralizer_order': 144, 'aut_label': '56.n1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '56.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1.a1', '28.f1.a1', '28.m1.a1', '28.o1.a1'], 'contains': ['112.d1.a1', '112.i1.b1', '112.j1.a1', '168.k1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [751, -1, 1776, -1, 848, -1, 3843, -1], 'generators': [1, 58, 448, 672], 'label': '1344.9508.56.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.n1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.n1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506688
    {'ambient': '1344.9508', 'aut_centralizer_order': 144, 'aut_label': '56.n1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '56.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1.b1', '28.f1.b1', '28.m1.b1', '28.o1.a1'], 'contains': ['112.d1.b1', '112.i1.a1', '112.j1.a1', '168.k1.b1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [751, -1, 1914, -1, 848, -1, 3919, -1], 'generators': [337, 10, 448, 672], 'label': '1344.9508.56.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.n1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.n1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506689
    {'ambient': '1344.9508', 'aut_centralizer_order': 1008, 'aut_label': '56.o1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '8.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.w1.a1', '28.a1.a1', '28.n1.a1', '28.o1.a1'], 'contains': ['112.c1.a1', '112.d1.a1', '112.d1.b1', '168.l1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1035, -1, 1679, -1, 1153, -1, 3462, -1], 'generators': [1, 336, 448, 672], 'label': '1344.9508.56.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '28.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '56.o1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.o1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506690
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '56.p1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1344, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.x1.a1', '28.g1.a1', '28.r1.a1', '28.t1.a1'], 'contains': ['112.e1.a1', '112.f1.a1', '112.k1.a1', '168.m1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2331, -1, 3344, -1, 2292, -1, 4234, -1], 'generators': [789, 2, 672, 448], 'label': '1344.9508.56.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '56.p1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.p1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 74506691
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '56.p1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1344, 'centralizer': '336.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.x1.b1', '28.g1.b1', '28.r1.a1', '28.t1.b1'], 'contains': ['112.e1.a1', '112.f1.b1', '112.k1.b1', '168.m1.b1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2331, -1, 3288, -1, 2292, -1, 4433, -1], 'generators': [789, 722, 672, 448], 'label': '1344.9508.56.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '56.p1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.p1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 74506692
    {'ambient': '1344.9508', 'aut_centralizer_order': 672, 'aut_label': '56.q1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1344, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.y1.a1', '28.b1.a1', '28.r1.a1', '28.s1.a1'], 'contains': ['112.c1.a1', '112.e1.a1', '112.h1.a1', '168.n1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2404, -1, 3085, -1, 2746, -1, 4608, -1], 'generators': [5, 336, 672, 448], 'label': '1344.9508.56.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '28.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '56.q1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.q1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 74506693
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '56.r1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1344, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.z1.a1', '28.g1.b1', '28.s1.a1', '28.t1.a1'], 'contains': ['112.e1.a1', '112.i1.a1', '112.k1.a1', '168.o1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2053, -1, 3240, -1, 2431, -1, 4820, -1], 'generators': [789, 10, 672, 448], 'label': '1344.9508.56.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '56.r1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.r1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 74506694
    {'ambient': '1344.9508', 'aut_centralizer_order': 4, 'aut_label': '4.m1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '336.a1.a1', 'complements': ['336.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.h1.a1', '2.k1.a1'], 'contains': ['8.c1.a1', '8.j1.a1', '8.m1.a1', '12.q1.a1', '28.q1.a1'], 'core': '4.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7664, 5220, 7691, 3363, 6926, 3497, 6935, 6443], 'generators': [1, 192, 680, 672, 1174, 448], 'label': '1344.9508.4.m1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.m1.a1', 'normal_contained_in': ['2.c1.a1', '2.h1.a1', '2.k1.a1'], 'normal_contains': ['8.c1.a1', '8.j1.a1', '8.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.m1.a1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.m1.a1', 'subgroup_fusion': None, 'weyl_group': '336.161'}
  • id: 74506695
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '56.r1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1344, 'centralizer': '336.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.z1.b1', '28.g1.a1', '28.s1.a1', '28.t1.b1'], 'contains': ['112.e1.a1', '112.i1.b1', '112.k1.b1', '168.o1.b1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2053, -1, 3182, -1, 2431, -1, 4757, -1], 'generators': [789, 58, 672, 448], 'label': '1344.9508.56.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '56.r1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.r1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 74506696
    {'ambient': '1344.9508', 'aut_centralizer_order': 288, 'aut_label': '56.s1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '56.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '28.h1.a1', '28.l1.a1', '28.m1.b1', '28.t1.a1', '28.w1.a1', '28.x1.a1', '28.y1.a1'], 'contains': ['112.b1.a1', '112.f1.a1', '112.i1.a1', '168.q1.a1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5392, -1, 4826, -1, 5126, -1, 6173, -1], 'generators': [2, 8, 448, 672], 'label': '1344.9508.56.s1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.s1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.s1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506697
    {'ambient': '1344.9508', 'aut_centralizer_order': 288, 'aut_label': '56.s1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '56.s1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.b1', '28.h1.a1', '28.l1.b1', '28.m1.a1', '28.t1.b1', '28.w1.b1', '28.x1.b1', '28.y1.b1'], 'contains': ['112.b1.a1', '112.f1.b1', '112.i1.b1', '168.q1.b1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5392, -1, 4691, -1, 5126, -1, 6698, -1], 'generators': [722, 8, 448, 672], 'label': '1344.9508.56.s1.b1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.s1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.s1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506698
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '56.t1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1344, 'centralizer': '336.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ba1.a1', '28.g1.a1', '28.r1.a1', '28.w1.a1'], 'contains': ['112.f1.a1', '112.h1.a1', '112.k1.b1', '168.r1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2198, -1, 3594, -1, 2645, -1, 4295, -1], 'generators': [5, 2, 672, 448], 'label': '1344.9508.56.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '56.t1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.t1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 74506699
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '56.t1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1344, 'centralizer': '336.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ba1.b1', '28.g1.b1', '28.r1.a1', '28.w1.b1'], 'contains': ['112.f1.b1', '112.h1.a1', '112.k1.a1', '168.r1.b1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2198, -1, 3705, -1, 2645, -1, 4373, -1], 'generators': [5, 722, 672, 448], 'label': '1344.9508.56.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '56.t1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.t1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 74506700
    {'ambient': '1344.9508', 'aut_centralizer_order': 288, 'aut_label': '56.u1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '56.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '28.h1.a1', '28.n1.a1', '28.r1.a1'], 'contains': ['112.c1.a1', '112.f1.a1', '112.f1.b1', '168.s1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [1749, -1, 2306, -1, 1821, -1, 3989, -1], 'generators': [2, 336, 448, 672], 'label': '1344.9508.56.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.u1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.u1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506701
    {'ambient': '1344.9508', 'aut_centralizer_order': 288, 'aut_label': '56.v1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '56.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bb1.a1', '28.i1.a1', '28.n1.a1', '28.o1.a1'], 'contains': ['112.c1.a1', '112.g1.a1', '112.j1.a1', '168.t1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [1156, -1, 1845, -1, 1254, -1, 3660, -1], 'generators': [3, 336, 448, 672], 'label': '1344.9508.56.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.v1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.v1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506702
    {'ambient': '1344.9508', 'aut_centralizer_order': 288, 'aut_label': '56.w1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '56.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '28.i1.a1', '28.l1.a1', '28.l1.b1', '28.u1.a1', '28.z1.a1', '28.ba1.a1', '28.ba1.b1'], 'contains': ['112.b1.a1', '112.g1.a1', '168.u1.a1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5538, -1, 4896, -1, 5581, -1, 7189, -1], 'generators': [3, 8, 448, 672], 'label': '1344.9508.56.w1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.w1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.w1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 74506703
    {'ambient': '1344.9508', 'aut_centralizer_order': 288, 'aut_label': '56.x1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '56.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '28.i1.a1', '28.m1.a1', '28.m1.b1', '28.v1.a1', '28.bb1.a1', '28.bc1.a1', '28.bc1.b1'], 'contains': ['112.b1.a1', '112.j1.a1', '168.w1.a1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6842, -1, 5106, -1, 5489, -1, 6628, -1], 'generators': [51, 8, 448, 672], 'label': '1344.9508.56.x1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.x1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.x1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 74506704
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '56.y1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '48.38', 'aut_weyl_index': 672, 'centralizer': '168.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '28.j1.a1', '28.p1.b1', '28.q1.a1', '28.t1.a1', '28.w1.b1', '28.ba1.a1', '28.bc1.a1'], 'contains': ['112.b1.a1', '112.k1.a1', '168.x1.a1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6279, -1, 5465, -1, 5779, -1, 7706, -1], 'generators': [1175, 8, 672, 448], 'label': '1344.9508.56.y1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.y1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.y1.a1', 'subgroup_fusion': None, 'weyl_group': '24.8'}
  • id: 74506705
    {'ambient': '1344.9508', 'aut_centralizer_order': 4, 'aut_label': '4.m1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '336.a1.a1', 'complements': ['336.m1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.h1.b1', '2.k1.b1'], 'contains': ['8.c1.b1', '8.j1.b1', '8.m1.a1', '12.q1.b1', '28.q1.b1'], 'core': '4.m1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7664, 5220, 7302, 1870, 6926, 3497, 6423, 7085], 'generators': [337, 192, 680, 672, 1174, 448], 'label': '1344.9508.4.m1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.m1.b1', 'normal_contained_in': ['2.c1.a1', '2.h1.b1', '2.k1.b1'], 'normal_contains': ['8.c1.b1', '8.j1.b1', '8.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.m1.b1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.m1.b1', 'subgroup_fusion': None, 'weyl_group': '336.161'}
  • id: 74506706
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '56.y1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '48.38', 'aut_weyl_index': 672, 'centralizer': '168.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.b1', '28.j1.a1', '28.p1.a1', '28.q1.b1', '28.t1.b1', '28.w1.a1', '28.ba1.b1', '28.bc1.b1'], 'contains': ['112.b1.a1', '112.k1.b1', '168.x1.b1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6279, -1, 5536, -1, 5779, -1, 7529, -1], 'generators': [7, 8, 672, 448], 'label': '1344.9508.56.y1.b1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.y1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.y1.b1', 'subgroup_fusion': None, 'weyl_group': '24.8'}
  • id: 74506707
    {'ambient': '1344.9508', 'aut_centralizer_order': 192, 'aut_label': '56.z1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1344, 'centralizer': '84.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '28.k1.a1', '28.p1.a1', '28.p1.b1', '28.v1.a1', '28.x1.a1', '28.x1.b1', '28.z1.a1'], 'contains': ['112.b1.a1', '168.z1.a1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7150, -1, 7630, -1, 6693, -1, 8556, -1], 'generators': [6, 8, 672, 448], 'label': '1344.9508.56.z1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.z1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.z1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 74506708
    {'ambient': '1344.9508', 'aut_centralizer_order': 192, 'aut_label': '56.ba1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1344, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '28.k1.a1', '28.q1.a1', '28.q1.b1', '28.u1.a1', '28.y1.a1', '28.y1.b1', '28.bb1.a1'], 'contains': ['112.b1.a1', '168.ba1.a1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8226, -1, 7742, -1, 6755, -1, 8758, -1], 'generators': [1174, 680, 672, 448], 'label': '1344.9508.56.ba1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.ba1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 74506709
    {'ambient': '1344.9508', 'aut_centralizer_order': 288, 'aut_label': '56.bb1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '56.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '28.h1.a1', '28.o1.a1', '28.s1.a1'], 'contains': ['112.c1.a1', '112.i1.a1', '112.i1.b1', '168.bb1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [1611, -1, 2703, -1, 1913, -1, 4180, -1], 'generators': [10, 336, 448, 672], 'label': '1344.9508.56.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.bb1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506710
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '56.bc1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '48.38', 'aut_weyl_index': 672, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bc1.a1', '28.j1.a1', '28.r1.a1', '28.s1.a1'], 'contains': ['112.c1.a1', '112.k1.a1', '112.k1.b1', '168.bc1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2608, -1, 4057, -1, 2885, -1, 4554, -1], 'generators': [7, 336, 672, 448], 'label': '1344.9508.56.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '56.bc1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 74506711
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '56.bd1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1344, 'centralizer': '336.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.a1', '28.g1.b1', '28.s1.a1', '28.w1.a1'], 'contains': ['112.h1.a1', '112.i1.a1', '112.k1.b1', '168.bd1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [1980, -1, 3539, -1, 2823, -1, 4873, -1], 'generators': [5, 10, 672, 448], 'label': '1344.9508.56.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '56.bd1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 74506712
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '56.bd1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1344, 'centralizer': '336.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.b1', '28.g1.a1', '28.s1.a1', '28.w1.b1'], 'contains': ['112.h1.a1', '112.i1.b1', '112.k1.a1', '168.bd1.b1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [1980, -1, 3649, -1, 2823, -1, 4704, -1], 'generators': [5, 58, 672, 448], 'label': '1344.9508.56.bd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '56.bd1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.bd1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 74506713
    {'ambient': '1344.9508', 'aut_centralizer_order': 2688, 'aut_label': '64.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 2688, 'centralizer': '4.a1.a1', 'complements': ['21.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '32.c1.b1', '32.d1.a1', '32.e1.a1', '32.e1.b1', '32.f1.a1'], 'contains': ['192.a1.a1', '448.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [158, 1510, 243, 2911, 1261, 2931, 803, 3493], 'generators': [448, 192], 'label': '1344.9508.64.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': ['32.a1.a1'], 'normal_contains': ['192.a1.a1', '448.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.a1.a1', 'projective_image': '1344.9508', 'quotient_action_image': '4.2', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506714
    {'ambient': '1344.9508', 'aut_centralizer_order': 1008, 'aut_label': '84.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '32.49', 'aut_weyl_index': 1008, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '28.a1.a1', '42.a1.a1', '42.b1.a1', '42.c1.a1'], 'contains': ['168.a1.a1', '168.b1.a1', '168.b1.b1', '168.c1.a1', '168.l1.a1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6989, 8220, 4246, 8234, 5919, 4692, 5791, 5466], 'generators': [1, 8, 336], 'label': '1344.9508.84.a1.a1', 'mobius_quo': 0, 'mobius_sub': 42, 'normal_closure': '84.a1.a1', 'normal_contained_in': ['12.a1.a1', '28.a1.a1'], 'normal_contains': ['168.a1.a1', '168.b1.b1', '168.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '84.a1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506715
    {'ambient': '1344.9508', 'aut_centralizer_order': 144, 'aut_label': '84.b1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '112.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '28.f1.a1', '42.b1.a1'], 'contains': ['168.c1.a1', '168.e1.a1', '168.f1.a1', '168.h1.a1', '168.i1.b1', '168.j1.b1', '168.k1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2863, -1, 2067, -1, 3192, -1, 3270, -1], 'generators': [1, 2, 344], 'label': '1344.9508.84.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '84.b1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506716
    {'ambient': '1344.9508', 'aut_centralizer_order': 4, 'aut_label': '4.n1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '672.a1.a1', 'complements': ['336.l1.a1', '336.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.h1.a1', '2.i1.b1'], 'contains': ['8.d1.a1', '8.e1.a1', '8.j1.a1', '8.x1.a1', '8.z1.a1', '12.t1.a1', '28.t1.a1'], 'core': '4.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5506, 2716, 4810, 4574, 4633, 3217, 4400, 2863], 'generators': [789, 192, 8, 672, 2, 448], 'label': '1344.9508.4.n1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.n1.a1', 'normal_contained_in': ['2.d1.a1', '2.h1.a1', '2.i1.b1'], 'normal_contains': ['8.d1.a1', '8.e1.a1', '8.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.n1.a1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.n1.a1', 'subgroup_fusion': None, 'weyl_group': '672.1175'}
  • id: 74506717
    {'ambient': '1344.9508', 'aut_centralizer_order': 144, 'aut_label': '84.b1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '112.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.b1', '28.f1.b1', '42.b1.a1'], 'contains': ['168.c1.a1', '168.e1.b1', '168.f1.a1', '168.h1.b1', '168.i1.a1', '168.j1.a1', '168.k1.b1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2863, -1, 2142, -1, 3192, -1, 3206, -1], 'generators': [1, 722, 344], 'label': '1344.9508.84.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '84.b1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.b1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506718
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '84.c1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '336.k1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '28.g1.a1', '42.d1.a1'], 'contains': ['168.d1.a1', '168.e1.a1', '168.g1.a1', '168.m1.a1', '168.o1.b1', '168.r1.a1', '168.bd1.b1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [4350, -1, 6251, -1, 4824, -1, 4959, -1], 'generators': [5, 2, 344], 'label': '1344.9508.84.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.d1.a1', 'old_label': '84.c1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506719
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '84.c1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '336.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.b1', '28.g1.b1', '42.d1.a1'], 'contains': ['168.d1.a1', '168.e1.b1', '168.g1.a1', '168.m1.b1', '168.o1.a1', '168.r1.b1', '168.bd1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [4350, -1, 6080, -1, 4824, -1, 5001, -1], 'generators': [5, 722, 344], 'label': '1344.9508.84.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.d1.a1', 'old_label': '84.c1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.c1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506720
    {'ambient': '1344.9508', 'aut_centralizer_order': 672, 'aut_label': '84.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '28.b1.a1', '42.a1.a1', '42.d1.a1', '42.e1.a1'], 'contains': ['168.a1.a1', '168.d1.a1', '168.n1.a1', '168.p1.a1', '168.v1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7486, -1, 6961, -1, 6569, -1, 6113, -1], 'generators': [5, 8, 336], 'label': '1344.9508.84.d1.a1', 'mobius_quo': None, 'mobius_sub': 14, 'normal_closure': '28.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '84.d1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506721
    {'ambient': '1344.9508', 'aut_centralizer_order': 288, 'aut_label': '84.e1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '56.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '28.h1.a1', '42.b1.a1', '42.d1.a1', '42.f1.a1'], 'contains': ['168.a1.a1', '168.e1.a1', '168.e1.b1', '168.q1.a1', '168.q1.b1', '168.s1.a1', '168.bb1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6780, -1, 5208, -1, 5717, -1, 5630, -1], 'generators': [2, 8, 336], 'label': '1344.9508.84.e1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '84.e1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506722
    {'ambient': '1344.9508', 'aut_centralizer_order': 288, 'aut_label': '84.f1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '112.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '28.i1.a1', '42.b1.a1', '42.e1.a1', '42.g1.a1'], 'contains': ['168.a1.a1', '168.f1.a1', '168.t1.a1', '168.u1.a1', '168.w1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7104, -1, 4630, -1, 6151, -1, 5844, -1], 'generators': [3, 8, 336], 'label': '1344.9508.84.f1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '84.f1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.f1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506723
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '84.g1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '32.49', 'aut_weyl_index': 1008, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '28.j1.a1', '42.c1.a1', '42.d1.a1', '42.g1.a1'], 'contains': ['168.a1.a1', '168.g1.a1', '168.x1.a1', '168.x1.b1', '168.bc1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [7560, -1, 7241, -1, 6492, -1, 7384, -1], 'generators': [7, 8, 336], 'label': '1344.9508.84.g1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.g1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.g1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506724
    {'ambient': '1344.9508', 'aut_centralizer_order': 672, 'aut_label': '84.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '24.ba1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '28.c1.a1', '42.a1.a1', '42.f1.a1', '42.g1.a1'], 'contains': ['168.a1.a1', '168.y1.a1', '168.y1.b1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8274, -1, 9607, -1, 7505, -1, 8165, -1], 'generators': [4, 336], 'label': '1344.9508.84.h1.a1', 'mobius_quo': None, 'mobius_sub': 14, 'normal_closure': '28.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '84.h1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.h1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506725
    {'ambient': '1344.9508', 'aut_centralizer_order': 192, 'aut_label': '84.i1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '84.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '28.k1.a1', '42.c1.a1', '42.e1.a1', '42.f1.a1'], 'contains': ['168.a1.a1', '168.z1.a1', '168.ba1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [9441, -1, 9660, -1, 8166, -1, 8047, -1], 'generators': [6, 336], 'label': '1344.9508.84.i1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.i1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506726
    {'ambient': '1344.9508', 'aut_centralizer_order': 336, 'aut_label': '84.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '48.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '28.d1.a1', '42.a1.a1', '42.h1.a1', '42.i1.a1'], 'contains': ['168.b1.a1', '168.p1.a1', '168.y1.b1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8460, -1, 9974, -1, 6810, -1, 7043, -1], 'generators': [1, 124], 'label': '1344.9508.84.j1.a1', 'mobius_quo': None, 'mobius_sub': 14, 'normal_closure': '28.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '84.j1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.j1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506727
    {'ambient': '1344.9508', 'aut_centralizer_order': 4, 'aut_label': '4.n1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '672.a1.a1', 'complements': ['336.l1.a1', '336.m1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.h1.b1', '2.i1.a1'], 'contains': ['8.d1.a1', '8.e1.b1', '8.j1.b1', '8.x1.b1', '8.z1.b1', '12.t1.b1', '28.t1.b1'], 'core': '4.n1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5506, 2716, 4877, 2072, 4633, 3217, 4344, 3561], 'generators': [789, 192, 8, 672, 722, 448], 'label': '1344.9508.4.n1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.n1.b1', 'normal_contained_in': ['2.d1.a1', '2.h1.b1', '2.i1.a1'], 'normal_contains': ['8.d1.a1', '8.e1.b1', '8.j1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.n1.b1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.n1.b1', 'subgroup_fusion': None, 'weyl_group': '672.1175'}
  • id: 74506728
    {'ambient': '1344.9508', 'aut_centralizer_order': 336, 'aut_label': '84.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '48.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.b1', '28.d1.b1', '42.a1.a1', '42.h1.b1', '42.i1.b1'], 'contains': ['168.b1.b1', '168.p1.a1', '168.y1.a1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [8460, -1, 9256, -1, 6810, -1, 6945, -1], 'generators': [337, 4], 'label': '1344.9508.84.j1.b1', 'mobius_quo': None, 'mobius_sub': 14, 'normal_closure': '28.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '84.j1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.j1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506729
    {'ambient': '1344.9508', 'aut_centralizer_order': 144, 'aut_label': '84.k1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '112.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '28.l1.a1', '42.b1.a1', '42.h1.a1', '42.j1.a1'], 'contains': ['168.b1.a1', '168.h1.a1', '168.j1.a1', '168.q1.a1', '168.u1.a1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6901, -1, 4471, -1, 6073, -1, 6286, -1], 'generators': [1, 2, 8], 'label': '1344.9508.84.k1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '84.k1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.k1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506730
    {'ambient': '1344.9508', 'aut_centralizer_order': 144, 'aut_label': '84.k1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '112.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.b1', '28.l1.b1', '42.b1.a1', '42.h1.b1', '42.j1.b1'], 'contains': ['168.b1.b1', '168.h1.b1', '168.j1.b1', '168.q1.b1', '168.u1.a1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [6901, -1, 4762, -1, 6073, -1, 5984, -1], 'generators': [337, 722, 8], 'label': '1344.9508.84.k1.b1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '84.k1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.k1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506731
    {'ambient': '1344.9508', 'aut_centralizer_order': 144, 'aut_label': '84.l1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '112.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '28.m1.a1', '42.b1.a1', '42.i1.a1', '42.k1.a1'], 'contains': ['168.b1.a1', '168.i1.a1', '168.k1.a1', '168.q1.b1', '168.w1.a1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7259, -1, 4417, -1, 5996, -1, 5930, -1], 'generators': [1, 722, 8], 'label': '1344.9508.84.l1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '84.l1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.l1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506732
    {'ambient': '1344.9508', 'aut_centralizer_order': 144, 'aut_label': '84.l1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '112.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.b1', '28.m1.b1', '42.b1.a1', '42.i1.b1', '42.k1.b1'], 'contains': ['168.b1.b1', '168.i1.b1', '168.k1.b1', '168.q1.a1', '168.w1.a1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [7259, -1, 5507, -1, 5996, -1, 5887, -1], 'generators': [337, 2, 8], 'label': '1344.9508.84.l1.b1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '84.l1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.l1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506733
    {'ambient': '1344.9508', 'aut_centralizer_order': 144, 'aut_label': '84.m1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '112.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '28.n1.a1', '42.b1.a1'], 'contains': ['168.h1.a1', '168.h1.b1', '168.i1.a1', '168.i1.b1', '168.l1.a1', '168.s1.a1', '168.t1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [3122, -1, 2217, -1, 3557, -1, 3069, -1], 'generators': [1, 2, 336], 'label': '1344.9508.84.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '84.m1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.m1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506734
    {'ambient': '1344.9508', 'aut_centralizer_order': 144, 'aut_label': '84.n1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '112.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '28.o1.a1', '42.b1.a1'], 'contains': ['168.j1.a1', '168.j1.b1', '168.k1.a1', '168.k1.b1', '168.l1.a1', '168.t1.a1', '168.bb1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [3221, -1, 3305, -1, 3899, -1, 3783, -1], 'generators': [1, 10, 336], 'label': '1344.9508.84.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '84.n1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.n1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506735
    {'ambient': '1344.9508', 'aut_centralizer_order': 336, 'aut_label': '84.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '28.e1.a1', '42.a1.a1', '42.j1.a1', '42.k1.a1'], 'contains': ['168.b1.a1', '168.v1.a1', '168.y1.a1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8059, -1, 7734, -1, 7862, -1, 7244, -1], 'generators': [1, 4], 'label': '1344.9508.84.o1.a1', 'mobius_quo': None, 'mobius_sub': 14, 'normal_closure': '28.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '84.o1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.o1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506736
    {'ambient': '1344.9508', 'aut_centralizer_order': 336, 'aut_label': '84.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '48.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.b1', '28.e1.b1', '42.a1.a1', '42.j1.b1', '42.k1.b1'], 'contains': ['168.b1.b1', '168.v1.a1', '168.y1.b1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [8059, -1, 8042, -1, 7862, -1, 7485, -1], 'generators': [337, 124], 'label': '1344.9508.84.o1.b1', 'mobius_quo': None, 'mobius_sub': 14, 'normal_closure': '28.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '84.o1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.o1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506737
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '84.p1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '168.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1.a1', '28.p1.a1', '42.c1.a1', '42.i1.a1', '42.j1.a1'], 'contains': ['168.b1.a1', '168.x1.b1', '168.z1.a1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [8573, -1, 8533, -1, 7638, -1, 7574, -1], 'generators': [1, 6], 'label': '1344.9508.84.p1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.p1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.p1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 74506738
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '4.o1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '336.c1.a1', 'complements': ['336.l1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.h1.a1', '2.h1.b1'], 'contains': ['8.d1.a1', '8.g1.a1', '8.m1.a1', '12.u1.a1', '28.u1.a1'], 'core': '4.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7844, 4522, 6695, 6391, 6028, 5576, 5456, 6892], 'generators': [789, 192, 8, 672, 1174, 448], 'label': '1344.9508.4.o1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.o1.a1', 'normal_contained_in': ['2.e1.a1', '2.h1.b1', '2.h1.a1'], 'normal_contains': ['8.d1.a1', '8.g1.a1', '8.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.o1.a1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.o1.a1', 'subgroup_fusion': None, 'weyl_group': '336.161'}
  • id: 74506739
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '84.p1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '168.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1.b1', '28.p1.b1', '42.c1.a1', '42.i1.b1', '42.j1.b1'], 'contains': ['168.b1.b1', '168.x1.a1', '168.z1.a1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 21, 'diagramx': [8573, -1, 9034, -1, 7638, -1, 7750, -1], 'generators': [337, 6], 'label': '1344.9508.84.p1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.p1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.p1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 74506740
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '84.q1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1', '28.q1.a1', '42.c1.a1', '42.h1.a1', '42.k1.a1'], 'contains': ['168.b1.a1', '168.x1.a1', '168.ba1.a1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [8858, -1, 9104, -1, 7704, -1, 7947, -1], 'generators': [1, 1174], 'label': '1344.9508.84.q1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.q1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.q1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506741
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '84.q1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.b1', '28.q1.b1', '42.c1.a1', '42.h1.b1', '42.k1.b1'], 'contains': ['168.b1.b1', '168.x1.b1', '168.ba1.a1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 21, 'diagramx': [8858, -1, 8666, -1, 7704, -1, 7619, -1], 'generators': [337, 1174], 'label': '1344.9508.84.q1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.m1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.q1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.q1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506742
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '84.r1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '336.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1.a1', '28.r1.a1', '42.d1.a1'], 'contains': ['168.m1.a1', '168.m1.b1', '168.n1.a1', '168.r1.a1', '168.r1.b1', '168.s1.a1', '168.bc1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [4734, -1, 5857, -1, 4948, -1, 4916, -1], 'generators': [5, 2, 336], 'label': '1344.9508.84.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.d1.a1', 'old_label': '84.r1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.r1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506845
    {'ambient': '1344.9508', 'aut_centralizer_order': 576, 'aut_label': '224.e1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '28.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '112.f1.a1', '112.m1.a1'], 'contains': ['448.a1.a1', '672.e1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [91, -1, 210, -1, 1055, -1, 1130, -1], 'generators': [2, 448], 'label': '1344.9508.224.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.j1.a1', 'old_label': '224.e1.a1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506743
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '84.s1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '336.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1.a1', '28.s1.a1', '42.d1.a1'], 'contains': ['168.n1.a1', '168.o1.a1', '168.o1.b1', '168.bb1.a1', '168.bc1.a1', '168.bd1.a1', '168.bd1.b1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [4573, -1, 6317, -1, 5025, -1, 5055, -1], 'generators': [5, 10, 336], 'label': '1344.9508.84.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.d1.a1', 'old_label': '84.s1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.s1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506744
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '84.t1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1.a1', '28.t1.a1', '42.d1.a1', '42.h1.a1', '42.i1.b1'], 'contains': ['168.m1.a1', '168.o1.a1', '168.p1.a1', '168.q1.a1', '168.x1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [8337, -1, 8227, -1, 6415, -1, 6383, -1], 'generators': [789, 2, 8], 'label': '1344.9508.84.t1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.t1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.t1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506745
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '84.t1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '336.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1.b1', '28.t1.b1', '42.d1.a1', '42.h1.b1', '42.i1.a1'], 'contains': ['168.m1.b1', '168.o1.b1', '168.p1.a1', '168.q1.b1', '168.x1.b1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [8337, -1, 7330, -1, 6415, -1, 6340, -1], 'generators': [789, 722, 8], 'label': '1344.9508.84.t1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.n1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.t1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.t1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506746
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '84.u1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.u1.a1', '28.u1.a1', '42.e1.a1', '42.h1.a1', '42.h1.b1'], 'contains': ['168.p1.a1', '168.u1.a1', '168.ba1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [9586, -1, 9764, -1, 7264, -1, 7077, -1], 'generators': [789, 1174], 'label': '1344.9508.84.u1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.u1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.u1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506747
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '84.v1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '168.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1.a1', '28.v1.a1', '42.e1.a1', '42.i1.a1', '42.i1.b1'], 'contains': ['168.p1.a1', '168.w1.a1', '168.z1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [9661, -1, 9318, -1, 7052, -1, 6800, -1], 'generators': [341, 6], 'label': '1344.9508.84.v1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.v1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.v1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 74506748
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '84.w1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '336.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.w1.a1', '28.w1.a1', '42.d1.a1', '42.j1.a1', '42.k1.b1'], 'contains': ['168.q1.a1', '168.r1.a1', '168.v1.a1', '168.x1.b1', '168.bd1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [7388, -1, 7010, -1, 6973, -1, 6436, -1], 'generators': [5, 2, 8], 'label': '1344.9508.84.w1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.w1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.w1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506749
    {'ambient': '1344.9508', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '336.a1.a1', 'complements': ['672.e1.a1', '672.e1.b1', '672.d1.a1', '672.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.e1.a1', '4.g1.a1', '4.l1.a1', '4.l1.b1', '4.m1.a1', '4.m1.b1', '6.c1.a1', '14.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7834, 7004, 7457, 2800, 6409, 4103, 6395, 7254], 'generators': [1, 448, 336, 8, 6, 192, 672], 'label': '1344.9508.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.e1.a1', '4.g1.a1', '4.l1.b1', '4.l1.a1', '4.m1.b1', '4.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '672.1175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '336.161'}
  • id: 74506750
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '4.p1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '336.c1.a1', 'complements': ['336.l1.a1', '336.m1.a1', '336.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.i1.a1', '2.i1.b1'], 'contains': ['8.d1.a1', '8.i1.a1', '8.l1.a1', '12.v1.a1', '28.v1.a1'], 'core': '4.p1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6727, 5999, 6517, 6190, 5947, 8170, 5158, 5271], 'generators': [789, 192, 680, 672, 6, 448], 'label': '1344.9508.4.p1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.p1.a1', 'normal_contained_in': ['2.e1.a1', '2.i1.b1', '2.i1.a1'], 'normal_contains': ['8.d1.a1', '8.i1.a1', '8.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.p1.a1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.p1.a1', 'subgroup_fusion': None, 'weyl_group': '336.161'}
  • id: 74506751
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '84.w1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '336.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.w1.b1', '28.w1.b1', '42.d1.a1', '42.j1.b1', '42.k1.a1'], 'contains': ['168.q1.b1', '168.r1.b1', '168.v1.a1', '168.x1.a1', '168.bd1.b1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [7388, -1, 7133, -1, 6973, -1, 6896, -1], 'generators': [5, 722, 8], 'label': '1344.9508.84.w1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.q1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.w1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.w1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506752
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '84.x1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '84.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.x1.a1', '28.x1.a1', '42.f1.a1', '42.i1.b1', '42.j1.a1'], 'contains': ['168.q1.a1', '168.y1.a1', '168.z1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [8692, -1, 9395, -1, 8007, -1, 7892, -1], 'generators': [2, 4], 'label': '1344.9508.84.x1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.x1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.x1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506753
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '84.x1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '84.x1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.x1.b1', '28.x1.b1', '42.f1.a1', '42.i1.a1', '42.j1.b1'], 'contains': ['168.q1.b1', '168.y1.b1', '168.z1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [8692, -1, 9862, -1, 8007, -1, 8110, -1], 'generators': [722, 124], 'label': '1344.9508.84.x1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.r1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.x1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.x1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506754
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '84.y1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '168.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.y1.a1', '28.y1.a1', '42.f1.a1', '42.h1.a1', '42.k1.b1'], 'contains': ['168.q1.a1', '168.y1.b1', '168.ba1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [9103, -1, 9925, -1, 8086, -1, 8258, -1], 'generators': [2, 124], 'label': '1344.9508.84.y1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.y1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.y1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506755
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '84.y1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '168.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.y1.b1', '28.y1.b1', '42.f1.a1', '42.h1.b1', '42.k1.a1'], 'contains': ['168.q1.b1', '168.y1.a1', '168.ba1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [9103, -1, 9500, -1, 8086, -1, 8212, -1], 'generators': [722, 4], 'label': '1344.9508.84.y1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.s1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.y1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.y1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506756
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '84.z1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '168.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.z1.a1', '28.z1.a1', '42.e1.a1', '42.j1.a1', '42.j1.b1'], 'contains': ['168.u1.a1', '168.v1.a1', '168.z1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [7925, -1, 8186, -1, 7928, -1, 7439, -1], 'generators': [5, 6], 'label': '1344.9508.84.z1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.z1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.z1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 74506757
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '84.ba1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '336.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ba1.a1', '28.ba1.a1', '42.g1.a1', '42.h1.a1', '42.j1.b1'], 'contains': ['168.u1.a1', '168.x1.a1', '168.y1.b1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [8211, -1, 9184, -1, 7571, -1, 7992, -1], 'generators': [3, 124], 'label': '1344.9508.84.ba1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.ba1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506758
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '84.ba1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '336.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ba1.b1', '28.ba1.b1', '42.g1.a1', '42.h1.b1', '42.j1.a1'], 'contains': ['168.u1.a1', '168.x1.b1', '168.y1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [8211, -1, 8618, -1, 7571, -1, 7796, -1], 'generators': [3, 4], 'label': '1344.9508.84.ba1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.u1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.ba1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.ba1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506759
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '84.bb1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bb1.a1', '28.bb1.a1', '42.e1.a1', '42.k1.a1', '42.k1.b1'], 'contains': ['168.v1.a1', '168.w1.a1', '168.ba1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [9535, -1, 8130, -1, 8242, -1, 7288, -1], 'generators': [453, 1174], 'label': '1344.9508.84.bb1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.bb1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506760
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '84.bc1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bc1.a1', '28.bc1.a1', '42.g1.a1', '42.i1.b1', '42.k1.a1'], 'contains': ['168.w1.a1', '168.x1.a1', '168.y1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [8974, -1, 8747, -1, 7441, -1, 7839, -1], 'generators': [51, 4], 'label': '1344.9508.84.bc1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.bc1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506761
    {'ambient': '1344.9508', 'aut_centralizer_order': 4, 'aut_label': '4.q1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '672.a1.a1', 'complements': ['336.l1.a1', '336.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.j1.a1', '2.k1.b1'], 'contains': ['8.e1.a1', '8.h1.a1', '8.j1.b1', '8.ba1.a1', '8.bd1.a1', '12.w1.a1', '28.w1.a1'], 'core': '4.q1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4698, 4165, 5019, 1360, 4993, 3832, 4468, 2362], 'generators': [5, 192, 8, 672, 2, 448], 'label': '1344.9508.4.q1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.q1.a1', 'normal_contained_in': ['2.d1.a1', '2.j1.a1', '2.k1.b1'], 'normal_contains': ['8.e1.a1', '8.h1.a1', '8.j1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.q1.a1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.q1.a1', 'subgroup_fusion': None, 'weyl_group': '672.1175'}
  • id: 74506762
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '84.bc1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2016, 'centralizer': '336.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bc1.b1', '28.bc1.b1', '42.g1.a1', '42.i1.a1', '42.k1.b1'], 'contains': ['168.w1.a1', '168.x1.b1', '168.y1.b1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [8974, -1, 8709, -1, 7441, -1, 7663, -1], 'generators': [51, 124], 'label': '1344.9508.84.bc1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.w1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.bc1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.bc1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506763
    {'ambient': '1344.9508', 'aut_centralizer_order': 5376, 'aut_label': '96.a1', 'aut_quo_index': 192, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 5376, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.a1.a1', '48.b1.a1', '48.b1.b1', '48.c1.a1', '48.d1.a1', '48.e1.a1', '48.e1.b1', '48.f1.a1', '48.f1.b1', '48.g1.a1', '48.h1.a1', '48.i1.a1', '48.j1.a1', '48.k1.a1', '48.k1.b1'], 'contains': ['192.a1.a1', '672.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3715, 1996, 2919, 3757, 3885, 2704, 1798, 3127], 'generators': [672, 192], 'label': '1344.9508.96.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': ['32.a1.a1', '48.a1.a1', '48.b1.a1', '48.b1.b1', '48.c1.a1', '48.d1.a1', '48.e1.a1', '48.e1.b1'], 'normal_contains': ['192.a1.a1', '672.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '672.1175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '48.43', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506764
    {'ambient': '1344.9508', 'aut_centralizer_order': 2688, 'aut_label': '96.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '6.2', 'aut_weyl_index': 5376, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '48.a1.a1', '48.l1.a1'], 'contains': ['192.a1.a1', '672.b1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1589, -1, 499, -1, 1580, -1, 844, -1], 'generators': [344, 192], 'label': '1344.9508.96.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '96.b1.a1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506765
    {'ambient': '1344.9508', 'aut_centralizer_order': 672, 'aut_label': '96.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.2', 'aut_weyl_index': 5376, 'centralizer': '8.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '48.f1.a1', '48.l1.a1', '48.m1.a1'], 'contains': ['192.a1.a1', '672.c1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1168, -1, 94, -1, 1417, -1, 728, -1], 'generators': [1, 192], 'label': '1344.9508.96.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.x1.a1', 'old_label': '96.c1.a1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506766
    {'ambient': '1344.9508', 'aut_centralizer_order': 672, 'aut_label': '96.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.2', 'aut_weyl_index': 5376, 'centralizer': '8.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.b1', '48.f1.b1', '48.l1.a1', '48.m1.b1'], 'contains': ['192.a1.a1', '672.c1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1168, -1, 555, -1, 1417, -1, 687, -1], 'generators': [337, 192], 'label': '1344.9508.96.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.x1.b1', 'old_label': '96.c1.b1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506767
    {'ambient': '1344.9508', 'aut_centralizer_order': 448, 'aut_label': '96.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.2', 'aut_weyl_index': 5376, 'centralizer': '24.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '48.g1.a1'], 'contains': ['192.a1.a1', '672.d1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2611, -1, 5134, -1, 3250, -1, 2204, -1], 'generators': [789, 192], 'label': '1344.9508.96.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '96.d1.a1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506768
    {'ambient': '1344.9508', 'aut_centralizer_order': 192, 'aut_label': '96.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '42.1', 'aut_weyl_index': 768, 'centralizer': '28.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '48.b1.a1', '48.m1.a1'], 'contains': ['192.a1.a1', '672.e1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1366, -1, 130, -1, 1315, -1, 766, -1], 'generators': [2, 192], 'label': '1344.9508.96.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.j1.a1', 'old_label': '96.e1.a1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.e1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
  • id: 74506769
    {'ambient': '1344.9508', 'aut_centralizer_order': 192, 'aut_label': '96.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '42.1', 'aut_weyl_index': 768, 'centralizer': '28.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.b1', '48.b1.b1', '48.m1.b1'], 'contains': ['192.a1.a1', '672.e1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1366, -1, 1505, -1, 1315, -1, 650, -1], 'generators': [722, 192], 'label': '1344.9508.96.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.j1.b1', 'old_label': '96.e1.b1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.e1.b1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
  • id: 74506770
    {'ambient': '1344.9508', 'aut_centralizer_order': 192, 'aut_label': '96.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '42.1', 'aut_weyl_index': 768, 'centralizer': '56.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '48.h1.a1', '48.m1.a1', '48.m1.b1'], 'contains': ['192.a1.a1', '672.f1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1092, -1, 314, -1, 1363, -1, 561, -1], 'generators': [3, 192], 'label': '1344.9508.96.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.z1.a1', 'old_label': '96.f1.a1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.f1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
  • id: 74506771
    {'ambient': '1344.9508', 'aut_centralizer_order': 8064, 'aut_label': '112.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '56.a1.a1', '56.f1.a1', '56.g1.a1', '56.h1.a1', '56.h1.b1', '56.i1.a1', '56.j1.a1'], 'contains': ['224.a1.a1', '224.b1.a1', '336.a1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1640, 3100, 1803, 3994, 1875, 3697, 4037, 3993], 'generators': [344, 672, 448], 'label': '1344.9508.112.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '112.a1.a1', 'normal_contained_in': ['16.a1.a1', '56.a1.a1'], 'normal_contains': ['224.a1.a1', '336.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '112.a1.a1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '28.4', 'quotient_action_kernel_order': 28, 'quotient_fusion': None, 'short_label': '112.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506772
    {'ambient': '1344.9508', 'aut_centralizer_order': 4, 'aut_label': '4.q1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '672.a1.a1', 'complements': ['336.l1.a1', '336.m1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.j1.b1', '2.k1.a1'], 'contains': ['8.e1.b1', '8.h1.a1', '8.j1.a1', '8.ba1.b1', '8.bd1.b1', '12.w1.b1', '28.w1.b1'], 'core': '4.q1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4698, 4165, 4938, 3121, 4993, 3832, 4546, 2632], 'generators': [5, 192, 8, 672, 722, 448], 'label': '1344.9508.4.q1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.q1.b1', 'normal_contained_in': ['2.d1.a1', '2.j1.b1', '2.k1.a1'], 'normal_contains': ['8.e1.b1', '8.h1.a1', '8.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.q1.b1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.q1.b1', 'subgroup_fusion': None, 'weyl_group': '672.1175'}
  • id: 74506773
    {'ambient': '1344.9508', 'aut_centralizer_order': 8064, 'aut_label': '112.b1', 'aut_quo_index': 672, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '4.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '56.a1.a1', '56.b1.a1', '56.b1.b1', '56.c1.a1', '56.d1.a1', '56.e1.a1', '56.e1.b1', '56.s1.a1', '56.s1.b1', '56.w1.a1', '56.x1.a1', '56.y1.a1', '56.y1.b1', '56.z1.a1', '56.ba1.a1'], 'contains': ['224.a1.a1', '336.b1.a1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5680, 5545, 4985, 6445, 5619, 6529, 7060, 7227], 'generators': [8, 448, 672], 'label': '1344.9508.112.b1.a1', 'mobius_quo': 0, 'mobius_sub': -448, 'normal_closure': '112.b1.a1', 'normal_contained_in': ['16.c1.a1', '56.a1.a1', '56.b1.b1', '56.b1.a1', '56.c1.a1', '56.d1.a1', '56.e1.a1', '56.e1.b1'], 'normal_contains': ['224.a1.a1', '336.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '112.b1.a1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '28.3', 'quotient_action_kernel_order': 28, 'quotient_fusion': None, 'short_label': '112.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506774
    {'ambient': '1344.9508', 'aut_centralizer_order': 8064, 'aut_label': '112.c1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '56.a1.a1', '56.o1.a1', '56.q1.a1', '56.u1.a1', '56.v1.a1', '56.bb1.a1', '56.bc1.a1'], 'contains': ['224.a1.a1', '336.c1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1789, 2704, 2682, 4561, 2009, 3436, 4123, 3813], 'generators': [336, 448, 672], 'label': '1344.9508.112.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '112.c1.a1', 'normal_contained_in': ['16.d1.a1', '56.a1.a1'], 'normal_contains': ['224.a1.a1', '336.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '112.c1.a1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '28.3', 'quotient_action_kernel_order': 28, 'quotient_fusion': None, 'short_label': '112.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506775
    {'ambient': '1344.9508', 'aut_centralizer_order': 2016, 'aut_label': '112.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '4.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '56.b1.a1', '56.f1.a1', '56.k1.a1', '56.l1.a1', '56.m1.a1', '56.n1.a1', '56.o1.a1'], 'contains': ['224.a1.a1', '224.c1.a1', '336.d1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [494, -1, 950, -1, 1482, -1, 3355, -1], 'generators': [1, 672, 448], 'label': '1344.9508.112.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '56.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '112.d1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506776
    {'ambient': '1344.9508', 'aut_centralizer_order': 2016, 'aut_label': '112.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '4.x1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.b1', '56.b1.b1', '56.f1.a1', '56.k1.b1', '56.l1.b1', '56.m1.b1', '56.n1.b1', '56.o1.a1'], 'contains': ['224.a1.a1', '224.c1.b1', '336.d1.b1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [494, -1, 1177, -1, 1482, -1, 3482, -1], 'generators': [337, 672, 448], 'label': '1344.9508.112.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '56.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '112.d1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506777
    {'ambient': '1344.9508', 'aut_centralizer_order': 1344, 'aut_label': '112.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 2688, 'centralizer': '24.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '56.c1.a1', '56.g1.a1', '56.p1.a1', '56.p1.b1', '56.q1.a1', '56.r1.a1', '56.r1.b1'], 'contains': ['224.a1.a1', '224.d1.a1', '336.e1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2219, -1, 3116, -1, 2354, -1, 4385, -1], 'generators': [789, 672, 448], 'label': '1344.9508.112.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '56.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '112.e1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 74506778
    {'ambient': '1344.9508', 'aut_centralizer_order': 576, 'aut_label': '112.f1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '28.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '56.h1.a1', '56.k1.a1', '56.l1.b1', '56.p1.a1', '56.s1.a1', '56.t1.a1', '56.u1.a1'], 'contains': ['224.a1.a1', '224.e1.a1', '336.f1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [978, -1, 1626, -1, 1783, -1, 3877, -1], 'generators': [2, 672, 448], 'label': '1344.9508.112.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '112.f1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506779
    {'ambient': '1344.9508', 'aut_centralizer_order': 576, 'aut_label': '112.f1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '28.l1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.b1', '56.h1.b1', '56.k1.b1', '56.l1.a1', '56.p1.b1', '56.s1.b1', '56.t1.b1', '56.u1.a1'], 'contains': ['224.a1.a1', '224.e1.b1', '336.f1.b1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [978, -1, 1706, -1, 1783, -1, 3940, -1], 'generators': [722, 672, 448], 'label': '1344.9508.112.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '112.f1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.f1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506780
    {'ambient': '1344.9508', 'aut_centralizer_order': 576, 'aut_label': '112.g1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '28.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '56.i1.a1', '56.k1.a1', '56.k1.b1', '56.m1.a1', '56.m1.b1', '56.v1.a1', '56.w1.a1'], 'contains': ['224.a1.a1', '224.f1.a1', '336.g1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [703, -1, 1089, -1, 1574, -1, 3418, -1], 'generators': [3, 672, 448], 'label': '1344.9508.112.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '112.g1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506781
    {'ambient': '1344.9508', 'aut_centralizer_order': 1344, 'aut_label': '112.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 2688, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '56.d1.a1', '56.g1.a1', '56.q1.a1', '56.t1.a1', '56.t1.b1', '56.bd1.a1', '56.bd1.b1'], 'contains': ['224.a1.a1', '336.h1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2156, -1, 3561, -1, 2695, -1, 4466, -1], 'generators': [5, 672, 448], 'label': '1344.9508.112.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '56.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '112.h1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 74506782
    {'ambient': '1344.9508', 'aut_centralizer_order': 576, 'aut_label': '112.i1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '28.m1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '56.h1.b1', '56.m1.a1', '56.n1.b1', '56.r1.a1', '56.s1.a1', '56.bb1.a1', '56.bd1.a1'], 'contains': ['224.a1.a1', '336.i1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [1234, -1, 2742, -1, 1950, -1, 4239, -1], 'generators': [10, 448, 672], 'label': '1344.9508.112.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '112.i1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506783
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '4.r1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 16, 'centralizer': '336.b1.a1', 'complements': ['336.l1.a1', '336.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.i1.b1', '2.j1.a1'], 'contains': ['8.e1.a1', '8.k1.a1', '8.l1.a1', '12.x1.a1', '28.x1.a1'], 'core': '4.r1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6368, 6356, 7975, 1080, 7447, 6361, 6869, 5503], 'generators': [2, 192, 8, 672, 4, 448], 'label': '1344.9508.4.r1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.r1.a1', 'normal_contained_in': ['2.f1.a1', '2.i1.b1', '2.j1.a1'], 'normal_contains': ['8.e1.a1', '8.k1.a1', '8.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.r1.a1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.r1.a1', 'subgroup_fusion': None, 'weyl_group': '336.219'}
  • id: 74506784
    {'ambient': '1344.9508', 'aut_centralizer_order': 576, 'aut_label': '112.i1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '28.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.b1', '56.h1.a1', '56.m1.b1', '56.n1.a1', '56.r1.b1', '56.s1.b1', '56.bb1.a1', '56.bd1.b1'], 'contains': ['224.a1.a1', '336.i1.b1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [1234, -1, 2596, -1, 1950, -1, 4164, -1], 'generators': [58, 448, 672], 'label': '1344.9508.112.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '112.i1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.i1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506785
    {'ambient': '1344.9508', 'aut_centralizer_order': 576, 'aut_label': '112.j1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '28.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '56.i1.a1', '56.l1.a1', '56.l1.b1', '56.n1.a1', '56.n1.b1', '56.v1.a1', '56.x1.a1'], 'contains': ['224.a1.a1', '336.j1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [833, -1, 1350, -1, 1649, -1, 3825, -1], 'generators': [51, 448, 672], 'label': '1344.9508.112.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '112.j1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506786
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '112.k1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '12.4', 'aut_weyl_index': 2688, 'centralizer': '168.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '56.j1.a1', '56.p1.a1', '56.r1.a1', '56.t1.b1', '56.y1.a1', '56.bc1.a1', '56.bd1.b1'], 'contains': ['224.a1.a1', '336.k1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2342, -1, 3816, -1, 2583, -1, 4346, -1], 'generators': [1175, 672, 448], 'label': '1344.9508.112.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '112.k1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.k1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 74506787
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '112.k1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '12.4', 'aut_weyl_index': 2688, 'centralizer': '168.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.b1', '56.j1.a1', '56.p1.b1', '56.r1.b1', '56.t1.a1', '56.y1.b1', '56.bc1.a1', '56.bd1.a1'], 'contains': ['224.a1.a1', '336.k1.b1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2342, -1, 3716, -1, 2583, -1, 4423, -1], 'generators': [7, 672, 448], 'label': '1344.9508.112.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '112.k1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.k1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 74506788
    {'ambient': '1344.9508', 'aut_centralizer_order': 1008, 'aut_label': '112.l1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '8.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '56.f1.a1'], 'contains': ['224.b1.a1', '224.c1.a1', '224.c1.b1', '336.l1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [241, -1, 314, -1, 1221, -1, 1023, -1], 'generators': [1, 344, 448], 'label': '1344.9508.112.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '28.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.o1.a1', 'old_label': '112.l1.a1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.l1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 74506789
    {'ambient': '1344.9508', 'aut_centralizer_order': 144, 'aut_label': '112.m1', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '56.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.a1', '56.k1.a1'], 'contains': ['224.c1.a1', '224.e1.a1', '224.f1.a1', '336.m1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [129, -1, 93, -1, 825, -1, 960, -1], 'generators': [1, 2, 448], 'label': '1344.9508.112.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.k1.a1', 'old_label': '112.m1.a1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 74506790
    {'ambient': '1344.9508', 'aut_centralizer_order': 144, 'aut_label': '112.m1', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '56.k1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.b1', '56.k1.b1'], 'contains': ['224.c1.b1', '224.e1.b1', '224.f1.a1', '336.m1.b1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [129, -1, 407, -1, 825, -1, 896, -1], 'generators': [337, 722, 448], 'label': '1344.9508.112.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.k1.b1', 'old_label': '112.m1.b1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.m1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 74506791
    {'ambient': '1344.9508', 'aut_centralizer_order': 8064, 'aut_label': '168.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '4.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '56.a1.a1', '84.a1.a1', '84.d1.a1', '84.e1.a1', '84.f1.a1', '84.g1.a1', '84.h1.a1', '84.i1.a1'], 'contains': ['336.a1.a1', '336.b1.a1', '336.c1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7209, 4091, 5264, 5809, 6324, 4014, 5949, 4735], 'generators': [8, 336], 'label': '1344.9508.168.a1.a1', 'mobius_quo': 0, 'mobius_sub': -168, 'normal_closure': '168.a1.a1', 'normal_contained_in': ['24.b1.a1', '56.a1.a1', '84.a1.a1'], 'normal_contains': ['336.a1.a1', '336.b1.a1', '336.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '168.a1.a1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '42.5', 'quotient_action_kernel_order': 42, 'quotient_fusion': None, 'short_label': '168.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506792
    {'ambient': '1344.9508', 'aut_centralizer_order': 2016, 'aut_label': '168.b1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 4032, 'centralizer': '8.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '56.b1.a1', '84.a1.a1', '84.j1.a1', '84.k1.a1', '84.l1.a1', '84.o1.a1', '84.p1.a1', '84.q1.a1'], 'contains': ['336.b1.a1', '336.d1.a1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7698, 7982, 4508, 8342, 6815, 4581, 6911, 5334], 'generators': [1, 8], 'label': '1344.9508.168.b1.a1', 'mobius_quo': 0, 'mobius_sub': -168, 'normal_closure': '168.b1.a1', 'normal_contained_in': ['24.c1.a1', '56.b1.a1', '84.a1.a1'], 'normal_contains': ['336.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '168.b1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 74506793
    {'ambient': '1344.9508', 'aut_centralizer_order': 2016, 'aut_label': '168.b1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 4032, 'centralizer': '8.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.c1.b1', '56.b1.b1', '84.a1.a1', '84.j1.b1', '84.k1.b1', '84.l1.b1', '84.o1.b1', '84.p1.b1', '84.q1.b1'], 'contains': ['336.b1.a1', '336.d1.b1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7698, 7982, 5564, 8040, 6815, 4581, 6877, 4957], 'generators': [337, 8], 'label': '1344.9508.168.b1.b1', 'mobius_quo': 0, 'mobius_sub': -168, 'normal_closure': '168.b1.b1', 'normal_contained_in': ['24.c1.b1', '56.b1.b1', '84.a1.a1'], 'normal_contains': ['336.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '168.b1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.b1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 74506794
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '4.r1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 16, 'centralizer': '336.b1.a1', 'complements': ['336.l1.a1', '336.m1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.i1.a1', '2.j1.b1'], 'contains': ['8.e1.b1', '8.k1.b1', '8.l1.a1', '12.x1.b1', '28.x1.b1'], 'core': '4.r1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6368, 6356, 8726, 2314, 7447, 6361, 7148, 4306], 'generators': [722, 192, 680, 672, 124, 448], 'label': '1344.9508.4.r1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.r1.b1', 'normal_contained_in': ['2.f1.a1', '2.i1.a1', '2.j1.b1'], 'normal_contains': ['8.e1.b1', '8.k1.b1', '8.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.r1.b1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.r1.b1', 'subgroup_fusion': None, 'weyl_group': '336.219'}
  • id: 74506795
    {'ambient': '1344.9508', 'aut_centralizer_order': 2016, 'aut_label': '168.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 4032, 'centralizer': '8.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '56.f1.a1', '84.a1.a1', '84.b1.a1', '84.b1.b1'], 'contains': ['336.a1.a1', '336.d1.a1', '336.d1.b1', '336.l1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2685, -1, 1997, -1, 3055, -1, 3203, -1], 'generators': [1, 344, 672], 'label': '1344.9508.168.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '168.c1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506796
    {'ambient': '1344.9508', 'aut_centralizer_order': 1344, 'aut_label': '168.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '24.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '56.g1.a1', '84.c1.a1', '84.c1.b1', '84.d1.a1'], 'contains': ['336.a1.a1', '336.e1.a1', '336.h1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4269, -1, 5955, -1, 4318, -1, 4858, -1], 'generators': [5, 344], 'label': '1344.9508.168.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '28.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '168.d1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506797
    {'ambient': '1344.9508', 'aut_centralizer_order': 576, 'aut_label': '168.e1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '28.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '56.h1.a1', '84.b1.a1', '84.c1.a1', '84.e1.a1'], 'contains': ['336.a1.a1', '336.f1.a1', '336.i1.b1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [3478, -1, 2833, -1, 3942, -1, 4086, -1], 'generators': [2, 344], 'label': '1344.9508.168.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '168.e1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506798
    {'ambient': '1344.9508', 'aut_centralizer_order': 576, 'aut_label': '168.e1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '28.p1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b1', '56.h1.b1', '84.b1.b1', '84.c1.b1', '84.e1.a1'], 'contains': ['336.a1.a1', '336.f1.b1', '336.i1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [3478, -1, 4048, -1, 3942, -1, 4201, -1], 'generators': [722, 344], 'label': '1344.9508.168.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '168.e1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.e1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506799
    {'ambient': '1344.9508', 'aut_centralizer_order': 576, 'aut_label': '168.f1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '56.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '56.i1.a1', '84.b1.a1', '84.b1.b1', '84.f1.a1'], 'contains': ['336.a1.a1', '336.g1.a1', '336.j1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2846, -1, 2223, -1, 3521, -1, 3273, -1], 'generators': [3, 344], 'label': '1344.9508.168.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '168.f1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506800
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '168.g1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '8.3', 'aut_weyl_index': 4032, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '56.j1.a1', '84.c1.a1', '84.c1.b1', '84.g1.a1'], 'contains': ['336.a1.a1', '336.k1.a1', '336.k1.b1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [4183, -1, 6281, -1, 4447, -1, 4713, -1], 'generators': [7, 344], 'label': '1344.9508.168.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.d1.a1', 'old_label': '168.g1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506801
    {'ambient': '1344.9508', 'aut_centralizer_order': 288, 'aut_label': '168.h1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '56.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '56.k1.a1', '84.b1.a1', '84.k1.a1', '84.m1.a1'], 'contains': ['336.d1.a1', '336.f1.a1', '336.g1.a1', '336.m1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2738, -1, 1348, -1, 3110, -1, 3165, -1], 'generators': [1, 2, 672], 'label': '1344.9508.168.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '168.h1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506802
    {'ambient': '1344.9508', 'aut_centralizer_order': 288, 'aut_label': '168.h1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '56.k1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.b1', '56.k1.b1', '84.b1.b1', '84.k1.b1', '84.m1.a1'], 'contains': ['336.d1.b1', '336.f1.b1', '336.g1.a1', '336.m1.b1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2738, -1, 2159, -1, 3110, -1, 3127, -1], 'generators': [337, 722, 672], 'label': '1344.9508.168.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '168.h1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.h1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506803
    {'ambient': '1344.9508', 'aut_centralizer_order': 288, 'aut_label': '168.i1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '56.m1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '56.l1.a1', '84.b1.b1', '84.l1.a1', '84.m1.a1'], 'contains': ['336.d1.a1', '336.f1.b1', '336.j1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [3028, -1, 2252, -1, 3272, -1, 3239, -1], 'generators': [1, 722], 'label': '1344.9508.168.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '168.i1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506804
    {'ambient': '1344.9508', 'aut_centralizer_order': 288, 'aut_label': '168.i1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '56.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.b1', '56.l1.b1', '84.b1.a1', '84.l1.b1', '84.m1.a1'], 'contains': ['336.d1.b1', '336.f1.a1', '336.j1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [3028, -1, 2192, -1, 3272, -1, 3306, -1], 'generators': [337, 2], 'label': '1344.9508.168.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '168.i1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.i1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506805
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '4.s1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 16, 'centralizer': '336.b1.a1', 'complements': ['336.l1.a1', '336.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.h1.a1', '2.k1.b1'], 'contains': ['8.e1.a1', '8.k1.b1', '8.m1.a1', '12.y1.a1', '28.y1.a1'], 'core': '4.s1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7754, 3758, 8795, 1636, 7557, 4597, 7418, 6218], 'generators': [2, 192, 680, 672, 124, 448], 'label': '1344.9508.4.s1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.s1.a1', 'normal_contained_in': ['2.f1.a1', '2.h1.a1', '2.k1.b1'], 'normal_contains': ['8.e1.a1', '8.k1.b1', '8.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.s1.a1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.s1.a1', 'subgroup_fusion': None, 'weyl_group': '336.219'}
  • id: 74506806
    {'ambient': '1344.9508', 'aut_centralizer_order': 288, 'aut_label': '168.j1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '56.l1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '56.m1.a1', '84.b1.b1', '84.k1.a1', '84.n1.a1'], 'contains': ['336.d1.a1', '336.g1.a1', '336.i1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2968, -1, 2110, -1, 3381, -1, 3564, -1], 'generators': [1, 10], 'label': '1344.9508.168.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '168.j1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506807
    {'ambient': '1344.9508', 'aut_centralizer_order': 288, 'aut_label': '168.j1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '56.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.b1', '56.m1.b1', '84.b1.a1', '84.k1.b1', '84.n1.a1'], 'contains': ['336.d1.b1', '336.g1.a1', '336.i1.b1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2968, -1, 2410, -1, 3381, -1, 3661, -1], 'generators': [337, 58], 'label': '1344.9508.168.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '168.j1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.j1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506808
    {'ambient': '1344.9508', 'aut_centralizer_order': 288, 'aut_label': '168.k1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '56.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.a1', '56.n1.a1', '84.b1.a1', '84.l1.a1', '84.n1.a1'], 'contains': ['336.d1.a1', '336.i1.b1', '336.j1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [3202, -1, 2589, -1, 3451, -1, 3709, -1], 'generators': [1, 58], 'label': '1344.9508.168.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '168.k1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506809
    {'ambient': '1344.9508', 'aut_centralizer_order': 288, 'aut_label': '168.k1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '56.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.b1', '56.n1.b1', '84.b1.b1', '84.l1.b1', '84.n1.a1'], 'contains': ['336.d1.b1', '336.i1.a1', '336.j1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [3202, -1, 3310, -1, 3451, -1, 3772, -1], 'generators': [337, 10], 'label': '1344.9508.168.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '168.k1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.k1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506810
    {'ambient': '1344.9508', 'aut_centralizer_order': 2016, 'aut_label': '168.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 4032, 'centralizer': '8.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '56.o1.a1', '84.a1.a1', '84.m1.a1', '84.n1.a1'], 'contains': ['336.c1.a1', '336.d1.a1', '336.d1.b1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3269, -1, 2516, -1, 3632, -1, 3530, -1], 'generators': [1, 336], 'label': '1344.9508.168.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '168.l1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506811
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '168.m1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '168.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.r1.a1', '56.p1.a1', '84.c1.a1', '84.r1.a1', '84.t1.a1'], 'contains': ['336.e1.a1', '336.f1.a1', '336.k1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [4480, -1, 6566, -1, 4579, -1, 4504, -1], 'generators': [789, 2], 'label': '1344.9508.168.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.d1.a1', 'old_label': '168.m1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.m1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506812
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '168.m1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '168.bd1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.r1.b1', '56.p1.b1', '84.c1.b1', '84.r1.a1', '84.t1.b1'], 'contains': ['336.e1.a1', '336.f1.b1', '336.k1.b1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [4480, -1, 6099, -1, 4579, -1, 4664, -1], 'generators': [789, 722], 'label': '1344.9508.168.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.d1.a1', 'old_label': '168.m1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.m1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506813
    {'ambient': '1344.9508', 'aut_centralizer_order': 1344, 'aut_label': '168.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '24.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.a1', '56.q1.a1', '84.d1.a1', '84.r1.a1', '84.s1.a1'], 'contains': ['336.c1.a1', '336.e1.a1', '336.h1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4636, -1, 5396, -1, 4832, -1, 4810, -1], 'generators': [5, 336], 'label': '1344.9508.168.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '28.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '168.n1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.n1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506814
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '168.o1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '168.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1.a1', '56.r1.a1', '84.c1.b1', '84.s1.a1', '84.t1.a1'], 'contains': ['336.e1.a1', '336.i1.a1', '336.k1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [4389, -1, 6621, -1, 4649, -1, 5004, -1], 'generators': [789, 10], 'label': '1344.9508.168.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.d1.a1', 'old_label': '168.o1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.o1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506815
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '168.o1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '168.o1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1.b1', '56.r1.b1', '84.c1.a1', '84.s1.a1', '84.t1.b1'], 'contains': ['336.e1.a1', '336.i1.b1', '336.k1.b1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [4389, -1, 6502, -1, 4649, -1, 4940, -1], 'generators': [789, 58], 'label': '1344.9508.168.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.d1.a1', 'old_label': '168.o1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.o1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506816
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '4.s1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 16, 'centralizer': '336.b1.a1', 'complements': ['336.l1.a1', '336.m1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.h1.b1', '2.k1.a1'], 'contains': ['8.e1.b1', '8.k1.a1', '8.m1.a1', '12.y1.b1', '28.y1.b1'], 'core': '4.s1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7754, 3758, 8076, 480, 7557, 4597, 7343, 6668], 'generators': [722, 192, 8, 672, 4, 448], 'label': '1344.9508.4.s1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.s1.b1', 'normal_contained_in': ['2.f1.a1', '2.h1.b1', '2.k1.a1'], 'normal_contains': ['8.e1.b1', '8.k1.a1', '8.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.s1.b1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.s1.b1', 'subgroup_fusion': None, 'weyl_group': '336.219'}
  • id: 74506817
    {'ambient': '1344.9508', 'aut_centralizer_order': 1344, 'aut_label': '168.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 4032, 'centralizer': '24.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.u1.a1', '56.c1.a1', '84.d1.a1', '84.j1.a1', '84.j1.b1', '84.t1.a1', '84.t1.b1', '84.u1.a1', '84.v1.a1'], 'contains': ['336.b1.a1', '336.e1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8651, -1, 8687, -1, 6766, -1, 6800, -1], 'generators': [789, 8], 'label': '1344.9508.168.p1.a1', 'mobius_quo': None, 'mobius_sub': -56, 'normal_closure': '56.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '168.p1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.p1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 74506818
    {'ambient': '1344.9508', 'aut_centralizer_order': 576, 'aut_label': '168.q1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '28.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '56.s1.a1', '84.e1.a1', '84.k1.a1', '84.l1.b1', '84.t1.a1', '84.w1.a1', '84.x1.a1', '84.y1.a1'], 'contains': ['336.b1.a1', '336.f1.a1', '336.i1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7343, -1, 5881, -1, 6151, -1, 6208, -1], 'generators': [2, 8], 'label': '1344.9508.168.q1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '168.q1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.q1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506819
    {'ambient': '1344.9508', 'aut_centralizer_order': 576, 'aut_label': '168.q1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '28.x1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.b1', '56.s1.b1', '84.e1.a1', '84.k1.b1', '84.l1.a1', '84.t1.b1', '84.w1.b1', '84.x1.b1', '84.y1.b1'], 'contains': ['336.b1.a1', '336.f1.b1', '336.i1.b1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7343, -1, 5322, -1, 6151, -1, 6340, -1], 'generators': [722, 8], 'label': '1344.9508.168.q1.b1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '24.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '168.q1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.q1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506820
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '168.r1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '168.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.v1.a1', '56.t1.a1', '84.c1.a1', '84.r1.a1', '84.w1.a1'], 'contains': ['336.f1.a1', '336.h1.a1', '336.k1.b1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [4548, -1, 5455, -1, 4741, -1, 4553, -1], 'generators': [5, 2], 'label': '1344.9508.168.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.d1.a1', 'old_label': '168.r1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.r1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506821
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '168.r1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '168.r1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.v1.b1', '56.t1.b1', '84.c1.b1', '84.r1.a1', '84.w1.b1'], 'contains': ['336.f1.b1', '336.h1.a1', '336.k1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [4548, -1, 5813, -1, 4741, -1, 4616, -1], 'generators': [5, 722], 'label': '1344.9508.168.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.d1.a1', 'old_label': '168.r1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.r1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506822
    {'ambient': '1344.9508', 'aut_centralizer_order': 576, 'aut_label': '168.s1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '8.3', 'aut_weyl_index': 4032, 'centralizer': '28.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '56.u1.a1', '84.e1.a1', '84.m1.a1', '84.r1.a1'], 'contains': ['336.c1.a1', '336.f1.a1', '336.f1.b1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [4098, -1, 3539, -1, 4111, -1, 3989, -1], 'generators': [2, 336], 'label': '1344.9508.168.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '168.s1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.s1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506823
    {'ambient': '1344.9508', 'aut_centralizer_order': 576, 'aut_label': '168.t1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '56.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.w1.a1', '56.v1.a1', '84.f1.a1', '84.m1.a1', '84.n1.a1'], 'contains': ['336.c1.a1', '336.g1.a1', '336.j1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [3360, -1, 2961, -1, 3702, -1, 3612, -1], 'generators': [3, 336], 'label': '1344.9508.168.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '168.t1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.t1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506824
    {'ambient': '1344.9508', 'aut_centralizer_order': 576, 'aut_label': '168.u1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '8.3', 'aut_weyl_index': 4032, 'centralizer': '56.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '56.w1.a1', '84.f1.a1', '84.k1.a1', '84.k1.b1', '84.u1.a1', '84.z1.a1', '84.ba1.a1', '84.ba1.b1'], 'contains': ['336.b1.a1', '336.g1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7526, -1, 4718, -1, 6920, -1, 6945, -1], 'generators': [3, 8], 'label': '1344.9508.168.u1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '24.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '168.u1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.u1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 74506825
    {'ambient': '1344.9508', 'aut_centralizer_order': 1344, 'aut_label': '168.v1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 4032, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.x1.a1', '56.d1.a1', '84.d1.a1', '84.o1.a1', '84.o1.b1', '84.w1.a1', '84.w1.b1', '84.z1.a1', '84.bb1.a1'], 'contains': ['336.b1.a1', '336.h1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7795, -1, 7058, -1, 7185, -1, 6978, -1], 'generators': [5, 8], 'label': '1344.9508.168.v1.a1', 'mobius_quo': None, 'mobius_sub': -56, 'normal_closure': '56.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '168.v1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.v1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 74506826
    {'ambient': '1344.9508', 'aut_centralizer_order': 576, 'aut_label': '168.w1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '8.3', 'aut_weyl_index': 4032, 'centralizer': '56.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '56.x1.a1', '84.f1.a1', '84.l1.a1', '84.l1.b1', '84.v1.a1', '84.bb1.a1', '84.bc1.a1', '84.bc1.b1'], 'contains': ['336.b1.a1', '336.j1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8051, -1, 5742, -1, 6872, -1, 6291, -1], 'generators': [51, 8], 'label': '1344.9508.168.w1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '24.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '168.w1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.w1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 74506827
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '4.t1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '336.c1.a1', 'complements': ['336.l1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.j1.a1', '2.j1.b1'], 'contains': ['8.g1.a1', '8.h1.a1', '8.l1.a1', '12.z1.a1', '28.z1.a1'], 'core': '4.t1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6517, 7945, 7132, 5059, 7209, 7776, 6054, 4807], 'generators': [5, 192, 8, 672, 6, 448], 'label': '1344.9508.4.t1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.t1.a1', 'normal_contained_in': ['2.e1.a1', '2.j1.b1', '2.j1.a1'], 'normal_contains': ['8.g1.a1', '8.h1.a1', '8.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.t1.a1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.t1.a1', 'subgroup_fusion': None, 'weyl_group': '336.161'}
  • id: 74506846
    {'ambient': '1344.9508', 'aut_centralizer_order': 576, 'aut_label': '224.e1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '28.l1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.b1', '112.f1.b1', '112.m1.b1'], 'contains': ['448.a1.a1', '672.e1.b1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [91, -1, 574, -1, 1055, -1, 991, -1], 'generators': [722, 448], 'label': '1344.9508.224.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.j1.b1', 'old_label': '224.e1.b1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.e1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506828
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '168.x1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '8.3', 'aut_weyl_index': 4032, 'centralizer': '168.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1.a1', '56.y1.a1', '84.g1.a1', '84.p1.b1', '84.q1.a1', '84.t1.a1', '84.w1.b1', '84.ba1.a1', '84.bc1.a1'], 'contains': ['336.b1.a1', '336.k1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [8235, -1, 7829, -1, 6973, -1, 7401, -1], 'generators': [1175, 8], 'label': '1344.9508.168.x1.a1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '168.x1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.x1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 74506829
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '168.x1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '8.3', 'aut_weyl_index': 4032, 'centralizer': '168.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1.b1', '56.y1.b1', '84.g1.a1', '84.p1.a1', '84.q1.b1', '84.t1.b1', '84.w1.a1', '84.ba1.b1', '84.bc1.b1'], 'contains': ['336.b1.a1', '336.k1.b1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [8235, -1, 7235, -1, 6973, -1, 7368, -1], 'generators': [7, 8], 'label': '1344.9508.168.x1.b1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '8.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '168.x1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.x1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 74506830
    {'ambient': '1344.9508', 'aut_centralizer_order': 1344, 'aut_label': '168.y1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '12.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.z1.a1', '56.e1.a1', '84.h1.a1', '84.j1.b1', '84.o1.a1', '84.x1.a1', '84.y1.b1', '84.ba1.b1', '84.bc1.a1'], 'contains': ['336.b1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8504, -1, 8608, -1, 7538, -1, 7817, -1], 'generators': [4], 'label': '1344.9508.168.y1.a1', 'mobius_quo': None, 'mobius_sub': -56, 'normal_closure': '56.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '168.y1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.y1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506831
    {'ambient': '1344.9508', 'aut_centralizer_order': 1344, 'aut_label': '168.y1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '12.x1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.z1.b1', '56.e1.b1', '84.h1.a1', '84.j1.a1', '84.o1.b1', '84.x1.b1', '84.y1.a1', '84.ba1.a1', '84.bc1.b1'], 'contains': ['336.b1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8504, -1, 9789, -1, 7538, -1, 7971, -1], 'generators': [124], 'label': '1344.9508.168.y1.b1', 'mobius_quo': None, 'mobius_sub': -56, 'normal_closure': '56.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '168.y1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.y1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506832
    {'ambient': '1344.9508', 'aut_centralizer_order': 384, 'aut_label': '168.z1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '42.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1.a1', '56.z1.a1', '84.i1.a1', '84.p1.a1', '84.p1.b1', '84.v1.a1', '84.x1.a1', '84.x1.b1', '84.z1.a1'], 'contains': ['336.b1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [8749, -1, 8656, -1, 7787, -1, 7662, -1], 'generators': [6], 'label': '1344.9508.168.z1.a1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '168.z1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.z1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506833
    {'ambient': '1344.9508', 'aut_centralizer_order': 384, 'aut_label': '168.ba1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '84.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bb1.a1', '56.ba1.a1', '84.i1.a1', '84.q1.a1', '84.q1.b1', '84.u1.a1', '84.y1.a1', '84.y1.b1', '84.bb1.a1'], 'contains': ['336.b1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [9502, -1, 8883, -1, 7844, -1, 7872, -1], 'generators': [1174], 'label': '1344.9508.168.ba1.a1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '8.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '168.ba1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506834
    {'ambient': '1344.9508', 'aut_centralizer_order': 576, 'aut_label': '168.bb1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '8.3', 'aut_weyl_index': 4032, 'centralizer': '28.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '56.bb1.a1', '84.e1.a1', '84.n1.a1', '84.s1.a1'], 'contains': ['336.c1.a1', '336.i1.a1', '336.i1.b1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [3905, -1, 4173, -1, 4160, -1, 4276, -1], 'generators': [10, 336], 'label': '1344.9508.168.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '168.bb1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506835
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '168.bc1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '8.3', 'aut_weyl_index': 4032, 'centralizer': '168.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bc1.a1', '56.bc1.a1', '84.g1.a1', '84.r1.a1', '84.s1.a1'], 'contains': ['336.c1.a1', '336.k1.a1', '336.k1.b1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [4703, -1, 6204, -1, 4951, -1, 4761, -1], 'generators': [7, 336], 'label': '1344.9508.168.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.d1.a1', 'old_label': '168.bc1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506836
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '168.bd1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '168.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bd1.a1', '56.bd1.a1', '84.c1.b1', '84.s1.a1', '84.w1.a1'], 'contains': ['336.h1.a1', '336.i1.a1', '336.k1.b1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [4319, -1, 5986, -1, 4902, -1, 5052, -1], 'generators': [5, 10], 'label': '1344.9508.168.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.d1.a1', 'old_label': '168.bd1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506837
    {'ambient': '1344.9508', 'aut_centralizer_order': 96, 'aut_label': '168.bd1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '168.m1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bd1.b1', '56.bd1.b1', '84.c1.a1', '84.s1.a1', '84.w1.b1'], 'contains': ['336.h1.a1', '336.i1.b1', '336.k1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [4319, -1, 6173, -1, 4902, -1, 4892, -1], 'generators': [5, 58], 'label': '1344.9508.168.bd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.d1.a1', 'old_label': '168.bd1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bd1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506838
    {'ambient': '1344.9508', 'aut_centralizer_order': 4, 'aut_label': '4.u1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '672.a1.a1', 'complements': ['336.l1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.h1.a1', '2.j1.b1'], 'contains': ['8.g1.a1', '8.j1.a1', '8.k1.b1', '12.ba1.a1', '28.ba1.a1'], 'core': '4.u1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5857, 3013, 7484, 6952, 6765, 2938, 6991, 3368], 'generators': [3, 192, 680, 672, 124, 448], 'label': '1344.9508.4.u1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.u1.a1', 'normal_contained_in': ['2.g1.a1', '2.h1.a1', '2.j1.b1'], 'normal_contains': ['8.g1.a1', '8.j1.a1', '8.k1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.u1.a1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.u1.a1', 'subgroup_fusion': None, 'weyl_group': '672.1175'}
  • id: 74506839
    {'ambient': '1344.9508', 'aut_centralizer_order': 5376, 'aut_label': '192.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 5376, 'centralizer': '2.a1.a1', 'complements': ['7.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.a1.a1', '96.b1.a1', '96.c1.a1', '96.c1.b1', '96.d1.a1', '96.e1.a1', '96.e1.b1', '96.f1.a1'], 'contains': ['1344.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1311, 1624, 522, 2891, 1463, 2931, 784, 3493], 'generators': [192], 'label': '1344.9508.192.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '192.a1.a1', 'normal_contained_in': ['64.a1.a1', '96.a1.a1'], 'normal_contains': ['1344.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.a1.a1', 'projective_image': '1344.9508', 'quotient_action_image': '2.1', 'quotient_action_kernel': '96.139', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '192.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506840
    {'ambient': '1344.9508', 'aut_centralizer_order': 16128, 'aut_label': '224.a1', 'aut_quo_index': 32, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '112.a1.a1', '112.b1.a1', '112.c1.a1', '112.d1.a1', '112.d1.b1', '112.e1.a1', '112.f1.a1', '112.f1.b1', '112.g1.a1', '112.h1.a1', '112.i1.a1', '112.i1.b1', '112.j1.a1', '112.k1.a1', '112.k1.b1'], 'contains': ['448.a1.a1', '672.a1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1286, 2522, 1981, 3999, 1912, 3473, 4037, 3827], 'generators': [672, 448], 'label': '1344.9508.224.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '224.a1.a1', 'normal_contained_in': ['32.a1.a1', '112.a1.a1', '112.b1.a1', '112.c1.a1'], 'normal_contains': ['448.a1.a1', '672.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '224.a1.a1', 'projective_image': '672.1175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '112.42', 'quotient_action_kernel_order': 112, 'quotient_fusion': None, 'short_label': '224.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506841
    {'ambient': '1344.9508', 'aut_centralizer_order': 8064, 'aut_label': '224.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '112.a1.a1', '112.l1.a1'], 'contains': ['448.a1.a1', '672.b1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [364, -1, 307, -1, 1471, -1, 1164, -1], 'generators': [344, 448], 'label': '1344.9508.224.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '112.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '224.b1.a1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506842
    {'ambient': '1344.9508', 'aut_centralizer_order': 2016, 'aut_label': '224.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '4.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '112.d1.a1', '112.l1.a1', '112.m1.a1'], 'contains': ['448.a1.a1', '672.c1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [248, -1, 102, -1, 1152, -1, 1097, -1], 'generators': [1, 448], 'label': '1344.9508.224.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '56.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.x1.a1', 'old_label': '224.c1.a1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 74506843
    {'ambient': '1344.9508', 'aut_centralizer_order': 2016, 'aut_label': '224.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '4.x1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.b1', '112.d1.b1', '112.l1.a1', '112.m1.b1'], 'contains': ['448.a1.a1', '672.c1.b1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [248, -1, 385, -1, 1152, -1, 1025, -1], 'generators': [337, 448], 'label': '1344.9508.224.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '56.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.x1.b1', 'old_label': '224.c1.b1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 74506844
    {'ambient': '1344.9508', 'aut_centralizer_order': 1344, 'aut_label': '224.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '6.1', 'aut_weyl_index': 5376, 'centralizer': '24.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '112.e1.a1'], 'contains': ['448.a1.a1', '672.d1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2262, -1, 2877, -1, 2279, -1, 3275, -1], 'generators': [789, 448], 'label': '1344.9508.224.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '56.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bc1.a1', 'old_label': '224.d1.a1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 74506847
    {'ambient': '1344.9508', 'aut_centralizer_order': 576, 'aut_label': '224.f1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '28.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '112.g1.a1', '112.m1.a1', '112.m1.b1'], 'contains': ['448.a1.a1', '672.f1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [45, -1, 259, -1, 1103, -1, 958, -1], 'generators': [3, 448], 'label': '1344.9508.224.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.n1.a1', 'old_label': '224.f1.a1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 74506848
    {'ambient': '1344.9508', 'aut_centralizer_order': 16128, 'aut_label': '336.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '112.a1.a1', '168.a1.a1', '168.c1.a1', '168.d1.a1', '168.e1.a1', '168.e1.b1', '168.f1.a1', '168.g1.a1'], 'contains': ['672.a1.a1', '672.b1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3404, 2986, 2855, 4173, 3815, 3662, 4073, 3966], 'generators': [344, 672], 'label': '1344.9508.336.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '336.a1.a1', 'normal_contained_in': ['48.a1.a1', '112.a1.a1', '168.a1.a1'], 'normal_contains': ['672.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '336.a1.a1', 'projective_image': '672.1175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '168.38', 'quotient_action_kernel_order': 168, 'quotient_fusion': None, 'short_label': '336.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506849
    {'ambient': '1344.9508', 'aut_centralizer_order': 4, 'aut_label': '4.u1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '672.a1.a1', 'complements': ['336.l1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.h1.b1', '2.j1.a1'], 'contains': ['8.g1.a1', '8.j1.b1', '8.k1.a1', '12.ba1.b1', '28.ba1.b1'], 'core': '4.u1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5857, 3013, 7060, 3563, 6765, 2938, 6666, 4536], 'generators': [3, 192, 8, 672, 4, 448], 'label': '1344.9508.4.u1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.u1.b1', 'normal_contained_in': ['2.g1.a1', '2.h1.b1', '2.j1.a1'], 'normal_contains': ['8.g1.a1', '8.j1.b1', '8.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.u1.b1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.u1.b1', 'subgroup_fusion': None, 'weyl_group': '672.1175'}
  • id: 74506850
    {'ambient': '1344.9508', 'aut_centralizer_order': 16128, 'aut_label': '336.b1', 'aut_quo_index': 48, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '112.b1.a1', '168.a1.a1', '168.b1.a1', '168.b1.b1', '168.p1.a1', '168.q1.a1', '168.q1.b1', '168.u1.a1', '168.v1.a1', '168.w1.a1', '168.x1.a1', '168.x1.b1', '168.y1.a1', '168.y1.b1', '168.z1.a1', '168.ba1.a1'], 'contains': ['672.a1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7960, 4091, 6397, 6747, 6896, 4014, 6928, 4851], 'generators': [8], 'label': '1344.9508.336.b1.a1', 'mobius_quo': 0, 'mobius_sub': 1344, 'normal_closure': '336.b1.a1', 'normal_contained_in': ['48.c1.a1', '112.b1.a1', '168.a1.a1', '168.b1.b1', '168.b1.a1'], 'normal_contains': ['672.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '336.b1.a1', 'projective_image': '672.1175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '168.50', 'quotient_action_kernel_order': 168, 'quotient_fusion': None, 'short_label': '336.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506851
    {'ambient': '1344.9508', 'aut_centralizer_order': 16128, 'aut_label': '336.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '2.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '112.c1.a1', '168.a1.a1', '168.l1.a1', '168.n1.a1', '168.s1.a1', '168.t1.a1', '168.bb1.a1', '168.bc1.a1'], 'contains': ['672.a1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4023, 2679, 4076, 4497, 4084, 3306, 4114, 3712], 'generators': [336], 'label': '1344.9508.336.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '336.c1.a1', 'normal_contained_in': ['48.d1.a1', '112.c1.a1', '168.a1.a1'], 'normal_contains': ['672.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '336.c1.a1', 'projective_image': '672.1175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '168.15', 'quotient_action_kernel_order': 168, 'quotient_fusion': None, 'short_label': '336.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506852
    {'ambient': '1344.9508', 'aut_centralizer_order': 4032, 'aut_label': '336.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '4.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '112.d1.a1', '168.b1.a1', '168.c1.a1', '168.h1.a1', '168.i1.a1', '168.j1.a1', '168.k1.a1', '168.l1.a1'], 'contains': ['672.a1.a1', '672.c1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2884, -1, 1462, -1, 3193, -1, 3239, -1], 'generators': [1, 672], 'label': '1344.9508.336.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '168.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '336.d1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506853
    {'ambient': '1344.9508', 'aut_centralizer_order': 4032, 'aut_label': '336.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '4.x1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.b1', '112.d1.b1', '168.b1.b1', '168.c1.a1', '168.h1.b1', '168.i1.b1', '168.j1.b1', '168.k1.b1', '168.l1.a1'], 'contains': ['672.a1.a1', '672.c1.b1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2884, -1, 2261, -1, 3193, -1, 3482, -1], 'generators': [337, 672], 'label': '1344.9508.336.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '168.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '336.d1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506854
    {'ambient': '1344.9508', 'aut_centralizer_order': 2688, 'aut_label': '336.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '12.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '112.e1.a1', '168.d1.a1', '168.m1.a1', '168.m1.b1', '168.n1.a1', '168.o1.a1', '168.o1.b1', '168.p1.a1'], 'contains': ['672.a1.a1', '672.d1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4507, -1, 6510, -1, 4318, -1, 4664, -1], 'generators': [789, 672], 'label': '1344.9508.336.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '56.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '336.e1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506855
    {'ambient': '1344.9508', 'aut_centralizer_order': 1152, 'aut_label': '336.f1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '14.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '112.f1.a1', '168.e1.a1', '168.h1.a1', '168.i1.b1', '168.m1.a1', '168.q1.a1', '168.r1.a1', '168.s1.a1'], 'contains': ['672.a1.a1', '672.e1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [3685, -1, 2692, -1, 3942, -1, 3957, -1], 'generators': [2, 672], 'label': '1344.9508.336.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '336.f1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506856
    {'ambient': '1344.9508', 'aut_centralizer_order': 1152, 'aut_label': '336.f1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '14.j1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.b1', '112.f1.b1', '168.e1.b1', '168.h1.b1', '168.i1.a1', '168.m1.b1', '168.q1.b1', '168.r1.b1', '168.s1.a1'], 'contains': ['672.a1.a1', '672.e1.b1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [3685, -1, 3164, -1, 3942, -1, 3995, -1], 'generators': [722, 672], 'label': '1344.9508.336.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '336.f1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.f1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506857
    {'ambient': '1344.9508', 'aut_centralizer_order': 1152, 'aut_label': '336.g1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '28.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '112.g1.a1', '168.f1.a1', '168.h1.a1', '168.h1.b1', '168.j1.a1', '168.j1.b1', '168.t1.a1', '168.u1.a1'], 'contains': ['672.a1.a1', '672.f1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2761, -1, 1558, -1, 3381, -1, 3418, -1], 'generators': [3, 672], 'label': '1344.9508.336.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '336.g1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506858
    {'ambient': '1344.9508', 'aut_centralizer_order': 2688, 'aut_label': '336.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '12.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '112.h1.a1', '168.d1.a1', '168.n1.a1', '168.r1.a1', '168.r1.b1', '168.v1.a1', '168.bd1.a1', '168.bd1.b1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4666, -1, 5438, -1, 4452, -1, 4775, -1], 'generators': [5], 'label': '1344.9508.336.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '56.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '336.h1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506859
    {'ambient': '1344.9508', 'aut_centralizer_order': 1152, 'aut_label': '336.i1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '14.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '112.i1.a1', '168.e1.b1', '168.j1.a1', '168.k1.b1', '168.o1.a1', '168.q1.a1', '168.bb1.a1', '168.bd1.a1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [3568, -1, 4165, -1, 3995, -1, 4220, -1], 'generators': [10], 'label': '1344.9508.336.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '336.i1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506860
    {'ambient': '1344.9508', 'aut_centralizer_order': 2, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '672.a1.a1', 'complements': ['672.c1.a1', '672.c1.b1', '672.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.a1', '4.e1.a1', '4.n1.a1', '4.n1.b1', '4.q1.a1', '4.q1.b1', '4.y1.a1', '4.y1.b1', '4.bb1.a1', '4.bc1.a1', '6.d1.a1', '14.d1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4442, 2716, 4776, 2406, 4633, 3133, 4258, 2990], 'generators': [5, 448, 8, 336, 2, 192, 672], 'label': '1344.9508.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.c1.a1', '4.e1.a1', '4.n1.a1', '4.n1.b1', '4.q1.a1', '4.q1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '672.1175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': '672.1175'}
  • id: 74506878
    {'ambient': '1344.9508', 'aut_centralizer_order': 1152, 'aut_label': '672.f1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32256, 'centralizer': '28.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.f1.a1', '224.f1.a1', '336.g1.a1', '336.m1.a1', '336.m1.b1'], 'contains': ['1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [754, -1, 304, -1, 1363, -1, 940, -1], 'generators': [3], 'label': '1344.9508.672.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.n1.a1', 'old_label': '672.f1.a1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 74506861
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '4.v1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '336.c1.a1', 'complements': ['336.l1.a1', '336.m1.b1', '336.m1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.k1.a1', '2.k1.b1'], 'contains': ['8.h1.a1', '8.i1.a1', '8.m1.a1', '12.bb1.a1', '28.bb1.a1'], 'core': '4.v1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7573, 4869, 7425, 4068, 7337, 6743, 5863, 5959], 'generators': [5, 192, 680, 672, 1174, 448], 'label': '1344.9508.4.v1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.v1.a1', 'normal_contained_in': ['2.e1.a1', '2.k1.b1', '2.k1.a1'], 'normal_contains': ['8.h1.a1', '8.i1.a1', '8.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.v1.a1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.v1.a1', 'subgroup_fusion': None, 'weyl_group': '336.161'}
  • id: 74506862
    {'ambient': '1344.9508', 'aut_centralizer_order': 1152, 'aut_label': '336.i1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '14.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.b1', '112.i1.b1', '168.e1.a1', '168.j1.b1', '168.k1.a1', '168.o1.b1', '168.q1.b1', '168.bb1.a1', '168.bd1.b1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [3568, -1, 3585, -1, 3995, -1, 4153, -1], 'generators': [58], 'label': '1344.9508.336.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '336.i1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.i1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506863
    {'ambient': '1344.9508', 'aut_centralizer_order': 1152, 'aut_label': '336.j1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '28.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '112.j1.a1', '168.f1.a1', '168.i1.a1', '168.i1.b1', '168.k1.a1', '168.k1.b1', '168.t1.a1', '168.w1.a1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [3196, -1, 2725, -1, 3549, -1, 3661, -1], 'generators': [51], 'label': '1344.9508.336.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '336.j1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506864
    {'ambient': '1344.9508', 'aut_centralizer_order': 192, 'aut_label': '336.k1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '84.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.a1', '112.k1.a1', '168.g1.a1', '168.m1.a1', '168.o1.a1', '168.r1.b1', '168.x1.a1', '168.bc1.a1', '168.bd1.b1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [4299, -1, 6253, -1, 4614, -1, 4622, -1], 'generators': [1175], 'label': '1344.9508.336.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.d1.a1', 'old_label': '336.k1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506865
    {'ambient': '1344.9508', 'aut_centralizer_order': 192, 'aut_label': '336.k1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '84.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.b1', '112.k1.b1', '168.g1.a1', '168.m1.b1', '168.o1.b1', '168.r1.a1', '168.x1.b1', '168.bc1.a1', '168.bd1.a1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [4299, -1, 6010, -1, 4614, -1, 4706, -1], 'generators': [7], 'label': '1344.9508.336.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.d1.a1', 'old_label': '336.k1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.k1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506866
    {'ambient': '1344.9508', 'aut_centralizer_order': 2016, 'aut_label': '336.l1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '8.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.l1.a1', '112.l1.a1', '168.c1.a1'], 'contains': ['672.b1.a1', '672.c1.a1', '672.c1.b1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1296, -1, 408, -1, 1522, -1, 1061, -1], 'generators': [1, 344], 'label': '1344.9508.336.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.o1.a1', 'old_label': '336.l1.a1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.l1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 74506867
    {'ambient': '1344.9508', 'aut_centralizer_order': 288, 'aut_label': '336.m1', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32256, 'centralizer': '56.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.m1.a1', '112.m1.a1', '168.h1.a1'], 'contains': ['672.c1.a1', '672.e1.a1', '672.f1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [778, -1, 177, -1, 1204, -1, 922, -1], 'generators': [1, 2], 'label': '1344.9508.336.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.k1.a1', 'old_label': '336.m1.a1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 74506868
    {'ambient': '1344.9508', 'aut_centralizer_order': 288, 'aut_label': '336.m1', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32256, 'centralizer': '56.k1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.m1.b1', '112.m1.b1', '168.h1.b1'], 'contains': ['672.c1.b1', '672.e1.b1', '672.f1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [778, -1, 625, -1, 1204, -1, 884, -1], 'generators': [337, 722], 'label': '1344.9508.336.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.k1.b1', 'old_label': '336.m1.b1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.m1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 74506869
    {'ambient': '1344.9508', 'aut_centralizer_order': 16128, 'aut_label': '448.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '2.b1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '224.a1.a1', '224.b1.a1', '224.c1.a1', '224.c1.b1', '224.d1.a1', '224.e1.a1', '224.e1.b1', '224.f1.a1'], 'contains': ['1344.a1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [293, 1862, 339, 3339, 1263, 3180, 1126, 3639], 'generators': [448], 'label': '1344.9508.448.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '448.a1.a1', 'normal_contained_in': ['64.a1.a1', '224.a1.a1'], 'normal_contains': ['1344.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '448.a1.a1', 'projective_image': '1344.9508', 'quotient_action_image': '2.1', 'quotient_action_kernel': '224.180', 'quotient_action_kernel_order': 224, 'quotient_fusion': None, 'short_label': '448.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 74506870
    {'ambient': '1344.9508', 'aut_centralizer_order': 32256, 'aut_label': '672.a1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32256, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '224.a1.a1', '336.a1.a1', '336.b1.a1', '336.c1.a1', '336.d1.a1', '336.d1.b1', '336.e1.a1', '336.f1.a1', '336.f1.b1', '336.g1.a1', '336.h1.a1', '336.i1.a1', '336.i1.b1', '336.j1.a1', '336.k1.a1', '336.k1.b1'], 'contains': ['1344.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3593, 2599, 3038, 4084, 3913, 3390, 4055, 3769], 'generators': [672], 'label': '1344.9508.672.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '672.a1.a1', 'normal_contained_in': ['96.a1.a1', '224.a1.a1', '336.a1.a1', '336.b1.a1', '336.c1.a1'], 'normal_contains': ['1344.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '672.a1.a1', 'projective_image': '672.1175', 'quotient_action_image': '1.1', 'quotient_action_kernel': '672.1175', 'quotient_action_kernel_order': 672, 'quotient_fusion': None, 'short_label': '672.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 74506871
    {'ambient': '1344.9508', 'aut_centralizer_order': 16128, 'aut_label': '672.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32256, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1.a1', '224.b1.a1', '336.a1.a1', '336.l1.a1'], 'contains': ['1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1296, -1, 460, -1, 1522, -1, 1159, -1], 'generators': [344], 'label': '1344.9508.672.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '336.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '672.b1.a1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 74506872
    {'ambient': '1344.9508', 'aut_centralizer_order': 4, 'aut_label': '4.w1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '672.a1.a1', 'complements': ['336.l1.a1', '336.m1.a1', '336.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.i1.b1', '2.k1.a1'], 'contains': ['8.i1.a1', '8.j1.a1', '8.k1.a1', '12.bc1.a1', '28.bc1.a1'], 'core': '4.w1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6264, 3361, 6933, 3799, 6353, 4970, 6731, 3786], 'generators': [51, 192, 680, 672, 4, 448], 'label': '1344.9508.4.w1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.w1.a1', 'normal_contained_in': ['2.g1.a1', '2.i1.b1', '2.k1.a1'], 'normal_contains': ['8.i1.a1', '8.j1.a1', '8.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.w1.a1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.w1.a1', 'subgroup_fusion': None, 'weyl_group': '672.1175'}
  • id: 74506873
    {'ambient': '1344.9508', 'aut_centralizer_order': 4032, 'aut_label': '672.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32256, 'centralizer': '4.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.c1.a1', '224.c1.a1', '336.d1.a1', '336.l1.a1', '336.m1.a1'], 'contains': ['1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [907, -1, 177, -1, 1414, -1, 1059, -1], 'generators': [1], 'label': '1344.9508.672.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '168.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.x1.a1', 'old_label': '672.c1.a1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 74506874
    {'ambient': '1344.9508', 'aut_centralizer_order': 4032, 'aut_label': '672.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32256, 'centralizer': '4.x1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.c1.b1', '224.c1.b1', '336.d1.b1', '336.l1.a1', '336.m1.b1'], 'contains': ['1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [907, -1, 528, -1, 1414, -1, 1025, -1], 'generators': [337], 'label': '1344.9508.672.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '168.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.x1.b1', 'old_label': '672.c1.b1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 74506875
    {'ambient': '1344.9508', 'aut_centralizer_order': 2688, 'aut_label': '672.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32256, 'centralizer': '12.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.d1.a1', '224.d1.a1', '336.e1.a1'], 'contains': ['1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2307, -1, 3781, -1, 2726, -1, 2881, -1], 'generators': [789], 'label': '1344.9508.672.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '56.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '672.d1.a1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 74506876
    {'ambient': '1344.9508', 'aut_centralizer_order': 1152, 'aut_label': '672.e1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32256, 'centralizer': '14.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.e1.a1', '224.e1.a1', '336.f1.a1', '336.m1.a1'], 'contains': ['1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [852, -1, 217, -1, 1315, -1, 1092, -1], 'generators': [2], 'label': '1344.9508.672.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.j1.a1', 'old_label': '672.e1.a1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 74506877
    {'ambient': '1344.9508', 'aut_centralizer_order': 1152, 'aut_label': '672.e1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32256, 'centralizer': '14.j1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.e1.b1', '224.e1.b1', '336.f1.b1', '336.m1.b1'], 'contains': ['1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [852, -1, 625, -1, 1315, -1, 991, -1], 'generators': [722], 'label': '1344.9508.672.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.j1.b1', 'old_label': '672.e1.b1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 74506879
    {'ambient': '1344.9508', 'aut_centralizer_order': None, 'aut_label': '1344.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['192.a1.a1', '448.a1.a1', '672.a1.a1', '672.b1.a1', '672.c1.a1', '672.c1.b1', '672.d1.a1', '672.e1.a1', '672.e1.b1', '672.f1.a1'], 'contains': [], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [931, 1862, 471, 3339, 1438, 3180, 1075, 3639], 'generators': [], 'label': '1344.9508.1344.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1344.a1.a1', 'normal_contained_in': ['192.a1.a1', '448.a1.a1', '672.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '1344.a1.a1', 'projective_image': '1344.9508', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1344.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 74506880
    {'ambient': '1344.9508', 'aut_centralizer_order': 4, 'aut_label': '4.w1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '672.a1.a1', 'complements': ['336.l1.a1', '336.m1.a1', '336.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.i1.a1', '2.k1.b1'], 'contains': ['8.i1.a1', '8.j1.b1', '8.k1.b1', '12.bc1.b1', '28.bc1.b1'], 'core': '4.w1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6264, 3361, 7854, 4339, 6353, 4970, 6489, 4043], 'generators': [51, 192, 8, 672, 124, 448], 'label': '1344.9508.4.w1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.w1.b1', 'normal_contained_in': ['2.g1.a1', '2.i1.a1', '2.k1.b1'], 'normal_contains': ['8.i1.a1', '8.j1.b1', '8.k1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.w1.b1', 'projective_image': '672.1175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.w1.b1', 'subgroup_fusion': None, 'weyl_group': '672.1175'}
  • id: 74506881
    {'ambient': '1344.9508', 'aut_centralizer_order': 12, 'aut_label': '4.x1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '672.1266', 'aut_weyl_index': 48, 'centralizer': '112.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.a1.a1', '8.o1.a1', '8.q1.a1', '8.s1.a1', '8.t1.b1', '8.u1.b1', '8.v1.a1', '12.f1.a1', '28.f1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [986, -1, 1385, -1, 754, -1, 1059, -1], 'generators': [1, 192, 344, 448, 2, 672], 'label': '1344.9508.4.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.x1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.x1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506882
    {'ambient': '1344.9508', 'aut_centralizer_order': 12, 'aut_label': '4.x1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '672.1266', 'aut_weyl_index': 48, 'centralizer': '112.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.a1.b1', '8.o1.a1', '8.q1.a1', '8.s1.b1', '8.t1.a1', '8.u1.a1', '8.v1.b1', '12.f1.b1', '28.f1.b1'], 'core': '8.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [986, -1, 1014, -1, 754, -1, 918, -1], 'generators': [1, 192, 344, 448, 722, 672], 'label': '1344.9508.4.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.x1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.x1.b1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506883
    {'ambient': '1344.9508', 'aut_centralizer_order': 4, 'aut_label': '4.y1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': None, 'aut_weyl_index': 16, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.a1.a1', '8.p1.a1', '8.r1.a1', '8.x1.a1', '8.z1.b1', '8.ba1.a1', '8.bd1.b1', '12.g1.a1', '28.g1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2970, -1, 2966, -1, 2210, -1, 2199, -1], 'generators': [5, 192, 344, 672, 2, 448], 'label': '1344.9508.4.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.y1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.y1.a1', 'subgroup_fusion': None, 'weyl_group': '336.219'}
  • id: 74506884
    {'ambient': '1344.9508', 'aut_centralizer_order': 4, 'aut_label': '4.y1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': None, 'aut_weyl_index': 16, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.a1.b1', '8.p1.a1', '8.r1.a1', '8.x1.b1', '8.z1.a1', '8.ba1.b1', '8.bd1.a1', '12.g1.b1', '28.g1.b1'], 'core': '8.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2970, -1, 2843, -1, 2210, -1, 2297, -1], 'generators': [5, 192, 344, 672, 722, 448], 'label': '1344.9508.4.y1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.y1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.y1.b1', 'subgroup_fusion': None, 'weyl_group': '336.219'}
  • id: 74506885
    {'ambient': '1344.9508', 'aut_centralizer_order': 12, 'aut_label': '4.z1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1344.11434', 'aut_weyl_index': 24, 'centralizer': '224.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.f1.a1', '8.s1.a1', '8.s1.b1', '8.t1.a1', '8.t1.b1', '8.w1.a1', '8.bb1.a1', '12.m1.a1', '28.n1.a1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1125, -1, 1273, -1, 1196, -1, 781, -1], 'generators': [1, 192, 336, 448, 2, 672], 'label': '1344.9508.4.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.z1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.z1.a1', 'subgroup_fusion': None, 'weyl_group': '112.42'}
  • id: 74506886
    {'ambient': '1344.9508', 'aut_centralizer_order': 12, 'aut_label': '4.ba1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1344.11434', 'aut_weyl_index': 24, 'centralizer': '224.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.n1.a1', '8.u1.a1', '8.u1.b1', '8.v1.a1', '8.v1.b1', '8.w1.a1', '8.bb1.a1', '12.n1.a1', '28.o1.a1'], 'core': '8.n1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1251, -1, 2049, -1, 1347, -1, 1224, -1], 'generators': [1, 192, 336, 448, 10, 672], 'label': '1344.9508.4.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.ba1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '112.42'}
  • id: 74506887
    {'ambient': '1344.9508', 'aut_centralizer_order': 4, 'aut_label': '4.bb1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.f1.a1', '8.x1.a1', '8.x1.b1', '8.y1.a1', '8.ba1.a1', '8.ba1.b1', '8.bc1.a1', '12.r1.a1', '28.r1.a1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3529, -1, 3081, -1, 2417, -1, 1978, -1], 'generators': [5, 192, 336, 672, 2, 448], 'label': '1344.9508.4.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.bb1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '336.219'}
  • id: 74506888
    {'ambient': '1344.9508', 'aut_centralizer_order': 4, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '336.c1.a1', 'complements': ['672.e1.a1', '672.e1.b1', '672.c1.a1', '672.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.d1.a1', '4.g1.a1', '4.o1.a1', '4.p1.a1', '4.t1.a1', '4.v1.a1', '6.e1.a1', '14.e1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7677, 5418, 6643, 5680, 6561, 6741, 5465, 6892], 'generators': [5, 448, 336, 8, 6, 192, 672], 'label': '1344.9508.2.e1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.d1.a1', '4.g1.a1', '4.o1.a1', '4.p1.a1', '4.t1.a1', '4.v1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '672.1175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1.a1', 'subgroup_fusion': None, 'weyl_group': '336.161'}
  • id: 74506889
    {'ambient': '1344.9508', 'aut_centralizer_order': 4, 'aut_label': '4.bc1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.n1.a1', '8.y1.a1', '8.z1.a1', '8.z1.b1', '8.bc1.a1', '8.bd1.a1', '8.bd1.b1', '12.s1.a1', '28.s1.a1'], 'core': '8.n1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3434, -1, 2635, -1, 2584, -1, 2406, -1], 'generators': [5, 192, 336, 672, 10, 448], 'label': '1344.9508.4.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.bc1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '336.219'}
  • id: 74506890
    {'ambient': '1344.9508', 'aut_centralizer_order': 12, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2688.dt', 'aut_weyl_index': 12, 'centralizer': '224.a1.a1', 'complements': ['224.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.c1.a1', '12.d1.a1', '12.d1.b1', '12.e1.a1', '12.e1.b1', '12.f1.a1', '12.f1.b1', '12.m1.a1', '12.n1.a1', '42.b1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5568, 2664, 3821, 7637, 5120, 719, 3433, 496], 'generators': [1, 192, 8, 336, 2, 672], 'label': '1344.9508.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['12.a1.a1', '12.b1.a1', '12.c1.a1', '12.d1.b1', '12.d1.a1', '12.e1.b1', '12.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '672.1175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '224.178'}
  • id: 74506891
    {'ambient': '1344.9508', 'aut_centralizer_order': 28, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.19922', 'aut_weyl_index': 84, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.h1.a1', '12.j1.a1', '12.l1.a1', '12.l1.b1', '12.o1.a1', '12.o1.b1', '42.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8170, -1, 8076, -1, 8007, -1, 4864, -1], 'generators': [1, 672, 336, 192, 4, 8], 'label': '1344.9508.6.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 74506892
    {'ambient': '1344.9508', 'aut_centralizer_order': 4, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 12, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.i1.a1', '12.k1.a1', '12.p1.a1', '12.p1.b1', '12.q1.a1', '12.q1.b1', '42.c1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9459, -1, 9145, -1, 8417, -1, 6281, -1], 'generators': [1, 192, 336, 8, 6, 672], 'label': '1344.9508.6.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
  • id: 74506893
    {'ambient': '1344.9508', 'aut_centralizer_order': 4, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2688.dt', 'aut_weyl_index': 12, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.g1.a1', '12.g1.b1', '12.h1.a1', '12.i1.a1', '12.r1.a1', '12.s1.a1', '12.t1.a1', '12.t1.b1', '12.w1.a1', '12.w1.b1', '42.d1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6863, -1, 6293, -1, 5231, -1, 4000, -1], 'generators': [5, 192, 8, 336, 2, 672], 'label': '1344.9508.6.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': '224.178'}
  • id: 74506894
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1344.11434', 'aut_weyl_index': 24, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.h1.a1', '12.k1.a1', '12.u1.a1', '12.v1.a1', '12.z1.a1', '12.bb1.a1', '42.e1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9578, -1, 8551, -1, 8542, -1, 4936, -1], 'generators': [5, 192, 336, 8, 6, 672], 'label': '1344.9508.6.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.e1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
  • id: 74506895
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1344.11434', 'aut_weyl_index': 24, 'centralizer': '336.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.j1.a1', '12.k1.a1', '12.x1.a1', '12.x1.b1', '12.y1.a1', '12.y1.b1', '42.f1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9679, -1, 9736, -1, 8950, -1, 6799, -1], 'generators': [2, 192, 336, 8, 4, 672], 'label': '1344.9508.6.f1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.f1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1.a1', 'subgroup_fusion': None, 'weyl_group': '112.42'}
  • id: 74506896
    {'ambient': '1344.9508', 'aut_centralizer_order': 4, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2688.dt', 'aut_weyl_index': 12, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.i1.a1', '12.j1.a1', '12.ba1.a1', '12.ba1.b1', '12.bc1.a1', '12.bc1.b1', '42.g1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8330, -1, 9441, -1, 8230, -1, 6554, -1], 'generators': [3, 192, 336, 8, 4, 672], 'label': '1344.9508.6.g1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.g1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1.a1', 'subgroup_fusion': None, 'weyl_group': '224.178'}
  • id: 74506897
    {'ambient': '1344.9508', 'aut_centralizer_order': 4, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1344.11434', 'aut_weyl_index': 24, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.h1.a1', '3.a1.a1'], 'contains': ['12.d1.a1', '12.l1.a1', '12.q1.a1', '12.t1.a1', '12.u1.a1', '12.y1.a1', '12.ba1.a1', '42.h1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9323, -1, 9360, -1, 8301, -1, 5329, -1], 'generators': [1, 192, 124, 8, 2, 672], 'label': '1344.9508.6.h1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.h1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1.a1', 'subgroup_fusion': None, 'weyl_group': '224.178'}
  • id: 74506898
    {'ambient': '1344.9508', 'aut_centralizer_order': 4, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1344.11434', 'aut_weyl_index': 24, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.h1.b1', '3.a1.a1'], 'contains': ['12.d1.b1', '12.l1.b1', '12.q1.b1', '12.t1.b1', '12.u1.a1', '12.y1.b1', '12.ba1.b1', '42.h1.b1'], 'core': '12.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [9323, -1, 8881, -1, 8301, -1, 5207, -1], 'generators': [337, 192, 4, 680, 722, 672], 'label': '1344.9508.6.h1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.h1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1.b1', 'subgroup_fusion': None, 'weyl_group': '224.178'}
  • id: 74506899
    {'ambient': '1344.9508', 'aut_centralizer_order': 4, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '336.b1.a1', 'complements': ['672.c1.a1', '672.c1.b1', '672.d1.a1', '672.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.f1.a1', '4.g1.a1', '4.r1.a1', '4.r1.b1', '4.s1.a1', '4.s1.b1', '6.f1.a1', '14.f1.a1'], 'core': '2.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8120, 4912, 8347, 1358, 7270, 5298, 7106, 6274], 'generators': [2, 448, 336, 8, 4, 192, 672], 'label': '1344.9508.2.f1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.f1.a1', '4.g1.a1', '4.r1.a1', '4.r1.b1', '4.s1.a1', '4.s1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.f1.a1', 'projective_image': '672.1175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.f1.a1', 'subgroup_fusion': None, 'weyl_group': '336.219'}
  • id: 74506900
    {'ambient': '1344.9508', 'aut_centralizer_order': 4, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1344.11434', 'aut_weyl_index': 24, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.i1.a1', '3.a1.a1'], 'contains': ['12.e1.a1', '12.l1.a1', '12.p1.a1', '12.t1.b1', '12.v1.a1', '12.x1.b1', '12.bc1.b1', '42.i1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9043, -1, 9302, -1, 8130, -1, 5005, -1], 'generators': [1, 192, 124, 8, 722, 672], 'label': '1344.9508.6.i1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.i1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1.a1', 'subgroup_fusion': None, 'weyl_group': '224.178'}
  • id: 74506901
    {'ambient': '1344.9508', 'aut_centralizer_order': 4, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1344.11434', 'aut_weyl_index': 24, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.i1.b1', '3.a1.a1'], 'contains': ['12.e1.b1', '12.l1.b1', '12.p1.b1', '12.t1.a1', '12.v1.a1', '12.x1.a1', '12.bc1.a1', '42.i1.b1'], 'core': '12.e1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [9043, -1, 8180, -1, 8130, -1, 5088, -1], 'generators': [337, 192, 4, 680, 2, 672], 'label': '1344.9508.6.i1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.i1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1.b1', 'subgroup_fusion': None, 'weyl_group': '224.178'}
  • id: 74506902
    {'ambient': '1344.9508', 'aut_centralizer_order': 4, 'aut_label': '6.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1344.11434', 'aut_weyl_index': 24, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.j1.a1', '3.a1.a1'], 'contains': ['12.d1.a1', '12.o1.a1', '12.p1.a1', '12.w1.a1', '12.x1.a1', '12.z1.a1', '12.ba1.b1', '42.j1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7851, -1, 8721, -1, 8685, -1, 5535, -1], 'generators': [1, 192, 4, 8, 2, 672], 'label': '1344.9508.6.j1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.j1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.j1.a1', 'subgroup_fusion': None, 'weyl_group': '224.178'}
  • id: 74506903
    {'ambient': '1344.9508', 'aut_centralizer_order': 4, 'aut_label': '6.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1344.11434', 'aut_weyl_index': 24, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.j1.b1', '3.a1.a1'], 'contains': ['12.d1.b1', '12.o1.b1', '12.p1.b1', '12.w1.b1', '12.x1.b1', '12.z1.a1', '12.ba1.a1', '42.j1.b1'], 'core': '12.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [7851, -1, 8815, -1, 8685, -1, 5952, -1], 'generators': [337, 192, 124, 680, 722, 672], 'label': '1344.9508.6.j1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.j1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.j1.b1', 'subgroup_fusion': None, 'weyl_group': '224.178'}
  • id: 74506904
    {'ambient': '1344.9508', 'aut_centralizer_order': 4, 'aut_label': '6.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1344.11434', 'aut_weyl_index': 24, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.k1.a1', '3.a1.a1'], 'contains': ['12.e1.a1', '12.o1.a1', '12.q1.a1', '12.w1.b1', '12.y1.b1', '12.bb1.a1', '12.bc1.a1', '42.k1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8886, -1, 8251, -1, 8842, -1, 5677, -1], 'generators': [1, 192, 4, 8, 722, 672], 'label': '1344.9508.6.k1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.k1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.k1.a1', 'subgroup_fusion': None, 'weyl_group': '224.178'}
  • id: 74506905
    {'ambient': '1344.9508', 'aut_centralizer_order': 4, 'aut_label': '6.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1344.11434', 'aut_weyl_index': 24, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.k1.b1', '3.a1.a1'], 'contains': ['12.e1.b1', '12.o1.b1', '12.q1.b1', '12.w1.a1', '12.y1.a1', '12.bb1.a1', '12.bc1.b1', '42.k1.b1'], 'core': '12.e1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [8886, -1, 8646, -1, 8842, -1, 5617, -1], 'generators': [337, 192, 124, 680, 2, 672], 'label': '1344.9508.6.k1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.k1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.k1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.k1.b1', 'subgroup_fusion': None, 'weyl_group': '224.178'}
  • id: 74506906
    {'ambient': '1344.9508', 'aut_centralizer_order': 6, 'aut_label': '7.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '768.1076474', 'aut_weyl_index': 42, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['14.a1.a1', '14.b1.a1', '14.c1.a1', '14.d1.a1', '14.e1.a1', '14.f1.a1', '14.g1.a1', '14.h1.a1', '14.h1.b1', '14.i1.a1', '14.i1.b1', '14.j1.a1', '14.j1.b1', '14.k1.a1', '14.k1.b1', '21.a1.a1'], 'core': '14.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7271, -1, 7186, -1, 5647, -1, 7992, -1], 'generators': [1, 672, 8, 2, 448, 4, 336], 'label': '1344.9508.7.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '7.a1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7.a1.a1', 'subgroup_fusion': None, 'weyl_group': '96.219'}
  • id: 74506907
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '56.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.x1.a1', '4.y1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.e1.b1', '24.a1.a1', '56.h1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1363, 269, 1983, 2307, 1491, 815, 1493, 2023], 'generators': [2, 448, 672, 344, 192], 'label': '1344.9508.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.c1.a1'], 'normal_contains': ['16.a1.a1', '16.b1.a1', '16.e1.b1', '24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506908
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '56.b1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.x1.b1', '4.y1.b1'], 'contains': ['16.a1.a1', '16.b1.b1', '16.e1.a1', '24.a1.b1', '56.h1.b1'], 'core': '8.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1363, 269, 2207, 1981, 1491, 815, 1584, 955], 'generators': [722, 448, 672, 344, 192], 'label': '1344.9508.8.a1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': ['4.c1.a1'], 'normal_contains': ['16.a1.a1', '16.b1.b1', '16.e1.a1', '24.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.b1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 74506909
    {'ambient': '1344.9508', 'aut_centralizer_order': 672, 'aut_label': '8.b1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '48.52', 'aut_weyl_index': 672, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['16.a1.a1', '16.c1.a1', '16.d1.a1', '24.b1.a1', '56.a1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4157, 2266, 4293, 4512, 4055, 4238, 3627, 5225], 'generators': [8, 448, 192, 336, 672], 'label': '1344.9508.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'normal_contains': ['16.a1.a1', '16.c1.a1', '16.d1.a1', '24.b1.a1', '56.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '672.1175', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 74506910
    {'ambient': '1344.9508', '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': '672.a1.a1', 'complements': ['672.e1.a1', '672.e1.b1', '672.c1.a1', '672.c1.b1', '672.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.d1.a1', '4.e1.a1', '4.f1.a1', '4.u1.a1', '4.u1.b1', '4.w1.a1', '4.w1.b1', '6.g1.a1', '14.g1.a1'], 'core': '2.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6100, 3244, 7234, 5069, 6108, 2637, 6610, 3471], 'generators': [3, 448, 336, 8, 4, 192, 672], 'label': '1344.9508.2.g1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.d1.a1', '4.e1.a1', '4.f1.a1', '4.u1.a1', '4.u1.b1', '4.w1.a1', '4.w1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.g1.a1', 'projective_image': '672.1175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.g1.a1', 'subgroup_fusion': None, 'weyl_group': '672.1175'}
  • id: 74506911
    {'ambient': '1344.9508', 'aut_centralizer_order': 168, 'aut_label': '8.c1', 'aut_quo_index': 168, 'aut_stab_index': 2, 'aut_weyl_group': '96.221', 'aut_weyl_index': 336, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.h1.a1', '4.i1.a1', '4.j1.a1', '4.k1.a1', '4.l1.a1', '4.m1.a1'], 'contains': ['16.c1.a1', '16.f1.a1', '24.c1.a1', '56.b1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4985, 7617, 4103, 8471, 4499, 5009, 4699, 6015], 'generators': [1, 448, 192, 8, 672], 'label': '1344.9508.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.a1.a1', '4.h1.a1', '4.i1.a1', '4.j1.a1', '4.k1.a1', '4.l1.a1', '4.m1.a1'], 'normal_contains': ['16.c1.a1', '24.c1.a1', '56.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506912
    {'ambient': '1344.9508', 'aut_centralizer_order': 168, 'aut_label': '8.c1', 'aut_quo_index': 168, 'aut_stab_index': 2, 'aut_weyl_group': '96.221', 'aut_weyl_index': 336, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.h1.b1', '4.i1.b1', '4.j1.b1', '4.k1.b1', '4.l1.b1', '4.m1.b1'], 'contains': ['16.c1.a1', '16.f1.b1', '24.c1.b1', '56.b1.b1'], 'core': '8.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4985, 7617, 4854, 8195, 4499, 5009, 4515, 5752], 'generators': [337, 448, 192, 8, 672], 'label': '1344.9508.8.c1.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.c1.b1', 'normal_contained_in': ['4.a1.a1', '4.h1.b1', '4.i1.b1', '4.j1.b1', '4.k1.b1', '4.l1.b1', '4.m1.b1'], 'normal_contains': ['16.c1.a1', '24.c1.b1', '56.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 74506913
    {'ambient': '1344.9508', 'aut_centralizer_order': 112, 'aut_label': '8.d1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '288.992', 'aut_weyl_index': 112, 'centralizer': '48.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.h1.a1', '4.h1.b1', '4.n1.a1', '4.n1.b1', '4.o1.a1', '4.p1.a1'], 'contains': ['16.c1.a1', '16.g1.a1', '24.u1.a1', '56.c1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5832, 5525, 5024, 6583, 4610, 6338, 4163, 6817], 'generators': [789, 192, 672, 8, 448], 'label': '1344.9508.8.d1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.d1.a1', 'normal_contained_in': ['4.b1.a1', '4.h1.b1', '4.h1.a1', '4.n1.a1', '4.n1.b1', '4.o1.a1', '4.p1.a1'], 'normal_contains': ['16.c1.a1', '56.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 74506914
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '8.e1', 'aut_quo_index': 168, 'aut_stab_index': 2, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '112.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.i1.a1', '4.j1.b1', '4.n1.a1', '4.q1.a1', '4.r1.a1', '4.s1.a1'], 'contains': ['16.b1.a1', '16.c1.a1', '16.e1.a1', '24.d1.a1', '56.s1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4537, 1230, 4496, 2950, 3944, 2814, 4000, 3276], 'generators': [2, 448, 672, 8, 192], 'label': '1344.9508.8.e1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.e1.a1', 'normal_contained_in': ['4.c1.a1', '4.i1.a1', '4.j1.b1', '4.n1.a1', '4.q1.a1', '4.r1.a1', '4.s1.a1'], 'normal_contains': ['16.b1.a1', '16.c1.a1', '16.e1.a1', '24.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '112.42'}
  • id: 74506915
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '8.e1', 'aut_quo_index': 168, 'aut_stab_index': 2, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '112.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.i1.b1', '4.j1.a1', '4.n1.b1', '4.q1.b1', '4.r1.b1', '4.s1.b1'], 'contains': ['16.b1.b1', '16.c1.a1', '16.e1.b1', '24.d1.b1', '56.s1.b1'], 'core': '8.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4537, 1230, 4362, 3224, 3944, 2814, 3923, 3540], 'generators': [722, 448, 672, 8, 192], 'label': '1344.9508.8.e1.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.e1.b1', 'normal_contained_in': ['4.c1.a1', '4.i1.b1', '4.j1.a1', '4.n1.b1', '4.q1.b1', '4.r1.b1', '4.s1.b1'], 'normal_contains': ['16.b1.b1', '16.c1.a1', '16.e1.b1', '24.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.b1', 'subgroup_fusion': None, 'weyl_group': '112.42'}
  • id: 74506916
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '8.f1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 48, 'centralizer': '112.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.z1.a1', '4.bb1.a1'], 'contains': ['16.b1.a1', '16.b1.b1', '16.d1.a1', '24.e1.a1', '56.u1.a1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1816, 1731, 2130, 1681, 1612, 397, 1410, 1243], 'generators': [2, 448, 672, 336, 192], 'label': '1344.9508.8.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': ['4.c1.a1'], 'normal_contains': ['16.b1.a1', '16.b1.b1', '16.d1.a1', '24.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': '112.42'}
  • id: 74506917
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '8.g1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 48, 'centralizer': '112.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.i1.a1', '4.i1.b1', '4.o1.a1', '4.t1.a1', '4.u1.a1', '4.u1.b1'], 'contains': ['16.c1.a1', '16.h1.a1', '24.f1.a1', '56.w1.a1'], 'core': '8.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4830, 3612, 4696, 5963, 5070, 3578, 4775, 4073], 'generators': [3, 448, 672, 8, 192], 'label': '1344.9508.8.g1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.g1.a1', 'normal_contained_in': ['4.d1.a1', '4.i1.b1', '4.i1.a1', '4.o1.a1', '4.t1.a1', '4.u1.a1', '4.u1.b1'], 'normal_contains': ['16.c1.a1', '24.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.g1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1.a1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
  • id: 74506918
    {'ambient': '1344.9508', 'aut_centralizer_order': 112, 'aut_label': '8.h1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '288.992', 'aut_weyl_index': 112, 'centralizer': '48.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.k1.a1', '4.k1.b1', '4.q1.a1', '4.q1.b1', '4.t1.a1', '4.v1.a1'], 'contains': ['16.c1.a1', '16.i1.a1', '24.x1.a1', '56.d1.a1'], 'core': '8.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4671, 7205, 5125, 5086, 6504, 6724, 4983, 6282], 'generators': [5, 192, 672, 8, 448], 'label': '1344.9508.8.h1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.h1.a1', 'normal_contained_in': ['4.b1.a1', '4.k1.b1', '4.k1.a1', '4.q1.a1', '4.q1.b1', '4.t1.a1', '4.v1.a1'], 'normal_contains': ['16.c1.a1', '56.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.h1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.a1', 'subgroup_fusion': None, 'weyl_group': '48.43'}
  • id: 74506919
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '8.i1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 48, 'centralizer': '112.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.j1.a1', '4.j1.b1', '4.p1.a1', '4.v1.a1', '4.w1.a1', '4.w1.b1'], 'contains': ['16.c1.a1', '16.j1.a1', '24.g1.a1', '56.x1.a1'], 'core': '8.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6183, 4024, 4783, 5628, 4896, 4623, 3846, 3806], 'generators': [51, 448, 672, 8, 192], 'label': '1344.9508.8.i1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.i1.a1', 'normal_contained_in': ['4.d1.a1', '4.j1.b1', '4.j1.a1', '4.p1.a1', '4.v1.a1', '4.w1.a1', '4.w1.b1'], 'normal_contains': ['16.c1.a1', '24.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.i1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1.a1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
  • id: 74506920
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '8.j1', 'aut_quo_index': 168, 'aut_stab_index': 2, 'aut_weyl_group': '2016.eo', 'aut_weyl_index': 16, 'centralizer': '336.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.l1.b1', '4.m1.a1', '4.n1.a1', '4.q1.b1', '4.u1.a1', '4.w1.a1'], 'contains': ['16.c1.a1', '16.k1.a1', '24.y1.a1', '56.y1.a1'], 'core': '8.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5463, 4378, 5267, 4089, 5336, 3909, 6429, 4301], 'generators': [1175, 672, 448, 8, 192], 'label': '1344.9508.8.j1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.j1.a1', 'normal_contained_in': ['4.e1.a1', '4.l1.b1', '4.m1.a1', '4.n1.a1', '4.q1.b1', '4.u1.a1', '4.w1.a1'], 'normal_contains': ['16.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.j1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1.a1', 'subgroup_fusion': None, 'weyl_group': '336.161'}
  • id: 74506921
    {'ambient': '1344.9508', 'aut_centralizer_order': 2, 'aut_label': '2.h1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '672.a1.a1', 'complements': ['672.b1.a1', '672.e1.b1', '672.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.h1.a1', '4.i1.a1', '4.m1.a1', '4.n1.a1', '4.o1.a1', '4.s1.a1', '4.u1.a1', '6.h1.a1', '14.h1.a1'], 'core': '2.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7561, 3774, 7557, 6391, 6251, 3555, 5779, 5930], 'generators': [1, 448, 124, 8, 2, 192, 672], 'label': '1344.9508.2.h1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.h1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.h1.a1', '4.i1.a1', '4.m1.a1', '4.n1.a1', '4.o1.a1', '4.s1.a1', '4.u1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.h1.a1', 'projective_image': '672.1175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.h1.a1', 'subgroup_fusion': None, 'weyl_group': '672.1175'}
  • id: 74506922
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '8.j1', 'aut_quo_index': 168, 'aut_stab_index': 2, 'aut_weyl_group': '2016.eo', 'aut_weyl_index': 16, 'centralizer': '336.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.l1.a1', '4.m1.b1', '4.n1.b1', '4.q1.a1', '4.u1.b1', '4.w1.b1'], 'contains': ['16.c1.a1', '16.k1.b1', '24.y1.b1', '56.y1.b1'], 'core': '8.j1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5463, 4378, 5346, 3663, 5336, 3909, 5524, 4525], 'generators': [7, 672, 448, 8, 192], 'label': '1344.9508.8.j1.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.j1.b1', 'normal_contained_in': ['4.e1.a1', '4.l1.a1', '4.m1.b1', '4.n1.b1', '4.q1.a1', '4.u1.b1', '4.w1.b1'], 'normal_contains': ['16.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.j1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1.b1', 'subgroup_fusion': None, 'weyl_group': '336.161'}
  • id: 74506923
    {'ambient': '1344.9508', 'aut_centralizer_order': 112, 'aut_label': '8.k1', 'aut_quo_index': 168, 'aut_stab_index': 2, 'aut_weyl_group': '144.195', 'aut_weyl_index': 224, 'centralizer': '48.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.h1.b1', '4.k1.a1', '4.r1.a1', '4.s1.b1', '4.u1.b1', '4.w1.a1'], 'contains': ['16.c1.a1', '24.z1.a1', '56.e1.a1'], 'core': '8.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6052, 5937, 7829, 4788, 7577, 5673, 7434, 7084], 'generators': [4, 8, 672, 192, 448], 'label': '1344.9508.8.k1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.k1.a1', 'normal_contained_in': ['4.f1.a1', '4.h1.b1', '4.k1.a1', '4.r1.a1', '4.s1.b1', '4.u1.b1', '4.w1.a1'], 'normal_contains': ['16.c1.a1', '56.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.k1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 74506924
    {'ambient': '1344.9508', 'aut_centralizer_order': 112, 'aut_label': '8.k1', 'aut_quo_index': 168, 'aut_stab_index': 2, 'aut_weyl_group': '144.195', 'aut_weyl_index': 224, 'centralizer': '48.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.h1.a1', '4.k1.b1', '4.r1.b1', '4.s1.a1', '4.u1.a1', '4.w1.b1'], 'contains': ['16.c1.a1', '24.z1.b1', '56.e1.b1'], 'core': '8.k1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6052, 5937, 9649, 6242, 7577, 5673, 7567, 6550], 'generators': [124, 680, 672, 192, 448], 'label': '1344.9508.8.k1.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.k1.b1', 'normal_contained_in': ['4.f1.a1', '4.h1.a1', '4.k1.b1', '4.r1.b1', '4.s1.a1', '4.u1.a1', '4.w1.b1'], 'normal_contains': ['16.c1.a1', '56.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.k1.b1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1.b1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 74506925
    {'ambient': '1344.9508', 'aut_centralizer_order': 32, 'aut_label': '8.l1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 32, 'centralizer': '168.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.l1.a1', '4.l1.b1', '4.p1.a1', '4.r1.a1', '4.r1.b1', '4.t1.a1'], 'contains': ['16.c1.a1', '24.ba1.a1', '56.z1.a1'], 'core': '8.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6567, 6368, 7937, 3863, 7673, 6007, 7367, 4807], 'generators': [6, 672, 448, 8, 192], 'label': '1344.9508.8.l1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.l1.a1', 'normal_contained_in': ['4.g1.a1', '4.l1.b1', '4.l1.a1', '4.p1.a1', '4.r1.a1', '4.r1.b1', '4.t1.a1'], 'normal_contains': ['16.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.l1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1.a1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
  • id: 74506926
    {'ambient': '1344.9508', 'aut_centralizer_order': 32, 'aut_label': '8.m1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 32, 'centralizer': '168.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.m1.a1', '4.m1.b1', '4.o1.a1', '4.s1.a1', '4.s1.b1', '4.v1.a1'], 'contains': ['16.c1.a1', '24.bb1.a1', '56.ba1.a1'], 'core': '8.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8637, 5136, 8444, 3463, 7753, 5340, 7501, 4998], 'generators': [1174, 672, 448, 680, 192], 'label': '1344.9508.8.m1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.m1.a1', 'normal_contained_in': ['4.g1.a1', '4.m1.b1', '4.m1.a1', '4.o1.a1', '4.s1.a1', '4.s1.b1', '4.v1.a1'], 'normal_contains': ['16.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.m1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1.a1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
  • id: 74506927
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '8.n1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 48, 'centralizer': '112.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.ba1.a1', '4.bc1.a1'], 'contains': ['16.d1.a1', '16.e1.a1', '16.e1.b1', '24.h1.a1', '56.bb1.a1'], 'core': '8.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1691, 716, 2428, 2609, 1723, 1563, 1667, 1734], 'generators': [10, 448, 672, 336, 192], 'label': '1344.9508.8.n1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.n1.a1', 'normal_contained_in': ['4.c1.a1'], 'normal_contains': ['16.d1.a1', '16.e1.a1', '16.e1.b1', '24.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.n1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1.a1', 'subgroup_fusion': None, 'weyl_group': '112.42'}
  • id: 74506928
    {'ambient': '1344.9508', 'aut_centralizer_order': 168, 'aut_label': '8.o1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.221', 'aut_weyl_index': 336, 'centralizer': '8.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.x1.a1', '4.x1.b1'], 'contains': ['16.a1.a1', '16.f1.a1', '16.f1.b1', '16.l1.a1', '24.i1.a1', '56.f1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1096, -1, 591, -1, 200, -1, 279, -1], 'generators': [1, 672, 448, 344, 192], 'label': '1344.9508.8.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.o1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.o1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 74506929
    {'ambient': '1344.9508', 'aut_centralizer_order': 112, 'aut_label': '8.p1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '144.195', 'aut_weyl_index': 224, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.y1.a1', '4.y1.b1'], 'contains': ['16.a1.a1', '16.g1.a1', '16.i1.a1', '24.j1.a1', '56.g1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2379, -1, 2632, -1, 1916, -1, 2088, -1], 'generators': [5, 192, 672, 344, 448], 'label': '1344.9508.8.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.p1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.p1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 74506930
    {'ambient': '1344.9508', 'aut_centralizer_order': 48, 'aut_label': '8.q1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '56.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.x1.a1', '4.x1.b1'], 'contains': ['16.a1.a1', '16.h1.a1', '16.j1.a1', '24.k1.a1', '56.i1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1575, -1, 1175, -1, 1028, -1, 779, -1], 'generators': [3, 448, 672, 344, 192], 'label': '1344.9508.8.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.q1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.q1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 74506931
    {'ambient': '1344.9508', 'aut_centralizer_order': 8, 'aut_label': '8.r1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2016.eo', 'aut_weyl_index': 16, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.y1.a1', '4.y1.b1'], 'contains': ['16.a1.a1', '16.k1.a1', '16.k1.b1', '24.l1.a1', '56.j1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3520, -1, 3589, -1, 2149, -1, 2228, -1], 'generators': [7, 672, 448, 344, 192], 'label': '1344.9508.8.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.r1.a1', 'projective_image': '672.1175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.r1.a1', 'subgroup_fusion': None, 'weyl_group': '168.50'}