Abstract group data - 1344.8546

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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': [28, 12, 4, 2, 6, 12, 14, 6], 'aut_gens': [[1, 2, 4, 8], [1, 450, 244, 232], [673, 2, 1012, 584], [1, 1122, 1252, 1337], [673, 2, 868, 1336], [1, 2, 1060, 200], [1, 898, 820, 473], [673, 898, 916, 568], [673, 674, 580, 136]], 'aut_group': None, 'aut_hash': 9161810123478319507, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 32256, 'aut_permdeg': 42, 'aut_perms': [583550369770708210561592191385974893571751572414179, 764084665782828898446668915131421555778631620757370, 991647396469354839691729168086794734307777193668023, 135463909557276468182970101453166955853916448883382, 145794125113320540721590920375246730756219672035544, 297947856977588547619464234385086575903881336623854, 1199688577555279090395699842565137369163176260688166, 93602433051292623675165109035862341010583153906717], 'aut_phi_ratio': 84.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 6, 1, 2], [2, 28, 1, 1], [2, 28, 2, 1], [2, 84, 1, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 3, 2, 1], [4, 6, 1, 1], [4, 28, 1, 1], [4, 84, 1, 1], [4, 84, 2, 1], [6, 2, 1, 1], [6, 4, 1, 1], [6, 56, 1, 1], [6, 56, 2, 1], [7, 2, 3, 1], [8, 4, 2, 1], [8, 12, 2, 1], [12, 4, 1, 2], [12, 56, 1, 1], [14, 2, 3, 1], [14, 4, 3, 1], [14, 6, 6, 1], [14, 12, 3, 1], [21, 4, 3, 1], [24, 8, 2, 1], [28, 2, 6, 1], [28, 4, 3, 1], [28, 6, 6, 1], [28, 12, 3, 1], [42, 4, 3, 1], [42, 8, 3, 1], [56, 4, 12, 1], [56, 12, 12, 1], [84, 4, 6, 1], [84, 8, 3, 1], [168, 8, 12, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{21}.(C_6\\times D_4).C_2^5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '16.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': None, 'autcentquo_hash': 5451351369529179689, 'autcentquo_nilpotent': False, 'autcentquo_order': 2016, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^3\\times S_3\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 6, 2], [2, 28, 3], [2, 84, 1], [3, 2, 1], [4, 2, 2], [4, 3, 2], [4, 6, 1], [4, 28, 1], [4, 84, 3], [6, 2, 1], [6, 4, 1], [6, 56, 3], [7, 2, 3], [8, 4, 2], [8, 12, 2], [12, 4, 2], [12, 56, 1], [14, 2, 3], [14, 4, 3], [14, 6, 6], [14, 12, 3], [21, 4, 3], [24, 8, 2], [28, 2, 6], [28, 4, 3], [28, 6, 6], [28, 12, 3], [42, 4, 3], [42, 8, 3], [56, 4, 12], [56, 12, 12], [84, 4, 6], [84, 8, 3], [168, 8, 12]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '672.1141', 'commutator_count': 1, 'commutator_label': '84.6', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '7.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 8546, '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, 6, 1, 2], [2, 28, 1, 3], [2, 84, 1, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 3, 2, 1], [4, 6, 1, 1], [4, 28, 1, 1], [4, 84, 1, 3], [6, 2, 1, 1], [6, 4, 1, 1], [6, 56, 1, 3], [7, 2, 3, 1], [8, 4, 1, 2], [8, 12, 1, 2], [12, 4, 1, 2], [12, 56, 1, 1], [14, 2, 3, 1], [14, 4, 3, 1], [14, 6, 6, 1], [14, 12, 3, 1], [21, 4, 3, 1], [24, 8, 1, 2], [28, 2, 6, 1], [28, 4, 3, 1], [28, 6, 6, 1], [28, 12, 3, 1], [42, 4, 3, 1], [42, 8, 3, 1], [56, 4, 6, 2], [56, 12, 6, 2], [84, 4, 6, 1], [84, 8, 3, 1], [168, 8, 6, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 29877120, 'exponent': 168, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[8, -1, 6]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '336.219', 'hash': 8546, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 84, 'inner_gen_orders': [2, 2, 2, 84], 'inner_gens': [[1, 2, 4, 680], [1, 2, 4, 232], [1, 2, 4, 440], [673, 1122, 916, 8]], 'inner_hash': 1141, 'inner_nilpotent': False, 'inner_order': 672, 'inner_split': True, 'inner_tex': 'D_6\\times D_{28}', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 8, 'irrQ_degree': 48, 'irrQ_dim': 96, 'irrR_degree': 16, 'irrep_stats': [[1, 16], [2, 60], [4, 40], [8, 7]], 'label': '1344.8546', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D56:D6', 'ngens': 8, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 43, 'number_characteristic_subgroups': 78, 'number_conjugacy_classes': 123, 'number_divisions': 52, 'number_normal_subgroups': 136, 'number_subgroup_autclasses': 408, 'number_subgroup_classes': 524, 'number_subgroups': 4724, 'old_label': None, 'order': 1344, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 183], [3, 2], [4, 296], [6, 174], [7, 6], [8, 32], [12, 64], [14, 90], [21, 12], [24, 16], [28, 96], [42, 36], [56, 192], [84, 48], [168, 96]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 2, 6], 'outer_gen_pows': [0, 0, 0, 1], 'outer_gens': [[673, 2, 4, 8], [1, 674, 4, 8], [1, 2, 4, 1016], [1, 2, 4, 825]], '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, 2], [6, 8], [8, 2], [12, 8], [24, 2], [48, 2]], 'representations': {'PC': {'code': 18116660533071618689973858837564429626444513796312690912598283, 'gens': [1, 2, 3, 4], 'pres': [8, -2, -2, -2, -2, -2, -2, -3, -7, 5376, 21763, 3723, 3539, 91, 9292, 8820, 116, 22285, 5013, 141, 14350, 11670, 222, 18455]}, 'Perm': {'d': 26, 'gens': [621574835363066525758440, 355731555140686, 1621106561118, 3023250411916, 4398020226618, 5801212720938, 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': 'D_{56}:D_6', '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: 116986044
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 8546, 'group_order': 1344, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 116986079
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 8546, 'group_order': 1344, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 672, 'size': 1}
  • id: 116986090
    {'aut_label': '2B', 'centralizer': '2.b1.a1', 'counter': 3, 'group_counter': 8546, 'group_order': 1344, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 337, 'size': 2}
  • id: 116986101
    {'aut_label': '2C', 'centralizer': '6.d1.a1', 'counter': 4, 'group_counter': 8546, 'group_order': 1344, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 787, 'size': 6}
  • id: 116986112
    {'aut_label': '2D', 'centralizer': '6.b1.a1', 'counter': 5, 'group_counter': 8546, 'group_order': 1344, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 2, 'size': 6}
  • id: 116986123
    {'aut_label': '2E', 'centralizer': '28.s1.a1', 'counter': 6, 'group_counter': 8546, 'group_order': 1344, 'label': '2E', 'order': 2, 'powers': [1, 6, 6], 'representative': 532, 'size': 28}
  • id: 116986134
    {'aut_label': '2F', 'centralizer': '28.j1.a1', 'counter': 7, 'group_counter': 8546, 'group_order': 1344, 'label': '2F', 'order': 2, 'powers': [1, 7, 7], 'representative': 1133, 'size': 28}
  • id: 116986145
    {'aut_label': '2F', 'centralizer': '28.j1.a1', 'counter': 8, 'group_counter': 8546, 'group_order': 1344, 'label': '2G', 'order': 2, 'powers': [1, 8, 8], 'representative': 1132, 'size': 28}
  • id: 116986156
    {'aut_label': '2H', 'centralizer': '84.r1.a1', 'counter': 9, 'group_counter': 8546, 'group_order': 1344, 'label': '2H', 'order': 2, 'powers': [1, 9, 9], 'representative': 470, 'size': 84}
  • id: 116986045
    {'aut_label': '3A', 'centralizer': '2.d1.a1', 'counter': 10, 'group_counter': 8546, 'group_order': 1344, 'label': '3A', 'order': 3, 'powers': [10, 1, 10], 'representative': 896, 'size': 2}
  • id: 116986056
    {'aut_label': '4A', 'centralizer': '2.c1.a1', 'counter': 11, 'group_counter': 8546, 'group_order': 1344, 'label': '4A', 'order': 4, 'powers': [2, 11, 11], 'representative': 336, 'size': 2}
  • id: 116986067
    {'aut_label': '4B', 'centralizer': '2.a1.a1', 'counter': 12, 'group_counter': 8546, 'group_order': 1344, 'label': '4B', 'order': 4, 'powers': [2, 12, 12], 'representative': 1, 'size': 2}
  • id: 116986072
    {'aut_label': '4C1', 'centralizer': '3.a1.a1', 'counter': 13, 'group_counter': 8546, 'group_order': 1344, 'label': '4C1', 'order': 4, 'powers': [2, 14, 14], 'representative': 675, 'size': 3}
  • id: 116986073
    {'aut_label': '4C1', 'centralizer': '3.a1.a1', 'counter': 14, 'group_counter': 8546, 'group_order': 1344, 'label': '4C-1', 'order': 4, 'powers': [2, 13, 13], 'representative': 3, 'size': 3}
  • id: 116986074
    {'aut_label': '4D', 'centralizer': '6.c1.a1', 'counter': 15, 'group_counter': 8546, 'group_order': 1344, 'label': '4D', 'order': 4, 'powers': [2, 15, 15], 'representative': 114, 'size': 6}
  • id: 116986075
    {'aut_label': '4E', 'centralizer': '28.s1.a1', 'counter': 16, 'group_counter': 8546, 'group_order': 1344, 'label': '4E', 'order': 4, 'powers': [2, 16, 16], 'representative': 965, 'size': 28}
  • id: 116986076
    {'aut_label': '4F', 'centralizer': '84.g1.a1', 'counter': 17, 'group_counter': 8546, 'group_order': 1344, 'label': '4F', 'order': 4, 'powers': [2, 17, 17], 'representative': 270, 'size': 84}
  • id: 116986077
    {'aut_label': '4F', 'centralizer': '84.g1.a1', 'counter': 18, 'group_counter': 8546, 'group_order': 1344, 'label': '4G', 'order': 4, 'powers': [2, 18, 18], 'representative': 79, 'size': 84}
  • id: 116986078
    {'aut_label': '4H', 'centralizer': '84.r1.a1', 'counter': 19, 'group_counter': 8546, 'group_order': 1344, 'label': '4H', 'order': 4, 'powers': [2, 19, 19], 'representative': 1047, 'size': 84}
  • id: 116986080
    {'aut_label': '6A', 'centralizer': '2.d1.a1', 'counter': 20, 'group_counter': 8546, 'group_order': 1344, 'label': '6A', 'order': 6, 'powers': [10, 2, 20], 'representative': 224, 'size': 2}
  • id: 116986081
    {'aut_label': '6B', 'centralizer': '4.c1.a1', 'counter': 21, 'group_counter': 8546, 'group_order': 1344, 'label': '6B', 'order': 6, 'powers': [10, 3, 21], 'representative': 785, 'size': 4}
  • id: 116986082
    {'aut_label': '6C', 'centralizer': '56.u1.a1', 'counter': 22, 'group_counter': 8546, 'group_order': 1344, 'label': '6C', 'order': 6, 'powers': [10, 6, 22], 'representative': 84, 'size': 56}
  • id: 116986083
    {'aut_label': '6D', 'centralizer': '56.k1.a1', 'counter': 23, 'group_counter': 8546, 'group_order': 1344, 'label': '6D', 'order': 6, 'powers': [10, 7, 23], 'representative': 237, 'size': 56}
  • id: 116986084
    {'aut_label': '6D', 'centralizer': '56.k1.a1', 'counter': 24, 'group_counter': 8546, 'group_order': 1344, 'label': '6E', 'order': 6, 'powers': [10, 8, 24], 'representative': 236, 'size': 56}
  • id: 116986085
    {'aut_label': '7A1', 'centralizer': '2.c1.a1', 'counter': 25, 'group_counter': 8546, 'group_order': 1344, 'label': '7A1', 'order': 7, 'powers': [26, 27, 1], 'representative': 1152, 'size': 2}
  • id: 116986086
    {'aut_label': '7A1', 'centralizer': '2.c1.a1', 'counter': 26, 'group_counter': 8546, 'group_order': 1344, 'label': '7A2', 'order': 7, 'powers': [27, 25, 1], 'representative': 960, 'size': 2}
  • id: 116986087
    {'aut_label': '7A1', 'centralizer': '2.c1.a1', 'counter': 27, 'group_counter': 8546, 'group_order': 1344, 'label': '7A3', 'order': 7, 'powers': [25, 26, 1], 'representative': 768, 'size': 2}
  • id: 116986088
    {'aut_label': '8A', 'centralizer': '4.k1.a1', 'counter': 28, 'group_counter': 8546, 'group_order': 1344, 'label': '8A', 'order': 8, 'powers': [11, 28, 28], 'representative': 168, 'size': 4}
  • id: 116986089
    {'aut_label': '8A', 'centralizer': '4.k1.b1', 'counter': 29, 'group_counter': 8546, 'group_order': 1344, 'label': '8B', 'order': 8, 'powers': [11, 29, 29], 'representative': 169, 'size': 4}
  • id: 116986091
    {'aut_label': '8C', 'centralizer': '12.s1.b1', 'counter': 30, 'group_counter': 8546, 'group_order': 1344, 'label': '8C', 'order': 8, 'powers': [11, 30, 30], 'representative': 730, 'size': 12}
  • id: 116986092
    {'aut_label': '8C', 'centralizer': '12.s1.a1', 'counter': 31, 'group_counter': 8546, 'group_order': 1344, 'label': '8D', 'order': 8, 'powers': [11, 31, 31], 'representative': 731, 'size': 12}
  • id: 116986093
    {'aut_label': '12A', 'centralizer': '4.b1.a1', 'counter': 32, 'group_counter': 8546, 'group_order': 1344, 'label': '12A', 'order': 12, 'powers': [20, 12, 32], 'representative': 1121, 'size': 4}
  • id: 116986094
    {'aut_label': '12B', 'centralizer': '4.f1.a1', 'counter': 33, 'group_counter': 8546, 'group_order': 1344, 'label': '12B', 'order': 12, 'powers': [20, 11, 33], 'representative': 112, 'size': 4}
  • id: 116986095
    {'aut_label': '12C', 'centralizer': '56.u1.a1', 'counter': 34, 'group_counter': 8546, 'group_order': 1344, 'label': '12C', 'order': 12, 'powers': [20, 16, 34], 'representative': 1189, 'size': 56}
  • id: 116986096
    {'aut_label': '14A1', 'centralizer': '2.c1.a1', 'counter': 35, 'group_counter': 8546, 'group_order': 1344, 'label': '14A1', 'order': 14, 'powers': [27, 36, 2], 'representative': 1056, 'size': 2}
  • id: 116986097
    {'aut_label': '14A1', 'centralizer': '2.c1.a1', 'counter': 36, 'group_counter': 8546, 'group_order': 1344, 'label': '14A3', 'order': 14, 'powers': [26, 37, 2], 'representative': 480, 'size': 2}
  • id: 116986098
    {'aut_label': '14A1', 'centralizer': '2.c1.a1', 'counter': 37, 'group_counter': 8546, 'group_order': 1344, 'label': '14A5', 'order': 14, 'powers': [25, 35, 2], 'representative': 1248, 'size': 2}
  • id: 116986099
    {'aut_label': '14B1', 'centralizer': '4.a1.a1', 'counter': 38, 'group_counter': 8546, 'group_order': 1344, 'label': '14B1', 'order': 14, 'powers': [27, 39, 3], 'representative': 721, 'size': 4}
  • id: 116986100
    {'aut_label': '14B1', 'centralizer': '4.a1.a1', 'counter': 39, 'group_counter': 8546, 'group_order': 1344, 'label': '14B3', 'order': 14, 'powers': [26, 40, 3], 'representative': 145, 'size': 4}
  • id: 116986102
    {'aut_label': '14B1', 'centralizer': '4.a1.a1', 'counter': 40, 'group_counter': 8546, 'group_order': 1344, 'label': '14B5', 'order': 14, 'powers': [25, 38, 3], 'representative': 913, 'size': 4}
  • id: 116986103
    {'aut_label': '14C1', 'centralizer': '6.d1.a1', 'counter': 41, 'group_counter': 8546, 'group_order': 1344, 'label': '14C1', 'order': 14, 'powers': [25, 43, 4], 'representative': 19, 'size': 6}
  • id: 116986104
    {'aut_label': '14C1', 'centralizer': '6.d1.a1', 'counter': 42, 'group_counter': 8546, 'group_order': 1344, 'label': '14C-1', 'order': 14, 'powers': [25, 44, 4], 'representative': 211, 'size': 6}
  • id: 116986105
    {'aut_label': '14C1', 'centralizer': '6.d1.a1', 'counter': 43, 'group_counter': 8546, 'group_order': 1344, 'label': '14C3', 'order': 14, 'powers': [27, 46, 4], 'representative': 1171, 'size': 6}
  • id: 116986106
    {'aut_label': '14C1', 'centralizer': '6.d1.a1', 'counter': 44, 'group_counter': 8546, 'group_order': 1344, 'label': '14C-3', 'order': 14, 'powers': [27, 45, 4], 'representative': 51, 'size': 6}
  • id: 116986107
    {'aut_label': '14C1', 'centralizer': '6.d1.a1', 'counter': 45, 'group_counter': 8546, 'group_order': 1344, 'label': '14C5', 'order': 14, 'powers': [26, 41, 4], 'representative': 83, 'size': 6}
  • id: 116986108
    {'aut_label': '14C1', 'centralizer': '6.d1.a1', 'counter': 46, 'group_counter': 8546, 'group_order': 1344, 'label': '14C-5', 'order': 14, 'powers': [26, 42, 4], 'representative': 147, 'size': 6}
  • id: 116986109
    {'aut_label': '14D1', 'centralizer': '12.h1.a1', 'counter': 47, 'group_counter': 8546, 'group_order': 1344, 'label': '14D1', 'order': 14, 'powers': [26, 48, 5], 'representative': 194, 'size': 12}
  • id: 116986110
    {'aut_label': '14D1', 'centralizer': '12.h1.a1', 'counter': 48, 'group_counter': 8546, 'group_order': 1344, 'label': '14D3', 'order': 14, 'powers': [25, 49, 5], 'representative': 130, 'size': 12}
  • id: 116986111
    {'aut_label': '14D1', 'centralizer': '12.h1.a1', 'counter': 49, 'group_counter': 8546, 'group_order': 1344, 'label': '14D5', 'order': 14, 'powers': [27, 47, 5], 'representative': 66, 'size': 12}
  • id: 116986113
    {'aut_label': '21A1', 'centralizer': '4.f1.a1', 'counter': 50, 'group_counter': 8546, 'group_order': 1344, 'label': '21A1', 'order': 21, 'powers': [51, 27, 10], 'representative': 704, 'size': 4}
  • id: 116986114
    {'aut_label': '21A1', 'centralizer': '4.f1.a1', 'counter': 51, 'group_counter': 8546, 'group_order': 1344, 'label': '21A2', 'order': 21, 'powers': [52, 25, 10], 'representative': 64, 'size': 4}
  • id: 116986115
    {'aut_label': '21A1', 'centralizer': '4.f1.a1', 'counter': 52, 'group_counter': 8546, 'group_order': 1344, 'label': '21A4', 'order': 21, 'powers': [50, 26, 10], 'representative': 128, 'size': 4}
  • id: 116986116
    {'aut_label': '24A', 'centralizer': '8.n1.a1', 'counter': 53, 'group_counter': 8546, 'group_order': 1344, 'label': '24A', 'order': 24, 'powers': [33, 28, 53], 'representative': 56, 'size': 8}
  • id: 116986117
    {'aut_label': '24A', 'centralizer': '8.n1.b1', 'counter': 54, 'group_counter': 8546, 'group_order': 1344, 'label': '24B', 'order': 24, 'powers': [33, 29, 54], 'representative': 57, 'size': 8}
  • id: 116986118
    {'aut_label': '28A1', 'centralizer': '2.c1.a1', 'counter': 55, 'group_counter': 8546, 'group_order': 1344, 'label': '28A1', 'order': 28, 'powers': [36, 56, 11], 'representative': 240, 'size': 2}
  • id: 116986119
    {'aut_label': '28A1', 'centralizer': '2.c1.a1', 'counter': 56, 'group_counter': 8546, 'group_order': 1344, 'label': '28A3', 'order': 28, 'powers': [37, 58, 11], 'representative': 720, 'size': 2}
  • id: 116986120
    {'aut_label': '28A1', 'centralizer': '2.c1.a1', 'counter': 57, 'group_counter': 8546, 'group_order': 1344, 'label': '28A5', 'order': 28, 'powers': [35, 60, 11], 'representative': 1200, 'size': 2}
  • id: 116986121
    {'aut_label': '28A1', 'centralizer': '2.c1.a1', 'counter': 58, 'group_counter': 8546, 'group_order': 1344, 'label': '28A9', 'order': 28, 'powers': [35, 55, 11], 'representative': 816, 'size': 2}
  • id: 116986122
    {'aut_label': '28A1', 'centralizer': '2.c1.a1', 'counter': 59, 'group_counter': 8546, 'group_order': 1344, 'label': '28A11', 'order': 28, 'powers': [37, 57, 11], 'representative': 1296, 'size': 2}
  • id: 116986124
    {'aut_label': '28A1', 'centralizer': '2.c1.a1', 'counter': 60, 'group_counter': 8546, 'group_order': 1344, 'label': '28A13', 'order': 28, 'powers': [36, 59, 11], 'representative': 432, 'size': 2}
  • id: 116986125
    {'aut_label': '28B1', 'centralizer': '4.a1.a1', 'counter': 61, 'group_counter': 8546, 'group_order': 1344, 'label': '28B1', 'order': 28, 'powers': [35, 62, 12], 'representative': 865, 'size': 4}
  • id: 116986126
    {'aut_label': '28B1', 'centralizer': '4.a1.a1', 'counter': 62, 'group_counter': 8546, 'group_order': 1344, 'label': '28B3', 'order': 28, 'powers': [36, 63, 12], 'representative': 577, 'size': 4}
  • id: 116986127
    {'aut_label': '28B1', 'centralizer': '4.a1.a1', 'counter': 63, 'group_counter': 8546, 'group_order': 1344, 'label': '28B5', 'order': 28, 'powers': [37, 61, 12], 'representative': 289, 'size': 4}
  • id: 116986128
    {'aut_label': '28C1', 'centralizer': '6.d1.a1', 'counter': 64, 'group_counter': 8546, 'group_order': 1344, 'label': '28C1', 'order': 28, 'powers': [35, 66, 13], 'representative': 195, 'size': 6}
  • id: 116986129
    {'aut_label': '28C1', 'centralizer': '6.d1.a1', 'counter': 65, 'group_counter': 8546, 'group_order': 1344, 'label': '28C-1', 'order': 28, 'powers': [35, 67, 14], 'representative': 35, 'size': 6}
  • id: 116986130
    {'aut_label': '28C1', 'centralizer': '6.d1.a1', 'counter': 66, 'group_counter': 8546, 'group_order': 1344, 'label': '28C3', 'order': 28, 'powers': [36, 68, 14], 'representative': 99, 'size': 6}
  • id: 116986131
    {'aut_label': '28C1', 'centralizer': '6.d1.a1', 'counter': 67, 'group_counter': 8546, 'group_order': 1344, 'label': '28C-3', 'order': 28, 'powers': [36, 69, 13], 'representative': 131, 'size': 6}
  • id: 116986132
    {'aut_label': '28C1', 'centralizer': '6.d1.a1', 'counter': 68, 'group_counter': 8546, 'group_order': 1344, 'label': '28C5', 'order': 28, 'powers': [37, 65, 13], 'representative': 67, 'size': 6}
  • id: 116986133
    {'aut_label': '28C1', 'centralizer': '6.d1.a1', 'counter': 69, 'group_counter': 8546, 'group_order': 1344, 'label': '28C-5', 'order': 28, 'powers': [37, 64, 14], 'representative': 163, 'size': 6}
  • id: 116986135
    {'aut_label': '28D1', 'centralizer': '12.h1.a1', 'counter': 70, 'group_counter': 8546, 'group_order': 1344, 'label': '28D1', 'order': 28, 'powers': [36, 71, 15], 'representative': 18, 'size': 12}
  • id: 116986136
    {'aut_label': '28D1', 'centralizer': '12.h1.a1', 'counter': 71, 'group_counter': 8546, 'group_order': 1344, 'label': '28D3', 'order': 28, 'powers': [37, 72, 15], 'representative': 50, 'size': 12}
  • id: 116986137
    {'aut_label': '28D1', 'centralizer': '12.h1.a1', 'counter': 72, 'group_counter': 8546, 'group_order': 1344, 'label': '28D5', 'order': 28, 'powers': [35, 70, 15], 'representative': 82, 'size': 12}
  • id: 116986138
    {'aut_label': '42A1', 'centralizer': '4.f1.a1', 'counter': 73, 'group_counter': 8546, 'group_order': 1344, 'label': '42A1', 'order': 42, 'powers': [50, 35, 20], 'representative': 800, 'size': 4}
  • id: 116986139
    {'aut_label': '42A1', 'centralizer': '4.f1.a1', 'counter': 74, 'group_counter': 8546, 'group_order': 1344, 'label': '42A5', 'order': 42, 'powers': [51, 37, 20], 'representative': 1312, 'size': 4}
  • id: 116986140
    {'aut_label': '42A1', 'centralizer': '4.f1.a1', 'counter': 75, 'group_counter': 8546, 'group_order': 1344, 'label': '42A11', 'order': 42, 'powers': [52, 36, 20], 'representative': 736, 'size': 4}
  • id: 116986141
    {'aut_label': '42B1', 'centralizer': '8.b1.a1', 'counter': 76, 'group_counter': 8546, 'group_order': 1344, 'label': '42B1', 'order': 42, 'powers': [50, 38, 21], 'representative': 17, 'size': 8}
  • id: 116986142
    {'aut_label': '42B1', 'centralizer': '8.b1.a1', 'counter': 77, 'group_counter': 8546, 'group_order': 1344, 'label': '42B5', 'order': 42, 'powers': [51, 40, 21], 'representative': 81, 'size': 8}
  • id: 116986143
    {'aut_label': '42B1', 'centralizer': '8.b1.a1', 'counter': 78, 'group_counter': 8546, 'group_order': 1344, 'label': '42B11', 'order': 42, 'powers': [52, 39, 21], 'representative': 401, 'size': 8}
  • id: 116986144
    {'aut_label': '56A1', 'centralizer': '4.k1.a1', 'counter': 79, 'group_counter': 8546, 'group_order': 1344, 'label': '56A1', 'order': 56, 'powers': [59, 80, 28], 'representative': 24, 'size': 4}
  • id: 116986146
    {'aut_label': '56A1', 'centralizer': '4.k1.a1', 'counter': 80, 'group_counter': 8546, 'group_order': 1344, 'label': '56A3', 'order': 56, 'powers': [57, 82, 28], 'representative': 72, 'size': 4}
  • id: 116986147
    {'aut_label': '56A1', 'centralizer': '4.k1.a1', 'counter': 81, 'group_counter': 8546, 'group_order': 1344, 'label': '56A5', 'order': 56, 'powers': [55, 84, 28], 'representative': 120, 'size': 4}
  • id: 116986148
    {'aut_label': '56A1', 'centralizer': '4.k1.a1', 'counter': 82, 'group_counter': 8546, 'group_order': 1344, 'label': '56A9', 'order': 56, 'powers': [60, 79, 28], 'representative': 216, 'size': 4}
  • id: 116986149
    {'aut_label': '56A1', 'centralizer': '4.k1.a1', 'counter': 83, 'group_counter': 8546, 'group_order': 1344, 'label': '56A11', 'order': 56, 'powers': [58, 81, 28], 'representative': 264, 'size': 4}
  • id: 116986150
    {'aut_label': '56A1', 'centralizer': '4.k1.a1', 'counter': 84, 'group_counter': 8546, 'group_order': 1344, 'label': '56A13', 'order': 56, 'powers': [56, 83, 28], 'representative': 312, 'size': 4}
  • id: 116986151
    {'aut_label': '56A1', 'centralizer': '4.k1.b1', 'counter': 85, 'group_counter': 8546, 'group_order': 1344, 'label': '56B1', 'order': 56, 'powers': [59, 86, 29], 'representative': 25, 'size': 4}
  • id: 116986152
    {'aut_label': '56A1', 'centralizer': '4.k1.b1', 'counter': 86, 'group_counter': 8546, 'group_order': 1344, 'label': '56B3', 'order': 56, 'powers': [57, 88, 29], 'representative': 73, 'size': 4}
  • id: 116986153
    {'aut_label': '56A1', 'centralizer': '4.k1.b1', 'counter': 87, 'group_counter': 8546, 'group_order': 1344, 'label': '56B5', 'order': 56, 'powers': [55, 90, 29], 'representative': 121, 'size': 4}
  • id: 116986154
    {'aut_label': '56A1', 'centralizer': '4.k1.b1', 'counter': 88, 'group_counter': 8546, 'group_order': 1344, 'label': '56B9', 'order': 56, 'powers': [60, 85, 29], 'representative': 217, 'size': 4}
  • id: 116986155
    {'aut_label': '56A1', 'centralizer': '4.k1.b1', 'counter': 89, 'group_counter': 8546, 'group_order': 1344, 'label': '56B11', 'order': 56, 'powers': [58, 87, 29], 'representative': 265, 'size': 4}
  • id: 116986157
    {'aut_label': '56A1', 'centralizer': '4.k1.b1', 'counter': 90, 'group_counter': 8546, 'group_order': 1344, 'label': '56B13', 'order': 56, 'powers': [56, 89, 29], 'representative': 313, 'size': 4}
  • id: 116986158
    {'aut_label': '56C1', 'centralizer': '12.s1.b1', 'counter': 91, 'group_counter': 8546, 'group_order': 1344, 'label': '56C1', 'order': 56, 'powers': [55, 92, 30], 'representative': 10, 'size': 12}
  • id: 116986159
    {'aut_label': '56C1', 'centralizer': '12.s1.b1', 'counter': 92, 'group_counter': 8546, 'group_order': 1344, 'label': '56C3', 'order': 56, 'powers': [56, 94, 30], 'representative': 202, 'size': 12}
  • id: 116986160
    {'aut_label': '56C1', 'centralizer': '12.s1.b1', 'counter': 93, 'group_counter': 8546, 'group_order': 1344, 'label': '56C5', 'order': 56, 'powers': [57, 96, 30], 'representative': 42, 'size': 12}
  • id: 116986161
    {'aut_label': '56C1', 'centralizer': '12.s1.b1', 'counter': 94, 'group_counter': 8546, 'group_order': 1344, 'label': '56C9', 'order': 56, 'powers': [58, 91, 30], 'representative': 74, 'size': 12}
  • id: 116986162
    {'aut_label': '56C1', 'centralizer': '12.s1.b1', 'counter': 95, 'group_counter': 8546, 'group_order': 1344, 'label': '56C11', 'order': 56, 'powers': [59, 93, 30], 'representative': 138, 'size': 12}
  • id: 116986163
    {'aut_label': '56C1', 'centralizer': '12.s1.b1', 'counter': 96, 'group_counter': 8546, 'group_order': 1344, 'label': '56C13', 'order': 56, 'powers': [60, 95, 30], 'representative': 778, 'size': 12}
  • id: 116986164
    {'aut_label': '56C1', 'centralizer': '12.s1.a1', 'counter': 97, 'group_counter': 8546, 'group_order': 1344, 'label': '56D1', 'order': 56, 'powers': [55, 98, 31], 'representative': 11, 'size': 12}
  • id: 116986165
    {'aut_label': '56C1', 'centralizer': '12.s1.a1', 'counter': 98, 'group_counter': 8546, 'group_order': 1344, 'label': '56D3', 'order': 56, 'powers': [56, 100, 31], 'representative': 203, 'size': 12}
  • id: 116986166
    {'aut_label': '56C1', 'centralizer': '12.s1.a1', 'counter': 99, 'group_counter': 8546, 'group_order': 1344, 'label': '56D5', 'order': 56, 'powers': [57, 102, 31], 'representative': 43, 'size': 12}
  • id: 116986046
    {'aut_label': '56C1', 'centralizer': '12.s1.a1', 'counter': 100, 'group_counter': 8546, 'group_order': 1344, 'label': '56D9', 'order': 56, 'powers': [58, 97, 31], 'representative': 75, 'size': 12}
  • id: 116986047
    {'aut_label': '56C1', 'centralizer': '12.s1.a1', 'counter': 101, 'group_counter': 8546, 'group_order': 1344, 'label': '56D11', 'order': 56, 'powers': [59, 99, 31], 'representative': 139, 'size': 12}
  • id: 116986048
    {'aut_label': '56C1', 'centralizer': '12.s1.a1', 'counter': 102, 'group_counter': 8546, 'group_order': 1344, 'label': '56D13', 'order': 56, 'powers': [60, 101, 31], 'representative': 779, 'size': 12}
  • id: 116986049
    {'aut_label': '84A1', 'centralizer': '4.f1.a1', 'counter': 103, 'group_counter': 8546, 'group_order': 1344, 'label': '84A1', 'order': 84, 'powers': [74, 59, 33], 'representative': 16, 'size': 4}
  • id: 116986050
    {'aut_label': '84A1', 'centralizer': '4.f1.a1', 'counter': 104, 'group_counter': 8546, 'group_order': 1344, 'label': '84A5', 'order': 84, 'powers': [75, 55, 33], 'representative': 80, 'size': 4}
  • id: 116986051
    {'aut_label': '84A1', 'centralizer': '4.f1.a1', 'counter': 105, 'group_counter': 8546, 'group_order': 1344, 'label': '84A11', 'order': 84, 'powers': [73, 58, 33], 'representative': 176, 'size': 4}
  • id: 116986052
    {'aut_label': '84A1', 'centralizer': '4.f1.a1', 'counter': 106, 'group_counter': 8546, 'group_order': 1344, 'label': '84A13', 'order': 84, 'powers': [74, 56, 33], 'representative': 208, 'size': 4}
  • id: 116986053
    {'aut_label': '84A1', 'centralizer': '4.f1.a1', 'counter': 107, 'group_counter': 8546, 'group_order': 1344, 'label': '84A19', 'order': 84, 'powers': [75, 60, 33], 'representative': 304, 'size': 4}
  • id: 116986054
    {'aut_label': '84A1', 'centralizer': '4.f1.a1', 'counter': 108, 'group_counter': 8546, 'group_order': 1344, 'label': '84A25', 'order': 84, 'powers': [73, 57, 33], 'representative': 400, 'size': 4}
  • id: 116986055
    {'aut_label': '84B1', 'centralizer': '8.b1.a1', 'counter': 109, 'group_counter': 8546, 'group_order': 1344, 'label': '84B1', 'order': 84, 'powers': [73, 61, 32], 'representative': 65, 'size': 8}
  • id: 116986057
    {'aut_label': '84B1', 'centralizer': '8.b1.a1', 'counter': 110, 'group_counter': 8546, 'group_order': 1344, 'label': '84B5', 'order': 84, 'powers': [74, 63, 32], 'representative': 129, 'size': 8}
  • id: 116986058
    {'aut_label': '84B1', 'centralizer': '8.b1.a1', 'counter': 111, 'group_counter': 8546, 'group_order': 1344, 'label': '84B11', 'order': 84, 'powers': [75, 62, 32], 'representative': 33, 'size': 8}
  • id: 116986059
    {'aut_label': '168A1', 'centralizer': '8.n1.a1', 'counter': 112, 'group_counter': 8546, 'group_order': 1344, 'label': '168A1', 'order': 168, 'powers': [103, 79, 53], 'representative': 8, 'size': 8}
  • id: 116986060
    {'aut_label': '168A1', 'centralizer': '8.n1.a1', 'counter': 113, 'group_counter': 8546, 'group_order': 1344, 'label': '168A5', 'order': 168, 'powers': [104, 81, 53], 'representative': 40, 'size': 8}
  • id: 116986061
    {'aut_label': '168A1', 'centralizer': '8.n1.a1', 'counter': 114, 'group_counter': 8546, 'group_order': 1344, 'label': '168A11', 'order': 168, 'powers': [105, 83, 53], 'representative': 136, 'size': 8}
  • id: 116986062
    {'aut_label': '168A1', 'centralizer': '8.n1.a1', 'counter': 115, 'group_counter': 8546, 'group_order': 1344, 'label': '168A13', 'order': 168, 'powers': [106, 84, 53], 'representative': 776, 'size': 8}
  • id: 116986063
    {'aut_label': '168A1', 'centralizer': '8.n1.a1', 'counter': 116, 'group_counter': 8546, 'group_order': 1344, 'label': '168A19', 'order': 168, 'powers': [107, 82, 53], 'representative': 968, 'size': 8}
  • id: 116986064
    {'aut_label': '168A1', 'centralizer': '8.n1.a1', 'counter': 117, 'group_counter': 8546, 'group_order': 1344, 'label': '168A25', 'order': 168, 'powers': [108, 80, 53], 'representative': 200, 'size': 8}
  • id: 116986065
    {'aut_label': '168A1', 'centralizer': '8.n1.b1', 'counter': 118, 'group_counter': 8546, 'group_order': 1344, 'label': '168B1', 'order': 168, 'powers': [103, 85, 54], 'representative': 9, 'size': 8}
  • id: 116986066
    {'aut_label': '168A1', 'centralizer': '8.n1.b1', 'counter': 119, 'group_counter': 8546, 'group_order': 1344, 'label': '168B5', 'order': 168, 'powers': [104, 87, 54], 'representative': 41, 'size': 8}
  • id: 116986068
    {'aut_label': '168A1', 'centralizer': '8.n1.b1', 'counter': 120, 'group_counter': 8546, 'group_order': 1344, 'label': '168B11', 'order': 168, 'powers': [105, 89, 54], 'representative': 137, 'size': 8}
  • id: 116986069
    {'aut_label': '168A1', 'centralizer': '8.n1.b1', 'counter': 121, 'group_counter': 8546, 'group_order': 1344, 'label': '168B13', 'order': 168, 'powers': [106, 90, 54], 'representative': 777, 'size': 8}
  • id: 116986070
    {'aut_label': '168A1', 'centralizer': '8.n1.b1', 'counter': 122, 'group_counter': 8546, 'group_order': 1344, 'label': '168B19', 'order': 168, 'powers': [107, 88, 54], 'representative': 969, 'size': 8}
  • id: 116986071
    {'aut_label': '168A1', 'centralizer': '8.n1.b1', 'counter': 123, 'group_counter': 8546, 'group_order': 1344, 'label': '168B25', 'order': 168, 'powers': [108, 86, 54], 'representative': 201, 'size': 8}
• gps_qchar •

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

  
  
  • id: 6053220
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6053231
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6053242
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6053253
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6053264
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6053268
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6053269
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6053270
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6053271
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.1i', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6053221
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.1j', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6053222
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.1k', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6053223
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.1l', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6053224
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.1m', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6053225
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.1n', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6053226
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.1o', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6053227
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.1p', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6053228
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 0, 2, 2, 2, 0, -1, 2, 2, 0, 0, 0, 2, 0, 0, 0, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 0, 0, -1, -1, -1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6053229
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 0, 0, 0, 0, 2, -2, 2, 2, 2, -2, 0, 0, 0, 0, 2, -2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, -2, 0, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 0, 0, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6053230
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 2, -2, 0, 0, 0, 0, 2, -2, 2, -2, -2, 2, 0, 0, 0, 0, 2, -2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, -2, 0, 2, 2, 2, -2, -2, -2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 2, 2, 2, 0, 0, -2, -2, -2, -2, -2, -2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6053232
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, -2, -2, 0, 0, 0, 0, 2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, -2, -2, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6053233
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.2e', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 0, 0, 0, 0, 2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, -2, -2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6053234
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, 0, -2, -2, 2, 0, -1, 2, -2, 0, 0, 0, 2, 0, 0, 0, -1, 1, 1, 1, -1, 2, 2, 2, -2, 2, 0, 0, 1, -1, -1, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, -1, 2, 2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, 1, 2, -2, -2, -2, -2, 2, 2, -2, 2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6053235
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.2g', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, 0, -2, 2, -2, 0, -1, 2, -2, 0, 0, 0, 2, 0, 0, 0, -1, 1, 1, -1, 1, 2, 2, 2, 2, -2, 0, 0, 1, -1, -1, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 1, 2, 2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, 1, -2, 2, 2, 2, 2, -2, -2, 2, -2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6053236
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.2h', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, 0, 2, -2, 2, 0, -1, 2, -2, 0, 0, 0, -2, 0, 0, 0, -1, 1, -1, 1, -1, 2, 2, 2, 2, -2, 0, 0, 1, -1, 1, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 1, 2, 2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, 1, -2, 2, 2, 2, 2, -2, -2, 2, -2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6053237
    {'cdim': 2, 'counter': 25, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.2i', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, 0, 2, 2, -2, 0, -1, 2, -2, 0, 0, 0, -2, 0, 0, 0, -1, 1, -1, -1, 1, 2, 2, 2, -2, 2, 0, 0, 1, -1, 1, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, -1, 2, 2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, 1, 2, -2, -2, -2, -2, 2, 2, -2, 2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6053238
    {'cdim': 2, 'counter': 26, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.2j', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 0, -2, -2, -2, 0, -1, 2, 2, 0, 0, 0, -2, 0, 0, 0, -1, -1, 1, 1, 1, 2, 2, 2, 2, 2, 0, 0, -1, -1, 1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6053239
    {'cdim': 2, 'counter': 27, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.2k', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 0, -2, 2, 2, 0, -1, 2, 2, 0, 0, 0, -2, 0, 0, 0, -1, -1, 1, -1, -1, 2, 2, 2, -2, -2, 0, 0, -1, -1, 1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6053240
    {'cdim': 2, 'counter': 28, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.2l', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 0, 2, -2, -2, 0, -1, 2, 2, 0, 0, 0, 2, 0, 0, 0, -1, -1, -1, 1, 1, 2, 2, 2, -2, -2, 0, 0, -1, -1, -1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6053255
    {'cdim': 4, 'counter': 41, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.4a', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, 4, -4, 0, 0, 0, 0, 0, 0, -2, -4, 4, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, -2, 2, 0, 4, 4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, -4, -4, -4, -4, -4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6053256
    {'cdim': 4, 'counter': 42, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.4b', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, 4, 4, 0, 0, 0, 0, 0, 0, -2, -4, -4, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 2, 2, 0, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6053241
    {'cdim': 2, 'counter': 29, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.2m', 'multiplicity': 3, 'nt': [7, 2], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 6, 6, 0, 0, 0, -1, -1, -1, 6, 6, 6, 6, 6, 6, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 6, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6053243
    {'cdim': 2, 'counter': 30, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.2n', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, -6, -6, 6, 0, 0, 0, 0, 6, 6, -6, -6, -6, 6, 0, 0, 0, 0, 6, -6, 0, 0, 0, -1, -1, -1, -6, 6, -6, 6, -6, 6, 0, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -6, 6, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6053244
    {'cdim': 2, 'counter': 31, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.2o', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, -6, -6, 6, 0, 0, 0, 0, 6, 6, -6, -6, -6, 6, 0, 0, 0, 0, 6, -6, 0, 0, 0, -1, -1, -1, 6, -6, 6, -6, -6, 6, 0, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 6, -6, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6053245
    {'cdim': 2, 'counter': 32, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.2p', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, -6, 6, -6, 0, 0, 0, 0, 6, 6, -6, 6, 6, -6, 0, 0, 0, 0, 6, -6, 0, 0, 0, -1, -1, -1, -6, 6, 6, -6, -6, 6, 0, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -6, 6, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6053246
    {'cdim': 2, 'counter': 33, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.2q', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, -6, 6, -6, 0, 0, 0, 0, 6, 6, -6, 6, 6, -6, 0, 0, 0, 0, 6, -6, 0, 0, 0, -1, -1, -1, 6, -6, -6, 6, -6, 6, 0, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 6, -6, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6053247
    {'cdim': 2, 'counter': 34, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.2r', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, 6, -6, -6, 0, 0, 0, 0, 6, 6, 6, -6, -6, -6, 0, 0, 0, 0, 6, 6, 0, 0, 0, -1, -1, -1, -6, -6, 6, 6, 6, 6, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -6, -6, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6053248
    {'cdim': 2, 'counter': 35, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.2s', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, 6, -6, -6, 0, 0, 0, 0, 6, 6, 6, -6, -6, -6, 0, 0, 0, 0, 6, 6, 0, 0, 0, -1, -1, -1, 6, 6, -6, -6, 6, 6, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 6, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6053249
    {'cdim': 2, 'counter': 36, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.2t', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 6, 6, 0, 0, 0, -1, -1, -1, -6, -6, -6, -6, 6, 6, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -6, -6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6053257
    {'cdim': 4, 'counter': 43, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.4c', 'multiplicity': 2, 'nt': [16, 100], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 8, 8, 8, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 6053266
    {'cdim': 8, 'counter': 51, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.8a', '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, 0, 4, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 6053250
    {'cdim': 2, 'counter': 37, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.2u', 'multiplicity': 6, 'nt': [28, 10], 'qdim': 12, 'qvalues': [12, 12, -12, -12, 12, 0, 0, 0, 0, 12, -12, 12, 12, 12, -12, 0, 0, 0, 0, 12, -12, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 12, -12, 0, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6053251
    {'cdim': 2, 'counter': 38, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.2v', 'multiplicity': 6, 'nt': [28, 10], 'qdim': 12, 'qvalues': [12, 12, -12, 12, -12, 0, 0, 0, 0, 12, -12, 12, -12, -12, 12, 0, 0, 0, 0, 12, -12, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 12, -12, 0, -2, -2, -2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6053252
    {'cdim': 2, 'counter': 39, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.2w', 'multiplicity': 6, 'nt': [28, 10], 'qdim': 12, 'qvalues': [12, 12, 12, -12, -12, 0, 0, 0, 0, 12, -12, -12, 12, 12, 12, 0, 0, 0, 0, 12, 12, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, -12, -12, 0, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6053254
    {'cdim': 2, 'counter': 40, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.2x', 'multiplicity': 6, 'nt': [28, 10], 'qdim': 12, 'qvalues': [12, 12, 12, 12, 12, 0, 0, 0, 0, 12, -12, -12, -12, -12, -12, 0, 0, 0, 0, 12, 12, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, -12, -12, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6053258
    {'cdim': 4, 'counter': 44, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.4d', 'multiplicity': 3, 'nt': [21, 8], 'qdim': 12, 'qvalues': [12, 12, 12, 0, 0, 0, 0, 0, 0, -6, 12, 12, 0, 0, 0, 0, 0, 0, 0, -6, -6, 0, 0, 0, -2, -2, -2, 12, 12, 0, 0, -6, -6, 0, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, -6, -6, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6053259
    {'cdim': 4, 'counter': 45, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.4e', 'multiplicity': 3, 'nt': [42, 36], 'qdim': 12, 'qvalues': [12, 12, -12, 0, 0, 0, 0, 0, 0, -6, 12, -12, 0, 0, 0, 0, 0, 0, 0, -6, 6, 0, 0, 0, -2, -2, -2, -12, 12, 0, 0, 6, -6, 0, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 6, -6, -2, -2, -2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, -1, -1, -1, -2, 2, 2, 2, 2, -2, -2, 2, -2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6053260
    {'cdim': 4, 'counter': 46, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.4f', 'multiplicity': 3, 'nt': [42, 36], 'qdim': 12, 'qvalues': [12, 12, -12, 0, 0, 0, 0, 0, 0, -6, 12, -12, 0, 0, 0, 0, 0, 0, 0, -6, 6, 0, 0, 0, -2, -2, -2, 12, -12, 0, 0, 6, -6, 0, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, -6, 6, -2, -2, -2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, -1, -1, -1, 2, -2, -2, -2, -2, 2, 2, -2, 2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6053261
    {'cdim': 4, 'counter': 47, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.4g', 'multiplicity': 3, 'nt': [42, 36], 'qdim': 12, 'qvalues': [12, 12, 12, 0, 0, 0, 0, 0, 0, -6, 12, 12, 0, 0, 0, 0, 0, 0, 0, -6, -6, 0, 0, 0, -2, -2, -2, -12, -12, 0, 0, -6, -6, 0, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 6, 6, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6053262
    {'cdim': 4, 'counter': 48, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.4h', '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, 0, -12, 12, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, -12, 12, 0, -4, -4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 4, 4, 4, 4, 4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6053263
    {'cdim': 4, 'counter': 49, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.4i', '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, 0, -12, -12, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, 12, 12, 0, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6053265
    {'cdim': 4, 'counter': 50, 'faithful': False, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.4j', 'multiplicity': 12, 'nt': [112, 0], 'qdim': 48, 'qvalues': [48, -48, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, -8, -8, -8, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 6053267
    {'cdim': 8, 'counter': 52, 'faithful': True, 'group': '1344.8546', 'group_order': 1344, 'image': None, 'label': '1344.8546.8b', '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, 0, 24, 0, 0, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
• gps_char •

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

  
  
  • id: 12577665
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 1344, 'label': '1344.8546.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 12577700
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.k1.b1', 'kernel_order': 672, 'label': '1344.8546.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 12577711
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.k1.a1', 'kernel_order': 672, 'label': '1344.8546.1c', '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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[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: 12577722
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  • id: 12577733
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  • id: 12577744
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  • id: 12577755
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  • id: 12577766
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  • id: 12577777
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  • id: 12577666
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  • id: 12577677
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  • id: 12577688
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  • id: 12577693
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  • id: 12577694
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  • id: 12577695
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  • id: 12577696
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  • id: 12577697
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  • id: 12577698
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  • id: 12577699
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  • id: 12577701
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  • id: 12577702
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  • id: 12577703
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  • id: 12577704
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  • id: 12577705
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  • id: 12577706
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  • id: 12577707
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  • id: 12577708
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  • id: 12577709
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 224, 'counter': 28, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 112, 'label': '1344.8546.2l', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 12577710
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 29, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '14.1', 'image_order': 14, 'indicator': 1, 'kernel': '14.a1.a1', 'kernel_order': 96, 'label': '1344.8546.2m1', 'nt': [7, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[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, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[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, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[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, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]]]}
  • id: 12577712
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 30, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '14.1', 'image_order': 14, 'indicator': 1, 'kernel': '14.a1.a1', 'kernel_order': 96, 'label': '1344.8546.2m2', 'nt': [7, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[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, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[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, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[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, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 12577713
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 31, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '14.1', 'image_order': 14, 'indicator': 1, 'kernel': '14.a1.a1', 'kernel_order': 96, 'label': '1344.8546.2m3', 'nt': [7, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[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, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[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, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[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, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]]]}
  • id: 12577714
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 32, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.e1.b1', 'kernel_order': 48, 'label': '1344.8546.2n1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 0]], [[2, 0]], [[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, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-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, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[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, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]]]}
  • id: 12577715
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 33, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.e1.b1', 'kernel_order': 48, 'label': '1344.8546.2n2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-2, 0]], [[2, 0]], [[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, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-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, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[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, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 12577716
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 34, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.e1.b1', 'kernel_order': 48, 'label': '1344.8546.2n3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-2, 0]], [[2, 0]], [[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, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-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, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[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, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]]]}
  • id: 12577717
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 35, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.e1.a1', 'kernel_order': 48, 'label': '1344.8546.2o1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[-2, 0]], [[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, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-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, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-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, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 12577718
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 36, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.e1.a1', 'kernel_order': 48, 'label': '1344.8546.2o2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 0]], [[-2, 0]], [[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, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-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, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-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, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 12577719
    {'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': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.e1.a1', 'kernel_order': 48, 'label': '1344.8546.2o3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 0]], [[-2, 0]], [[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, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-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, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-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, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]]]}
  • id: 12577720
    {'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': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.d1.b1', 'kernel_order': 48, 'label': '1344.8546.2p1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 0]], [[2, 0]], [[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, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[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, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[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, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]]]}
  • id: 12577721
    {'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': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.d1.b1', 'kernel_order': 48, 'label': '1344.8546.2p2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-2, 0]], [[2, 0]], [[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, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[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, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[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, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 12577723
    {'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': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.d1.b1', 'kernel_order': 48, 'label': '1344.8546.2p3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-2, 0]], [[2, 0]], [[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, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[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, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[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, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]]]}
  • id: 12577724
    {'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': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.d1.a1', 'kernel_order': 48, 'label': '1344.8546.2q1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[-2, 0]], [[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, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[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, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-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, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 12577725
    {'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': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.d1.a1', 'kernel_order': 48, 'label': '1344.8546.2q2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 0]], [[-2, 0]], [[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, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[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, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-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, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 12577726
    {'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': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.d1.a1', 'kernel_order': 48, 'label': '1344.8546.2q3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 0]], [[-2, 0]], [[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, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[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, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-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, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]]]}
  • id: 12577727
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 44, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.c1.a1', 'kernel_order': 48, 'label': '1344.8546.2r1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 0]], [[-2, 0]], [[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, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-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, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-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, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 12577728
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 45, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.c1.a1', 'kernel_order': 48, 'label': '1344.8546.2r2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-2, 0]], [[-2, 0]], [[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, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-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, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-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, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 12577729
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 46, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.c1.a1', 'kernel_order': 48, 'label': '1344.8546.2r3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-2, 0]], [[-2, 0]], [[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, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-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, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-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, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]]]}
  • id: 12577730
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 47, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1.a1', 'kernel_order': 48, 'label': '1344.8546.2s1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[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, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-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, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[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, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]]]}
  • id: 12577731
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 48, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1.a1', 'kernel_order': 48, 'label': '1344.8546.2s2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[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, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-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, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[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, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 12577732
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 49, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1.a1', 'kernel_order': 48, 'label': '1344.8546.2s3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[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, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-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, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[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, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]]]}
  • id: 12577734
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 50, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1.a1', 'kernel_order': 48, 'label': '1344.8546.2t1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 0]], [[-2, 0]], [[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, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[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, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-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, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 12577735
    {'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': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1.a1', 'kernel_order': 48, 'label': '1344.8546.2t2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-2, 0]], [[-2, 0]], [[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, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[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, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-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, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 12577736
    {'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': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1.a1', 'kernel_order': 48, 'label': '1344.8546.2t3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-2, 0]], [[-2, 0]], [[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, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[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, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-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, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]]]}
  • id: 12577737
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 53, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.g1.a1', 'kernel_order': 24, 'label': '1344.8546.2u1', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 12577738
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 54, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.g1.a1', 'kernel_order': 24, 'label': '1344.8546.2u2', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 12577739
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 55, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.g1.a1', 'kernel_order': 24, 'label': '1344.8546.2u3', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]]]}
  • id: 12577740
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 56, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.g1.a1', 'kernel_order': 24, 'label': '1344.8546.2u4', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]]]}
  • id: 12577741
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 57, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.g1.a1', 'kernel_order': 24, 'label': '1344.8546.2u5', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]]]}
  • id: 12577742
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 58, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.g1.a1', 'kernel_order': 24, 'label': '1344.8546.2u6', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]]]}
  • id: 12577743
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 59, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.e1.a1', 'kernel_order': 24, 'label': '1344.8546.2v1', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 12577745
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 60, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.e1.a1', 'kernel_order': 24, 'label': '1344.8546.2v2', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 12577746
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 61, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.e1.a1', 'kernel_order': 24, 'label': '1344.8546.2v3', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]]]}
  • id: 12577747
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 62, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.e1.a1', 'kernel_order': 24, 'label': '1344.8546.2v4', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]]]}
  • id: 12577748
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 63, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.e1.a1', 'kernel_order': 24, 'label': '1344.8546.2v5', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]]]}
  • id: 12577749
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  • id: 12577750
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  • id: 12577751
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  • id: 12577752
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  • id: 12577753
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  • id: 12577754
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 69, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.c1.a1', 'kernel_order': 24, 'label': '1344.8546.2w5', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]]]}
  • id: 12577756
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 70, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.c1.a1', 'kernel_order': 24, 'label': '1344.8546.2w6', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]]]}
  • id: 12577757
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 71, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.a1.a1', 'kernel_order': 24, 'label': '1344.8546.2x1', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 12577758
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 72, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.a1.a1', 'kernel_order': 24, 'label': '1344.8546.2x2', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 12577759
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 73, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.a1.a1', 'kernel_order': 24, 'label': '1344.8546.2x3', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]]]}
  • id: 12577760
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 74, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.a1.a1', 'kernel_order': 24, 'label': '1344.8546.2x4', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]]]}
  • id: 12577761
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 75, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.a1.a1', 'kernel_order': 24, 'label': '1344.8546.2x5', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]]]}
  • id: 12577762
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 76, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.a1.a1', 'kernel_order': 24, 'label': '1344.8546.2x6', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]]]}
  • id: 12577763
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  • id: 12577764
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 56, 'counter': 78, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '48.38', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1.a1', 'kernel_order': 28, 'label': '1344.8546.4b', 'nt': [12, 28], '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]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12577765
    {'center': '16.f1.a1', 'center_index': 16, 'center_order': 84, 'counter': 79, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '64.256', 'image_order': 64, 'indicator': 0, 'kernel': '64.a1.a1', 'kernel_order': 21, 'label': '1344.8546.4c1', 'nt': [16, 100], '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]], [[-4, 1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 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]], [[-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]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, 1]], [[-4, 1]], [[-4, 1]], [[-4, 1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12577767
    {'center': '16.f1.a1', 'center_index': 16, 'center_order': 84, 'counter': 80, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '64.256', 'image_order': 64, 'indicator': 0, 'kernel': '64.a1.a1', 'kernel_order': 21, 'label': '1344.8546.4c2', '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]], [[4, 1]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 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]], [[-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]], [[0, 0]], [[0, 0]], [[-4, 1]], [[-4, 1]], [[4, 1]], [[4, 1]], [[4, 1]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12577768
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 81, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '84.8', 'image_order': 84, 'indicator': 1, 'kernel': '84.a1.a1', 'kernel_order': 16, 'label': '1344.8546.4d1', 'nt': [21, 8], '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]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-2, 0]], [[-2, 0]], [[2, 3], [2, -3]], [[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, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[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, 1], [2, -1]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 12577769
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 82, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '84.8', 'image_order': 84, 'indicator': 1, 'kernel': '84.a1.a1', 'kernel_order': 16, 'label': '1344.8546.4d2', 'nt': [21, 8], '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]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-2, 0]], [[-2, 0]], [[2, 2], [2, -2]], [[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, 1], [2, -1]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[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, 3], [2, -3]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 12577770
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 83, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '84.8', 'image_order': 84, 'indicator': 1, 'kernel': '84.a1.a1', 'kernel_order': 16, 'label': '1344.8546.4d3', 'nt': [21, 8], '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]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-2, 0]], [[-2, 0]], [[2, 1], [2, -1]], [[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, 3], [2, -3]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[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, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]]]}
  • id: 12577771
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 84, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.b1.b1', 'kernel_order': 8, 'label': '1344.8546.4e1', 'nt': [42, 36], '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]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[2, 0]], [[-2, 0]], [[2, 3], [2, -3]], [[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, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 2], [2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-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, 1], [2, -1]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 12577772
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 85, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.b1.b1', 'kernel_order': 8, 'label': '1344.8546.4e2', 'nt': [42, 36], '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]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[2, 0]], [[-2, 0]], [[2, 2], [2, -2]], [[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, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-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, 3], [2, -3]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 12577773
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 86, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.b1.b1', 'kernel_order': 8, 'label': '1344.8546.4e3', 'nt': [42, 36], '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]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[2, 0]], [[-2, 0]], [[2, 1], [2, -1]], [[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, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 3], [2, -3]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-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, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]]]}
  • id: 12577774
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 87, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.b1.a1', 'kernel_order': 8, 'label': '1344.8546.4f1', 'nt': [42, 36], '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]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-2, 0]], [[2, 0]], [[2, 3], [2, -3]], [[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, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-2, 2], [-2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[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, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]]]}
  • id: 12577775
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 88, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.b1.a1', 'kernel_order': 8, 'label': '1344.8546.4f2', 'nt': [42, 36], '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]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-2, 0]], [[2, 0]], [[2, 2], [2, -2]], [[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, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[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, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 12577776
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  • id: 12577778
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 90, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.a1.a1', 'kernel_order': 8, 'label': '1344.8546.4g1', 'nt': [42, 36], '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]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[2, 0]], [[2, 0]], [[2, 3], [2, -3]], [[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, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-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, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]]]}
  • id: 12577779
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 91, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.a1.a1', 'kernel_order': 8, 'label': '1344.8546.4g2', 'nt': [42, 36], '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]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[2, 0]], [[2, 0]], [[2, 2], [2, -2]], [[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, 1], [2, -1]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-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, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 12577780
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 92, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.a1.a1', 'kernel_order': 8, 'label': '1344.8546.4g3', 'nt': [42, 36], '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]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[2, 0]], [[2, 0]], [[2, 1], [2, -1]], [[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, 3], [2, -3]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-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, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]]]}
  • id: 12577781
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 93, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '336.149', 'image_order': 336, 'indicator': 1, 'kernel': '336.c1.a1', 'kernel_order': 4, 'label': '1344.8546.4h1', '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]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[-2, 6], [-2, -6]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[-2, 2], [-2, -2]], [[-2, 6], [-2, -6]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[2, 5], [2, -5]], [[-2, 5], [-2, -5]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 12577782
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 94, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '336.149', 'image_order': 336, 'indicator': 1, 'kernel': '336.c1.a1', 'kernel_order': 4, 'label': '1344.8546.4h2', '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]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[-2, 6], [-2, -6]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[-2, 2], [-2, -2]], [[-2, 6], [-2, -6]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-2, 5], [-2, -5]], [[2, 5], [2, -5]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 12577783
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 95, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '336.149', 'image_order': 336, 'indicator': 1, 'kernel': '336.c1.a1', 'kernel_order': 4, 'label': '1344.8546.4h3', '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]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 6], [-2, -6]], [[2, 4], [2, -4]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[-2, 6], [-2, -6]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-2, 3], [-2, -3]], [[2, 5], [2, -5]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-2, 5], [-2, -5]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]]]}
  • id: 12577784
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 96, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '336.149', 'image_order': 336, 'indicator': 1, 'kernel': '336.c1.a1', 'kernel_order': 4, 'label': '1344.8546.4h4', '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]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 6], [-2, -6]], [[2, 4], [2, -4]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[-2, 6], [-2, -6]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[2, 3], [2, -3]], [[-2, 5], [-2, -5]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[2, 5], [2, -5]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]]]}
  • id: 12577785
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 97, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '336.149', 'image_order': 336, 'indicator': 1, 'kernel': '336.c1.a1', 'kernel_order': 4, 'label': '1344.8546.4h5', '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]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-2, 5], [-2, -5]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[2, 5], [2, -5]], [[2, 5], [2, -5]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]]]}
  • id: 12577786
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 98, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '336.149', 'image_order': 336, 'indicator': 1, 'kernel': '336.c1.a1', 'kernel_order': 4, 'label': '1344.8546.4h6', '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]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[2, 5], [2, -5]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[-2, 5], [-2, -5]], [[-2, 5], [-2, -5]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]]]}
  • id: 12577787
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  • id: 12577667
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 100, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '336.149', 'image_order': 336, 'indicator': 1, 'kernel': '336.a1.a1', 'kernel_order': 4, 'label': '1344.8546.4i2', '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]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[-2, 6], [-2, -6]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[2, 5], [2, -5]], [[-2, 5], [-2, -5]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 12577668
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 101, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '336.149', 'image_order': 336, 'indicator': 1, 'kernel': '336.a1.a1', 'kernel_order': 4, 'label': '1344.8546.4i3', '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]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 6], [-2, -6]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[-2, 6], [-2, -6]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[2, 5], [2, -5]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]]]}
  • id: 12577669
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 102, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '336.149', 'image_order': 336, 'indicator': 1, 'kernel': '336.a1.a1', 'kernel_order': 4, 'label': '1344.8546.4i4', '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]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 6], [-2, -6]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[-2, 6], [-2, -6]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-2, 5], [-2, -5]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]]]}
  • id: 12577670
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 103, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '336.149', 'image_order': 336, 'indicator': 1, 'kernel': '336.a1.a1', 'kernel_order': 4, 'label': '1344.8546.4i5', '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]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[-2, 6], [-2, -6]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[2, 5], [2, -5]], [[2, 5], [2, -5]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]]]}
  • id: 12577671
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  • id: 12577672
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  • id: 12577682
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  • id: 12577683
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  • id: 12577684
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  • id: 12577673
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  • id: 12577674
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  • id: 12577675
    {'center': '112.f1.a1', 'center_index': 112, 'center_order': 12, 'counter': 108, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '448.1201', 'image_order': 448, 'indicator': 0, 'kernel': '448.a1.a1', 'kernel_order': 3, 'label': '1344.8546.4j4', 'nt': [112, 12], '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]], [[4, 7]], [[-4, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, 10]], [[2, 6], [2, 8]], [[-2, 0], [4, 2], [-2, 4], [2, 6], [-2, 8], [2, 10]], [[-2, 6], [-2, 8]], [[2, 0], [-4, 2], [2, 4], [-2, 6], [2, 8], [-2, 10]], [[2, 4], [2, 10]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[2, 5], [2, -5]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [-2, 5], [2, 7], [-2, 9], [2, 11]], [[2, 5], [2, 9]], [[-2, 3], [2, 5], [-2, 7], [2, 9], [-2, 11]], [[2, 3], [2, 11]], [[-2, 5], [-2, 9]], [[-2, 3], [-2, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[2, 5], [2, -5]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12577676
    {'center': '112.f1.a1', 'center_index': 112, 'center_order': 12, 'counter': 109, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '448.1201', 'image_order': 448, 'indicator': 0, 'kernel': '448.a1.a1', 'kernel_order': 3, 'label': '1344.8546.4j5', 'nt': [112, 0], '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]], [[-4, 7]], [[4, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [-4, 2], [2, 4], [-2, 6], [2, 8], [-2, 10]], [[-2, 4], [-2, 10]], [[2, 6], [2, 8]], [[2, 4], [2, 10]], [[-2, 6], [-2, 8]], [[-2, 0], [4, 2], [-2, 4], [2, 6], [-2, 8], [2, 10]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[-2, 5], [-2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, 11]], [[-2, 3], [2, 5], [-2, 7], [2, 9], [-2, 11]], [[-2, 3], [-2, 11]], [[2, 5], [2, 9]], [[2, 3], [-2, 5], [2, 7], [-2, 9], [2, 11]], [[-2, 5], [-2, 9]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-2, 5], [-2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12577678
    {'center': '112.f1.a1', 'center_index': 112, 'center_order': 12, 'counter': 110, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '448.1201', 'image_order': 448, 'indicator': 0, 'kernel': '448.a1.a1', 'kernel_order': 3, 'label': '1344.8546.4j6', 'nt': [112, 12], '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]], [[4, 7]], [[-4, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [4, 2], [-2, 4], [2, 6], [-2, 8], [2, 10]], [[2, 4], [2, 10]], [[-2, 6], [-2, 8]], [[-2, 4], [-2, 10]], [[2, 6], [2, 8]], [[2, 0], [-4, 2], [2, 4], [-2, 6], [2, 8], [-2, 10]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[-2, 5], [-2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, 11]], [[2, 3], [-2, 5], [2, 7], [-2, 9], [2, 11]], [[2, 3], [2, 11]], [[-2, 5], [-2, 9]], [[-2, 3], [2, 5], [-2, 7], [2, 9], [-2, 11]], [[2, 5], [2, 9]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-2, 5], [-2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12577679
    {'center': '112.f1.a1', 'center_index': 112, 'center_order': 12, 'counter': 111, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '448.1201', 'image_order': 448, 'indicator': 0, 'kernel': '448.a1.a1', 'kernel_order': 3, 'label': '1344.8546.4j7', 'nt': [112, 0], '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]], [[-4, 7]], [[4, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [4, 2], [-2, 4], [2, 6], [-2, 8], [2, 10]], [[2, 4], [2, 10]], [[-2, 6], [-2, 8]], [[-2, 4], [-2, 10]], [[2, 6], [2, 8]], [[2, 0], [-4, 2], [2, 4], [-2, 6], [2, 8], [-2, 10]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[2, 5], [2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, 11]], [[-2, 3], [2, 5], [-2, 7], [2, 9], [-2, 11]], [[-2, 3], [-2, 11]], [[2, 5], [2, 9]], [[2, 3], [-2, 5], [2, 7], [-2, 9], [2, 11]], [[-2, 5], [-2, 9]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[2, 5], [2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12577680
    {'center': '112.f1.a1', 'center_index': 112, 'center_order': 12, 'counter': 112, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '448.1201', 'image_order': 448, 'indicator': 0, 'kernel': '448.a1.a1', 'kernel_order': 3, 'label': '1344.8546.4j8', 'nt': [112, 12], '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]], [[4, 7]], [[-4, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [-4, 2], [2, 4], [-2, 6], [2, 8], [-2, 10]], [[-2, 4], [-2, 10]], [[2, 6], [2, 8]], [[2, 4], [2, 10]], [[-2, 6], [-2, 8]], [[-2, 0], [4, 2], [-2, 4], [2, 6], [-2, 8], [2, 10]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[2, 5], [2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, 11]], [[2, 3], [-2, 5], [2, 7], [-2, 9], [2, 11]], [[2, 3], [2, 11]], [[-2, 5], [-2, 9]], [[-2, 3], [2, 5], [-2, 7], [2, 9], [-2, 11]], [[2, 5], [2, 9]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[2, 5], [2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12577681
    {'center': '112.f1.a1', 'center_index': 112, 'center_order': 12, 'counter': 113, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '448.1201', 'image_order': 448, 'indicator': 0, 'kernel': '448.a1.a1', 'kernel_order': 3, 'label': '1344.8546.4j9', 'nt': [112, 0], '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]], [[-4, 7]], [[4, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, 8]], [[2, 0], [-4, 2], [2, 4], [-2, 6], [2, 8], [-2, 10]], [[-2, 4], [-2, 10]], [[-2, 0], [4, 2], [-2, 4], [2, 6], [-2, 8], [2, 10]], [[2, 4], [2, 10]], [[2, 6], [2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[2, 5], [2, -5]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 5], [-2, 9]], [[2, 3], [2, 11]], [[2, 5], [2, 9]], [[2, 3], [-2, 5], [2, 7], [-2, 9], [2, 11]], [[-2, 3], [-2, 11]], [[-2, 3], [2, 5], [-2, 7], [2, 9], [-2, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 5], [-2, -5]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[2, 5], [2, -5]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12577685
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 14, 'counter': 117, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '192.1332', 'image_order': 192, 'indicator': -1, 'kernel': '192.a1.a1', 'kernel_order': 7, 'label': '1344.8546.8a', '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]], [[0, 0]], [[4, 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]], [[-8, 0]], [[-8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12577686
    {'center': '672.a1.a1', 'center_index': 672, 'center_order': 2, 'counter': 118, 'cyclotomic_n': 28, 'dim': 8, 'faithful': True, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '1344.8546', 'image_order': 1344, 'indicator': -1, 'kernel': '1344.a1.a1', 'kernel_order': 1, 'label': '1344.8546.8b1', '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]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 2], [-4, -2]], [[4, 4], [4, -4]], [[-4, 6], [-4, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 4], [-4, -4]], [[4, 2], [4, -2]], [[4, 6], [4, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[-4, 5], [-4, -5]], [[4, 3], [4, -3]], [[4, 5], [4, -5]], [[4, 1], [4, -1]], [[-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]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[2, 5], [2, -5]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12577687
    {'center': '672.a1.a1', 'center_index': 672, 'center_order': 2, 'counter': 119, 'cyclotomic_n': 28, 'dim': 8, 'faithful': True, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '1344.8546', 'image_order': 1344, 'indicator': -1, 'kernel': '1344.a1.a1', 'kernel_order': 1, 'label': '1344.8546.8b2', '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]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 2], [-4, -2]], [[4, 4], [4, -4]], [[-4, 6], [-4, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 4], [-4, -4]], [[4, 2], [4, -2]], [[4, 6], [4, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[4, 5], [4, -5]], [[-4, 3], [-4, -3]], [[-4, 5], [-4, -5]], [[-4, 1], [-4, -1]], [[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]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[-2, 5], [-2, -5]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12577689
    {'center': '672.a1.a1', 'center_index': 672, 'center_order': 2, 'counter': 120, 'cyclotomic_n': 28, 'dim': 8, 'faithful': True, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '1344.8546', 'image_order': 1344, 'indicator': -1, 'kernel': '1344.a1.a1', 'kernel_order': 1, 'label': '1344.8546.8b3', '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]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 6], [-4, -6]], [[-4, 2], [-4, -2]], [[4, 4], [4, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 2], [4, -2]], [[4, 6], [4, -6]], [[-4, 4], [-4, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[-4, 1], [-4, -1]], [[4, 5], [4, -5]], [[4, 1], [4, -1]], [[-4, 3], [-4, -3]], [[4, 3], [4, -3]], [[-4, 5], [-4, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[2, 5], [2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12577690
    {'center': '672.a1.a1', 'center_index': 672, 'center_order': 2, 'counter': 121, 'cyclotomic_n': 28, 'dim': 8, 'faithful': True, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '1344.8546', 'image_order': 1344, 'indicator': -1, 'kernel': '1344.a1.a1', 'kernel_order': 1, 'label': '1344.8546.8b4', '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]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 6], [-4, -6]], [[-4, 2], [-4, -2]], [[4, 4], [4, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 2], [4, -2]], [[4, 6], [4, -6]], [[-4, 4], [-4, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[4, 1], [4, -1]], [[-4, 5], [-4, -5]], [[-4, 1], [-4, -1]], [[4, 3], [4, -3]], [[-4, 3], [-4, -3]], [[4, 5], [4, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-2, 5], [-2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12577691
    {'center': '672.a1.a1', 'center_index': 672, 'center_order': 2, 'counter': 122, 'cyclotomic_n': 28, 'dim': 8, 'faithful': True, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '1344.8546', 'image_order': 1344, 'indicator': -1, 'kernel': '1344.a1.a1', 'kernel_order': 1, 'label': '1344.8546.8b5', '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]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 4], [4, -4]], [[-4, 6], [-4, -6]], [[-4, 2], [-4, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 6], [4, -6]], [[-4, 4], [-4, -4]], [[4, 2], [4, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[-4, 3], [-4, -3]], [[-4, 1], [-4, -1]], [[4, 3], [4, -3]], [[4, 5], [4, -5]], [[-4, 5], [-4, -5]], [[4, 1], [4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 5], [-2, -5]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[2, 5], [2, -5]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12577692
    {'center': '672.a1.a1', 'center_index': 672, 'center_order': 2, 'counter': 123, 'cyclotomic_n': 28, 'dim': 8, 'faithful': True, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8546', 'group_counter': 8546, 'group_order': 1344, 'image': None, 'image_isoclass': '1344.8546', 'image_order': 1344, 'indicator': -1, 'kernel': '1344.a1.a1', 'kernel_order': 1, 'label': '1344.8546.8b6', '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]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 4], [4, -4]], [[-4, 6], [-4, -6]], [[-4, 2], [-4, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 6], [4, -6]], [[-4, 4], [-4, -4]], [[4, 2], [4, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[4, 3], [4, -3]], [[4, 1], [4, -1]], [[-4, 3], [-4, -3]], [[-4, 5], [-4, -5]], [[4, 5], [4, -5]], [[-4, 1], [-4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5], [2, -5]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[-2, 5], [-2, -5]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 74052726
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1344, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 42, 'label': '1344.8546.1.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': '1344.8546', 'subgroup_hash': 8546, 'subgroup_order': 1344, 'subgroup_tex': 'D_{56}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74052837
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 672, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.1144', 'subgroup_hash': 1144, 'subgroup_order': 672, 'subgroup_tex': 'D_{28}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74052948
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 672, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.2.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': '672.1127', 'subgroup_hash': 1127, 'subgroup_order': 672, 'subgroup_tex': 'D_{28}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74053059
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': True, 'core_order': 672, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.885', 'subgroup_hash': 885, 'subgroup_order': 672, 'subgroup_tex': 'C_{56}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74053170
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 672, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.2.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': '672.801', 'subgroup_hash': 801, 'subgroup_order': 672, 'subgroup_tex': 'C_{24}:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74053206
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 672, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.457', 'subgroup_hash': 457, 'subgroup_order': 672, 'subgroup_tex': 'C_{12}.D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74053217
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 672, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.2.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': '672.456', 'subgroup_hash': 456, 'subgroup_order': 672, 'subgroup_tex': 'D_{84}:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 74053228
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 672, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.2.g1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.974', 'subgroup_hash': 974, 'subgroup_order': 672, 'subgroup_tex': 'C_4.D_{84}', 'supersolvable': True, 'sylow': 0}
  • id: 74053239
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 672, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.2.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': '672.417', 'subgroup_hash': 417, 'subgroup_order': 672, 'subgroup_tex': 'D_{56}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74052727
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 672, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.2.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': '672.417', 'subgroup_hash': 417, 'subgroup_order': 672, 'subgroup_tex': 'D_{56}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74052738
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 672, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.2.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': '672.416', 'subgroup_hash': 416, 'subgroup_order': 672, 'subgroup_tex': 'C_{24}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052749
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 672, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.2.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': '672.416', 'subgroup_hash': 416, 'subgroup_order': 672, 'subgroup_tex': 'C_{24}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052760
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 672, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.2.j1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.398', 'subgroup_hash': 398, 'subgroup_order': 672, 'subgroup_tex': 'C_{24}:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052771
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 672, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.2.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': '672.398', 'subgroup_hash': 398, 'subgroup_order': 672, 'subgroup_tex': 'C_{24}:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052782
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 672, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.2.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': '672.418', 'subgroup_hash': 418, 'subgroup_order': 672, 'subgroup_tex': 'C_{24}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052793
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 672, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.2.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': '672.418', 'subgroup_hash': 418, 'subgroup_order': 672, 'subgroup_tex': 'C_{24}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052804
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 224, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 14, 'label': '1344.8546.3.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': '448.1201', 'subgroup_hash': 1201, 'subgroup_order': 448, 'subgroup_tex': 'D_{56}:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 74052815
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 336, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.185', 'subgroup_hash': 185, 'subgroup_order': 336, 'subgroup_tex': 'D_6\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052826
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 336, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.177', 'subgroup_hash': 177, 'subgroup_order': 336, 'subgroup_tex': 'D_{28}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74052838
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 336, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.176', 'subgroup_hash': 176, 'subgroup_order': 336, 'subgroup_tex': 'C_6\\times D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052849
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 336, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.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': '336.197', 'subgroup_hash': 197, 'subgroup_order': 336, 'subgroup_tex': 'D_{84}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052860
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 336, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.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: 74052871
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': True, 'core_order': 336, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.110', 'subgroup_hash': 110, 'subgroup_order': 336, 'subgroup_tex': '\\OD_{16}\\times C_{21}', 'supersolvable': True, 'sylow': 0}
  • id: 74052882
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': True, 'core_order': 336, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.80', 'subgroup_hash': 80, 'subgroup_order': 336, 'subgroup_tex': 'C_{12}.C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052893
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 336, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 74052904
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 336, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 74052915
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 336, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.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': True, '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: 74052926
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 336, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.142', 'subgroup_hash': 142, 'subgroup_order': 336, 'subgroup_tex': 'D_{84}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052937
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 336, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.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': '336.74', 'subgroup_hash': 74, 'subgroup_order': 336, 'subgroup_tex': 'S_3\\times C_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 74052949
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 336, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.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': '336.74', 'subgroup_hash': 74, 'subgroup_order': 336, 'subgroup_tex': 'S_3\\times C_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 74052960
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 336, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.149', 'subgroup_hash': 149, 'subgroup_order': 336, 'subgroup_tex': 'S_3\\times D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052971
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 336, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.138', 'subgroup_hash': 138, 'subgroup_order': 336, 'subgroup_tex': 'D_{28}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74052982
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 336, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.138', 'subgroup_hash': 138, 'subgroup_order': 336, 'subgroup_tex': 'D_{28}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74052993
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 336, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.140', 'subgroup_hash': 140, 'subgroup_order': 336, 'subgroup_tex': 'C_{12}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74053004
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 336, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.75', 'subgroup_hash': 75, 'subgroup_order': 336, 'subgroup_tex': 'C_{168}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74053015
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 336, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.75', 'subgroup_hash': 75, 'subgroup_order': 336, 'subgroup_tex': 'C_{168}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74053026
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 336, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.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': '336.61', 'subgroup_hash': 61, 'subgroup_order': 336, 'subgroup_tex': 'C_3\\times D_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 74053037
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 336, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.61', 'subgroup_hash': 61, 'subgroup_order': 336, 'subgroup_tex': 'C_3\\times D_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 74053048
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.34', 'subgroup_hash': 34, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74053060
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.34', 'subgroup_hash': 34, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74053071
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.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': '336.30', 'subgroup_hash': 30, 'subgroup_order': 336, 'subgroup_tex': 'C_3:D_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 74053082
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.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': '336.30', 'subgroup_hash': 30, 'subgroup_order': 336, 'subgroup_tex': 'C_3:D_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 74053093
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 336, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.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': '336.60', 'subgroup_hash': 60, 'subgroup_order': 336, 'subgroup_tex': 'C_{168}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74053104
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 336, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.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': '336.60', 'subgroup_hash': 60, 'subgroup_order': 336, 'subgroup_tex': 'C_{168}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74053115
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.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': '336.34', 'subgroup_hash': 34, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74053126
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.34', 'subgroup_hash': 34, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74053137
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.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': '336.92', 'subgroup_hash': 92, 'subgroup_order': 336, 'subgroup_tex': 'C_{168}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74053148
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.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': '336.92', 'subgroup_hash': 92, 'subgroup_order': 336, 'subgroup_tex': 'C_{168}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74053159
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.39', 'subgroup_hash': 39, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74053171
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.39', 'subgroup_hash': 39, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74053182
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.94', 'subgroup_hash': 94, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74053193
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.4.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.94', 'subgroup_hash': 94, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74053199
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.4.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.162', 'subgroup_hash': 162, 'subgroup_order': 336, 'subgroup_tex': 'D_6:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74053200
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.4.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': '336.157', 'subgroup_hash': 157, 'subgroup_order': 336, 'subgroup_tex': 'C_{42}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053201
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.4.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.152', 'subgroup_hash': 152, 'subgroup_order': 336, 'subgroup_tex': 'D_{14}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74053202
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.4.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': '336.151', 'subgroup_hash': 151, 'subgroup_order': 336, 'subgroup_tex': 'D_{14}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74053203
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.4.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': '336.144', 'subgroup_hash': 144, 'subgroup_order': 336, 'subgroup_tex': 'C_{12}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74053204
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.4.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': '336.138', 'subgroup_hash': 138, 'subgroup_order': 336, 'subgroup_tex': 'D_{28}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74053205
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.4.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.147', 'subgroup_hash': 147, 'subgroup_order': 336, 'subgroup_tex': 'C_{12}:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74053207
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.4.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.138', 'subgroup_hash': 138, 'subgroup_order': 336, 'subgroup_tex': 'D_{28}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74053208
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': True, 'centralizer_order': 12, 'characteristic': True, 'core_order': 224, 'counter': 61, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.6.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': '224.103', 'subgroup_hash': 103, 'subgroup_order': 224, 'subgroup_tex': 'C_8:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74053209
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 112, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '224.177', 'subgroup_hash': 177, 'subgroup_order': 224, 'subgroup_tex': 'D_{28}:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 74053210
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 112, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.6.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': '224.177', 'subgroup_hash': 177, 'subgroup_order': 224, 'subgroup_tex': 'D_{28}:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 74053211
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 112, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '224.165', 'subgroup_hash': 165, 'subgroup_order': 224, 'subgroup_tex': 'C_{14}\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74053212
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '224.104', 'subgroup_hash': 104, 'subgroup_order': 224, 'subgroup_tex': 'C_4.D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74053213
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.6.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': '224.103', 'subgroup_hash': 103, 'subgroup_order': 224, 'subgroup_tex': 'C_8:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74053214
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.6.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: 74053215
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.6.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': '224.99', 'subgroup_hash': 99, 'subgroup_order': 224, 'subgroup_tex': 'D_{56}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74053216
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.6.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': '224.99', 'subgroup_hash': 99, 'subgroup_order': 224, 'subgroup_tex': 'D_{56}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74053218
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.6.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': '224.99', 'subgroup_hash': 99, 'subgroup_order': 224, 'subgroup_tex': 'D_{56}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74053219
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.6.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': '224.99', 'subgroup_hash': 99, 'subgroup_order': 224, 'subgroup_tex': 'D_{56}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74053220
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.6.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': '224.103', 'subgroup_hash': 103, 'subgroup_order': 224, 'subgroup_tex': 'C_8:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74053221
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.6.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': '224.103', 'subgroup_hash': 103, 'subgroup_order': 224, 'subgroup_tex': 'C_8:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74053222
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.6.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '224.104', 'subgroup_hash': 104, 'subgroup_order': 224, 'subgroup_tex': 'C_4.D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74053223
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.6.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '224.104', 'subgroup_hash': 104, 'subgroup_order': 224, 'subgroup_tex': 'C_4.D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74053224
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 96, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '1344.8546.7.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': '192.1332', 'subgroup_hash': 1332, 'subgroup_order': 192, 'subgroup_tex': 'D_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74053225
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 168, 'counter': 77, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.55', 'subgroup_hash': 55, 'subgroup_order': 168, 'subgroup_tex': 'D_6\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74053226
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 168, 'counter': 78, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.39', 'subgroup_hash': 39, 'subgroup_order': 168, 'subgroup_tex': 'C_2\\times C_{84}', 'supersolvable': True, 'sylow': 0}
  • id: 74053227
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 168, 'counter': 79, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.32', 'subgroup_hash': 32, 'subgroup_order': 168, 'subgroup_tex': 'C_6:C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74053229
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 168, 'counter': 80, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.30', 'subgroup_hash': 30, 'subgroup_order': 168, 'subgroup_tex': 'S_3\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74053230
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 168, 'counter': 81, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.30', 'subgroup_hash': 30, 'subgroup_order': 168, 'subgroup_tex': 'S_3\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74053231
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 168, 'counter': 82, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.30', 'subgroup_hash': 30, 'subgroup_order': 168, 'subgroup_tex': 'S_3\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74053232
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 168, 'counter': 83, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.30', 'subgroup_hash': 30, 'subgroup_order': 168, 'subgroup_tex': 'S_3\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74053233
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 168, 'counter': 84, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.26', 'subgroup_hash': 26, 'subgroup_order': 168, 'subgroup_tex': 'C_3\\times D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74053234
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 168, 'counter': 85, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.8.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': '168.26', 'subgroup_hash': 26, 'subgroup_order': 168, 'subgroup_tex': 'C_3\\times D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74053235
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 168, 'counter': 86, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.8.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.i1.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': '168.26', 'subgroup_hash': 26, 'subgroup_order': 168, 'subgroup_tex': 'C_3\\times D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74053236
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 168, 'counter': 87, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.8.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': '168.36', 'subgroup_hash': 36, 'subgroup_order': 168, 'subgroup_tex': 'D_{84}', 'supersolvable': True, 'sylow': 0}
  • id: 74053237
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 168, 'counter': 88, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.8.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.24', 'subgroup_hash': 24, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74053238
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 89, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.8.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.34', 'subgroup_hash': 34, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74053240
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 90, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.8.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.34', 'subgroup_hash': 34, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74053241
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 168, 'counter': 91, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.8.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.34', 'subgroup_hash': 34, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74053242
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 168, 'counter': 92, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8546.8.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.6', 'subgroup_hash': 6, 'subgroup_order': 168, 'subgroup_tex': 'C_{168}', 'supersolvable': True, 'sylow': 0}
  • id: 74053243
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 168, 'counter': 93, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8546.8.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.6', 'subgroup_hash': 6, 'subgroup_order': 168, 'subgroup_tex': 'C_{168}', 'supersolvable': True, 'sylow': 0}
  • id: 74053244
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 168, 'counter': 94, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.8.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.3', 'subgroup_hash': 3, 'subgroup_order': 168, 'subgroup_tex': 'C_3:C_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 74053245
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 168, 'counter': 95, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.8.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.3', 'subgroup_hash': 3, 'subgroup_order': 168, 'subgroup_tex': 'C_3:C_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 74053246
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 84, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.8.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.28', 'subgroup_hash': 28, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053247
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 84, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.8.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '168.54', 'subgroup_hash': 54, 'subgroup_order': 168, 'subgroup_tex': 'C_6\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74053248
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.8.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': '168.38', 'subgroup_hash': 38, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053249
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.8.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.37', 'subgroup_hash': 37, 'subgroup_order': 168, 'subgroup_tex': 'C_{42}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052728
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.8.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': '168.15', 'subgroup_hash': 15, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052729
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.8.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': '168.15', 'subgroup_hash': 15, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052730
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.8.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': '168.15', 'subgroup_hash': 15, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052731
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.8.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': '168.17', 'subgroup_hash': 17, 'subgroup_order': 168, 'subgroup_tex': 'C_7:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74052732
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.8.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.50', 'subgroup_hash': 50, 'subgroup_order': 168, 'subgroup_tex': 'S_3\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052733
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.8.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: 74052734
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.8.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: 74052735
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.8.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.13', 'subgroup_hash': 13, 'subgroup_order': 168, 'subgroup_tex': 'C_6.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052736
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.8.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.16', 'subgroup_hash': 16, 'subgroup_order': 168, 'subgroup_tex': 'C_3:D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052737
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 84, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.8.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.25', 'subgroup_hash': 25, 'subgroup_order': 168, 'subgroup_tex': 'C_{12}\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74052739
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.8.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.12', 'subgroup_hash': 12, 'subgroup_order': 168, 'subgroup_tex': 'C_6.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052740
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.8.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': '168.12', 'subgroup_hash': 12, 'subgroup_order': 168, 'subgroup_tex': 'C_6.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052741
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.8.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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: 74052742
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.8.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': '168.12', 'subgroup_hash': 12, 'subgroup_order': 168, 'subgroup_tex': 'C_6.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052743
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.8.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': '168.12', 'subgroup_hash': 12, 'subgroup_order': 168, 'subgroup_tex': 'C_6.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052744
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 84, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.8.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.26', 'subgroup_hash': 26, 'subgroup_order': 168, 'subgroup_tex': 'C_3\\times D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052745
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.8.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.35', 'subgroup_hash': 35, 'subgroup_order': 168, 'subgroup_tex': 'C_4\\times D_{21}', 'supersolvable': True, 'sylow': 0}
  • id: 74052746
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.8.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.14', 'subgroup_hash': 14, 'subgroup_order': 168, 'subgroup_tex': 'D_{21}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052747
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.8.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.34', 'subgroup_hash': 34, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74052748
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.8.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.18', 'subgroup_hash': 18, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74052750
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 112, 'counter': 120, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '112.30', 'subgroup_hash': 30, 'subgroup_order': 112, 'subgroup_tex': 'D_{28}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052751
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 112, 'counter': 121, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '112.29', 'subgroup_hash': 29, 'subgroup_order': 112, 'subgroup_tex': 'C_2\\times D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052752
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 112, 'counter': 122, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '112.23', 'subgroup_hash': 23, 'subgroup_order': 112, 'subgroup_tex': 'C_7\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052753
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 112, 'counter': 123, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '112.6', 'subgroup_hash': 6, 'subgroup_order': 112, 'subgroup_tex': 'D_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 74052754
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 112, 'counter': 124, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.12.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '112.6', 'subgroup_hash': 6, 'subgroup_order': 112, 'subgroup_tex': 'D_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 74052755
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 112, 'counter': 125, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '112.5', 'subgroup_hash': 5, 'subgroup_order': 112, 'subgroup_tex': 'C_{56}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052756
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 112, 'counter': 126, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.12.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '112.5', 'subgroup_hash': 5, 'subgroup_order': 112, 'subgroup_tex': 'C_{56}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052757
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.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: 74052758
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.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': '112.36', 'subgroup_hash': 36, 'subgroup_order': 112, 'subgroup_tex': 'C_{14}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052759
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 56, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.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': '112.37', 'subgroup_hash': 37, 'subgroup_order': 112, 'subgroup_tex': 'C_2^2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052761
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.30', 'subgroup_hash': 30, 'subgroup_order': 112, 'subgroup_tex': 'D_{28}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052762
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.28', 'subgroup_hash': 28, 'subgroup_order': 112, 'subgroup_tex': 'C_4\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052763
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 56, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.30', 'subgroup_hash': 30, 'subgroup_order': 112, 'subgroup_tex': 'D_{28}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052764
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 56, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '112.27', 'subgroup_hash': 27, 'subgroup_order': 112, 'subgroup_tex': 'C_{14}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74052765
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 56, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '112.23', 'subgroup_hash': 23, 'subgroup_order': 112, 'subgroup_tex': 'C_7\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052766
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.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': '112.30', 'subgroup_hash': 30, 'subgroup_order': 112, 'subgroup_tex': 'D_{28}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052767
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 56, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.30', 'subgroup_hash': 30, 'subgroup_order': 112, 'subgroup_tex': 'D_{28}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052768
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 56, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.30', 'subgroup_hash': 30, 'subgroup_order': 112, 'subgroup_tex': 'D_{28}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052769
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 56, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.30', 'subgroup_hash': 30, 'subgroup_order': 112, 'subgroup_tex': 'D_{28}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052770
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.30', 'subgroup_hash': 30, 'subgroup_order': 112, 'subgroup_tex': 'D_{28}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052772
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 56, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.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: 74052773
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 56, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '112.22', 'subgroup_hash': 22, 'subgroup_order': 112, 'subgroup_tex': 'C_2\\times C_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 74052774
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 56, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.22', 'subgroup_hash': 22, 'subgroup_order': 112, 'subgroup_tex': 'C_2\\times C_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 74052775
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.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': '112.28', 'subgroup_hash': 28, 'subgroup_order': 112, 'subgroup_tex': 'C_4\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052776
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 56, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.29', 'subgroup_hash': 29, 'subgroup_order': 112, 'subgroup_tex': 'C_2\\times D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052777
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 56, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.30', 'subgroup_hash': 30, 'subgroup_order': 112, 'subgroup_tex': 'D_{28}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052778
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 56, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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: 74052779
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.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': '112.30', 'subgroup_hash': 30, 'subgroup_order': 112, 'subgroup_tex': 'D_{28}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052780
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 56, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '112.27', 'subgroup_hash': 27, 'subgroup_order': 112, 'subgroup_tex': 'C_{14}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74052781
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 56, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '112.23', 'subgroup_hash': 23, 'subgroup_order': 112, 'subgroup_tex': 'C_7\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052783
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 56, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '112.23', 'subgroup_hash': 23, 'subgroup_order': 112, 'subgroup_tex': 'C_7\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052784
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.5', 'subgroup_hash': 5, 'subgroup_order': 112, 'subgroup_tex': 'C_{56}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052785
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.z1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.5', 'subgroup_hash': 5, 'subgroup_order': 112, 'subgroup_tex': 'C_{56}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052786
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.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': '112.6', 'subgroup_hash': 6, 'subgroup_order': 112, 'subgroup_tex': 'D_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 74052787
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.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': '112.6', 'subgroup_hash': 6, 'subgroup_order': 112, 'subgroup_tex': 'D_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 74052788
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.5', 'subgroup_hash': 5, 'subgroup_order': 112, 'subgroup_tex': 'C_{56}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052789
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.bb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.5', 'subgroup_hash': 5, 'subgroup_order': 112, 'subgroup_tex': 'C_{56}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052790
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.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': '112.5', 'subgroup_hash': 5, 'subgroup_order': 112, 'subgroup_tex': 'C_{56}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052791
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.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': '112.5', 'subgroup_hash': 5, 'subgroup_order': 112, 'subgroup_tex': 'C_{56}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052792
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.7', 'subgroup_hash': 7, 'subgroup_order': 112, 'subgroup_tex': 'C_7:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052794
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.7', 'subgroup_hash': 7, 'subgroup_order': 112, 'subgroup_tex': 'C_7:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052795
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.7', 'subgroup_hash': 7, 'subgroup_order': 112, 'subgroup_tex': 'C_7:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052796
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.12.be1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.be1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.7', 'subgroup_hash': 7, 'subgroup_order': 112, 'subgroup_tex': 'C_7:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052797
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': True, 'core_order': 96, 'counter': 163, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.14.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '14.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '14.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 14, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_7', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.113', 'subgroup_hash': 113, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052798
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.14.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.215', 'subgroup_hash': 215, 'subgroup_order': 96, 'subgroup_tex': 'D_4:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74052799
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.14.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': '96.210', 'subgroup_hash': 210, 'subgroup_order': 96, 'subgroup_tex': 'D_4:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74052800
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 48, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.14.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.183', 'subgroup_hash': 183, 'subgroup_order': 96, 'subgroup_tex': 'D_8:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74052801
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.14.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.158', 'subgroup_hash': 158, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052802
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.14.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': '96.139', 'subgroup_hash': 139, 'subgroup_order': 96, 'subgroup_tex': 'D_{12}:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 74052803
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.14.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.116', 'subgroup_hash': 116, 'subgroup_order': 96, 'subgroup_tex': 'C_4.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74052805
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.14.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': '96.119', 'subgroup_hash': 119, 'subgroup_order': 96, 'subgroup_tex': 'D_8:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74052806
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.14.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': '96.119', 'subgroup_hash': 119, 'subgroup_order': 96, 'subgroup_tex': 'D_8:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74052807
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.14.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': '96.123', 'subgroup_hash': 123, 'subgroup_order': 96, 'subgroup_tex': 'C_8.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74052808
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.14.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': '96.123', 'subgroup_hash': 123, 'subgroup_order': 96, 'subgroup_tex': 'C_8.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74052809
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.14.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': '96.118', 'subgroup_hash': 118, 'subgroup_order': 96, 'subgroup_tex': 'C_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74052810
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.14.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': '96.118', 'subgroup_hash': 118, 'subgroup_order': 96, 'subgroup_tex': 'C_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74052811
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.14.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': '96.122', 'subgroup_hash': 122, 'subgroup_order': 96, 'subgroup_tex': 'C_8.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74052812
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.14.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': '96.122', 'subgroup_hash': 122, 'subgroup_order': 96, 'subgroup_tex': 'C_8.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74052813
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 84, 'counter': 178, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.16.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: 74052814
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 84, 'counter': 179, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.13', 'subgroup_hash': 13, 'subgroup_order': 84, 'subgroup_tex': 'S_3\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052816
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 84, 'counter': 180, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.13', 'subgroup_hash': 13, 'subgroup_order': 84, 'subgroup_tex': 'S_3\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052817
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 84, 'counter': 181, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8546.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.6', 'subgroup_hash': 6, 'subgroup_order': 84, 'subgroup_tex': 'C_{84}', 'supersolvable': True, 'sylow': 0}
  • id: 74052818
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 84, 'counter': 182, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8546.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.6', 'subgroup_hash': 6, 'subgroup_order': 84, 'subgroup_tex': 'C_{84}', 'supersolvable': True, 'sylow': 0}
  • id: 74052819
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 84, 'counter': 183, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.3', 'subgroup_hash': 3, 'subgroup_order': 84, 'subgroup_tex': 'C_3:C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052820
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 84, 'counter': 184, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.3', 'subgroup_hash': 3, 'subgroup_order': 84, 'subgroup_tex': 'C_3:C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052821
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 42, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.16.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: 74052822
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 42, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.16.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.12', 'subgroup_hash': 12, 'subgroup_order': 84, 'subgroup_tex': 'C_3\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052823
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 42, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.16.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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: 74052824
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 42, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.16.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '84.14', 'subgroup_hash': 14, 'subgroup_order': 84, 'subgroup_tex': 'D_{42}', 'supersolvable': True, 'sylow': 0}
  • id: 74052825
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 42, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.16.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.4', 'subgroup_hash': 4, 'subgroup_order': 84, 'subgroup_tex': 'C_7:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74052827
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 42, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.16.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.5', 'subgroup_hash': 5, 'subgroup_order': 84, 'subgroup_tex': 'C_{21}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052828
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 42, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.16.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.5', 'subgroup_hash': 5, 'subgroup_order': 84, 'subgroup_tex': 'C_{21}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052829
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 42, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.16.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.5', 'subgroup_hash': 5, 'subgroup_order': 84, 'subgroup_tex': 'C_{21}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052830
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 21, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.16.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.13', 'subgroup_hash': 13, 'subgroup_order': 84, 'subgroup_tex': 'S_3\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052831
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 21, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.16.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.12', 'subgroup_hash': 12, 'subgroup_order': 84, 'subgroup_tex': 'C_3\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052832
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 21, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.16.o1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.o1.a2', 'outer_equivalence': False, 'perfect': False, '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: 74052833
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 21, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.16.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.8', 'subgroup_hash': 8, 'subgroup_order': 84, 'subgroup_tex': 'S_3\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74052834
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 21, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.16.p1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.p1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.8', 'subgroup_hash': 8, 'subgroup_order': 84, 'subgroup_tex': 'S_3\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74052835
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1344.8546.21.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': '64.256', 'subgroup_hash': 256, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 2}
  • id: 74052836
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 56, 'counter': 199, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052839
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 56, 'counter': 200, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.5', 'subgroup_hash': 5, 'subgroup_order': 56, 'subgroup_tex': 'D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052840
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 56, 'counter': 201, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.5', 'subgroup_hash': 5, 'subgroup_order': 56, 'subgroup_tex': 'D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052841
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 56, 'counter': 202, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.24.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.5', 'subgroup_hash': 5, 'subgroup_order': 56, 'subgroup_tex': 'D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052842
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 56, 'counter': 203, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.3', 'subgroup_hash': 3, 'subgroup_order': 56, 'subgroup_tex': 'C_7:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74052843
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 56, 'counter': 204, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8546.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.2', 'subgroup_hash': 2, 'subgroup_order': 56, 'subgroup_tex': 'C_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 74052844
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 56, 'counter': 205, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8546.24.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.2', 'subgroup_hash': 2, 'subgroup_order': 56, 'subgroup_tex': 'C_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 74052845
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 28, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.13', 'subgroup_hash': 13, 'subgroup_order': 56, 'subgroup_tex': 'C_2^2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052846
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 28, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.7', 'subgroup_hash': 7, 'subgroup_order': 56, 'subgroup_tex': 'C_7:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052847
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 28, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.12', 'subgroup_hash': 12, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052848
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '56.7', 'subgroup_hash': 7, 'subgroup_order': 56, 'subgroup_tex': 'C_7:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052850
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 28, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052851
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.6', 'subgroup_hash': 6, 'subgroup_order': 56, 'subgroup_tex': 'C_{14}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052852
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.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': '56.7', 'subgroup_hash': 7, 'subgroup_order': 56, 'subgroup_tex': 'C_7:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052853
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '56.7', 'subgroup_hash': 7, 'subgroup_order': 56, 'subgroup_tex': 'C_7:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052854
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '56.7', 'subgroup_hash': 7, 'subgroup_order': 56, 'subgroup_tex': 'C_7:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052855
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.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: 74052856
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 28, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052857
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 28, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052858
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.12', 'subgroup_hash': 12, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052859
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.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: 74052861
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.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: 74052862
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 28, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.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: 74052863
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 28, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052864
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.6', 'subgroup_hash': 6, 'subgroup_order': 56, 'subgroup_tex': 'C_{14}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052865
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.5', 'subgroup_hash': 5, 'subgroup_order': 56, 'subgroup_tex': 'D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052866
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 28, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.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: 74052867
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.4', 'subgroup_hash': 4, 'subgroup_order': 56, 'subgroup_tex': 'C_4\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74052868
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.4', 'subgroup_hash': 4, 'subgroup_order': 56, 'subgroup_tex': 'C_4\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74052869
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.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': '56.4', 'subgroup_hash': 4, 'subgroup_order': 56, 'subgroup_tex': 'C_4\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74052870
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.4', 'subgroup_hash': 4, 'subgroup_order': 56, 'subgroup_tex': 'C_4\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74052872
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '56.4', 'subgroup_hash': 4, 'subgroup_order': 56, 'subgroup_tex': 'C_4\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74052873
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 28, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.5', 'subgroup_hash': 5, 'subgroup_order': 56, 'subgroup_tex': 'D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052874
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.4', 'subgroup_hash': 4, 'subgroup_order': 56, 'subgroup_tex': 'C_4\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74052875
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.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': '56.4', 'subgroup_hash': 4, 'subgroup_order': 56, 'subgroup_tex': 'C_4\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74052876
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.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': '56.5', 'subgroup_hash': 5, 'subgroup_order': 56, 'subgroup_tex': 'D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052877
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.3', 'subgroup_hash': 3, 'subgroup_order': 56, 'subgroup_tex': 'C_7:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74052878
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.be1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.be1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 74052879
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.3', 'subgroup_hash': 3, 'subgroup_order': 56, 'subgroup_tex': 'C_7:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74052880
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 28, 'counter': 238, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8546.24.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.2', 'subgroup_hash': 2, 'subgroup_order': 56, 'subgroup_tex': 'C_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 74052881
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 28, 'counter': 239, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8546.24.bg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.2', 'subgroup_hash': 2, 'subgroup_order': 56, 'subgroup_tex': 'C_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 74052883
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.3', 'subgroup_hash': 3, 'subgroup_order': 56, 'subgroup_tex': 'C_7:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74052884
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.24.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.3', 'subgroup_hash': 3, 'subgroup_order': 56, 'subgroup_tex': 'C_7:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74052885
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 48, 'counter': 242, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.28.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '28.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74052886
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': True, 'core_order': 48, 'counter': 243, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.28.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '28.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.24', 'subgroup_hash': 24, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052887
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': True, 'core_order': 48, 'counter': 244, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.28.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: 74052888
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 48, 'counter': 245, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.28.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': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74052889
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 48, 'counter': 246, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.28.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': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74052890
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 48, 'counter': 247, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.28.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '28.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.5', 'subgroup_hash': 5, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052891
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 48, 'counter': 248, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.28.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '28.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.5', 'subgroup_hash': 5, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052892
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052894
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052895
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74052896
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.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: 74052897
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.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': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 74052898
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052899
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.37', 'subgroup_hash': 37, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052900
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74052901
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.37', 'subgroup_hash': 37, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052902
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74052903
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74052905
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74052906
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74052907
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.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': '48.41', 'subgroup_hash': 41, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052908
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.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': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74052909
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052910
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74052911
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.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': 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: 74052912
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74052913
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74052914
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.25', 'subgroup_hash': 25, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 74052916
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.x1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.25', 'subgroup_hash': 25, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 74052917
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052918
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.y1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052919
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.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': '48.15', 'subgroup_hash': 15, 'subgroup_order': 48, 'subgroup_tex': 'C_3:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 74052920
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.z1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.15', 'subgroup_hash': 15, 'subgroup_order': 48, 'subgroup_tex': 'C_3:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 74052921
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052922
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052923
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.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': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052924
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.bb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.bb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052925
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.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': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052927
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.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': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052928
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.18', 'subgroup_hash': 18, 'subgroup_order': 48, 'subgroup_tex': 'C_3:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052929
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.bd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.18', 'subgroup_hash': 18, 'subgroup_order': 48, 'subgroup_tex': 'C_3:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052930
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.8', 'subgroup_hash': 8, 'subgroup_order': 48, 'subgroup_tex': 'C_3:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052931
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.28.be1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.be1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.8', 'subgroup_hash': 8, 'subgroup_order': 48, 'subgroup_tex': 'C_3:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052932
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 42, 'counter': 285, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8546.32.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: 74052933
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 21, 'counter': 286, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8546.32.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: 74052934
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 21, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '42.3', 'subgroup_hash': 3, 'subgroup_order': 42, 'subgroup_tex': 'S_3\\times C_7', 'supersolvable': True, 'sylow': 0}
  • id: 74052935
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 21, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.32.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: 74052936
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 21, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.32.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: 74052938
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 21, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.32.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: 74052939
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 21, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.32.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 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: 74052940
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 21, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.32.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.5', 'subgroup_hash': 5, 'subgroup_order': 42, 'subgroup_tex': 'D_{21}', 'supersolvable': True, 'sylow': 0}
  • id: 74052941
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.42.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 74052942
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.42.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': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 74052943
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 16, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.42.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052944
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 16, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.42.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': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052945
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.42.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052946
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.42.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': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052947
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.42.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: 74052950
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.42.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': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052951
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.42.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': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052952
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.42.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: 74052953
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.42.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: 74052954
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.42.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': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052955
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.42.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': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052956
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.42.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: 74052957
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.42.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: 74052958
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 28, 'counter': 308, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.38', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052959
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 28, 'counter': 309, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8546.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.51', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 51, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052961
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 28, 'counter': 310, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8546.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.38', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052962
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 14, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052963
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 14, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.48.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052964
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 14, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.48.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052965
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 14, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.48.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052966
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 14, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.48.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 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: 74052967
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.48.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: 74052968
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 14, 'counter': 317, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8546.48.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: 74052969
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 14, 'counter': 318, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8546.48.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052970
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 14, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.48.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: 74052972
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.48.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.1', 'subgroup_hash': 1, 'subgroup_order': 28, 'subgroup_tex': 'C_7:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052973
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.48.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.1', 'subgroup_hash': 1, 'subgroup_order': 28, 'subgroup_tex': 'C_7:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052974
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.48.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.1', 'subgroup_hash': 1, 'subgroup_order': 28, 'subgroup_tex': 'C_7:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052975
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 7, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.48.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052976
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 7, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.48.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052977
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 7, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.48.o1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.o1.a2', 'outer_equivalence': False, 'perfect': False, '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: 74052978
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 7, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.48.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 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: 74052979
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 7, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.48.p1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.p1.a2', 'outer_equivalence': False, 'perfect': False, '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: 74052980
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 24, 'counter': 328, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.56.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '56.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.5', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{28}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74052981
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 24, 'counter': 329, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.56.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '56.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74052983
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 24, 'counter': 330, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.56.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '56.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.5', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{28}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052984
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 24, 'counter': 331, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.56.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '56.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74052985
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 24, 'counter': 332, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.56.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '56.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.5', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{28}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74052986
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 24, 'counter': 333, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.56.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '56.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74052987
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 24, 'counter': 334, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.56.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '56.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.5', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{28}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74052988
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 24, 'counter': 335, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8546.56.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '56.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 74052989
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 24, 'counter': 336, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8546.56.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '56.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 74052990
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 24, 'counter': 337, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.56.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '56.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74052991
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 24, 'counter': 338, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.56.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '56.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74052992
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052994
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.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: 74052995
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052996
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052997
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052998
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052999
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053000
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74053001
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74053002
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053003
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053005
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74053006
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053007
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74053008
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053009
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.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: 74053010
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053011
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.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': 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: 74053012
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053013
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053014
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053016
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.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': 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: 74053017
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053018
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74053019
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74053020
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74053021
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74053022
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74053023
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.bf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.bf1.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: 74053024
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74053025
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74053027
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.56.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74053028
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 21, 'counter': 371, 'cyclic': True, 'direct': False, 'hall': 21, 'label': '1344.8546.64.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': '64.256', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 256, '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: 74053029
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 16, 'counter': 372, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.84.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '84.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '84.8', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 84, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_7', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74053030
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.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: 74053031
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053032
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 8, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053033
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.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: 74053034
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.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: 74053035
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053036
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053038
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74053039
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74053040
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 8, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74053041
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.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: 74053042
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74053043
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.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: 74053044
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74053045
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74053046
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74053047
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 8, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74053049
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 8, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74053050
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053051
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053052
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.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: 74053053
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.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: 74053054
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74053055
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74053056
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 8, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74053057
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 8, 'counter': 398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74053058
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 74053061
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 74053062
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74053063
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.y1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74053064
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 74053065
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.z1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 74053066
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.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: 74053067
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.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: 74053068
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74053069
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.bb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.bb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74053070
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74053072
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74053073
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74053074
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.bd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74053075
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74053076
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.84.be1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.be1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74053077
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 14, 'counter': 415, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8546.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.209', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 209, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74053078
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 7, 'counter': 416, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8546.96.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: 74053079
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 7, 'counter': 417, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8546.96.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: 74053080
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 7, 'counter': 418, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8546.96.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: 74053081
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 7, 'counter': 419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.96.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: 74053083
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 7, 'counter': 420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.96.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: 74053084
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 7, 'counter': 421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.96.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 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: 74053085
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 7, 'counter': 422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.96.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 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: 74053086
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 12, 'counter': 423, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.112.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '112.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '112.29', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 29, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{28}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74053087
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 12, 'counter': 424, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.112.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '112.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '112.29', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 29, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{28}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74053088
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 12, 'counter': 425, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.112.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '112.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '112.29', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 29, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{28}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74053089
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 12, 'counter': 426, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8546.112.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '112.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '112.42', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 42, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74053090
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 12, 'counter': 427, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8546.112.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '112.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '112.29', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 29, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{28}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74053091
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': True, 'centralizer_order': 224, 'characteristic': True, 'core_order': 12, 'counter': 428, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.112.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '112.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '112.29', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 29, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{28}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053092
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 12, 'counter': 429, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.112.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '112.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '112.29', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 29, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{28}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053094
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.112.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74053095
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.112.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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74053096
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.112.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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74053097
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.112.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74053098
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 434, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8546.112.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74053099
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.112.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053100
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.112.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053101
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.112.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053102
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 3, 'counter': 438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.112.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74053103
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.112.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74053105
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.112.o1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.o1.a2', 'outer_equivalence': False, 'perfect': False, '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: 74053106
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.112.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.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': 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: 74053107
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.112.p1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.p1.a2', 'outer_equivalence': False, 'perfect': False, '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: 74053108
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 8, 'counter': 443, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.168.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: 74053109
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 8, 'counter': 444, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8546.168.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '168.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '168.50', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 50, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 168, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74053110
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 8, 'counter': 445, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8546.168.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '168.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '168.50', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 50, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 168, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74053111
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 4, 'counter': 446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.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: 74053112
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.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: 74053113
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 74053114
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.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: 74053116
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 4, 'counter': 450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.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: 74053117
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053118
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.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: 74053119
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.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: 74053120
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.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: 74053121
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053122
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 4, 'counter': 456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053123
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 4, 'counter': 457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053124
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 74053125
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053127
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053128
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 4, 'counter': 461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053129
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 4, 'counter': 462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.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: 74053130
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.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: 74053131
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.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: 74053132
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.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: 74053133
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053134
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053135
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053136
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.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': 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: 74053138
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053139
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053140
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053141
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053142
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053143
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053144
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053145
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053146
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.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: 74053147
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74053149
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.be1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.be1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 74053150
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74053151
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 4, 'counter': 482, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8546.168.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74053152
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 4, 'counter': 483, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8546.168.bg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.bg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74053153
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74053154
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.168.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74053155
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 7, 'counter': 486, 'cyclic': True, 'direct': False, 'hall': 7, 'label': '1344.8546.192.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': '192.1332', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1332, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8:D_6', 'simple': True, 'solvable': True, 'special_labels': ['C7'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 7}
  • id: 74053156
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 6, 'counter': 487, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8546.224.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '224.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '224.176', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 176, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 224, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_{28}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74053157
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 3, 'counter': 488, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8546.224.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: 74053158
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 3, 'counter': 489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.224.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74053160
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 3, 'counter': 490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.224.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: 74053161
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 491, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8546.224.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: 74053162
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 492, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8546.224.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: 74053163
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 493, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8546.224.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.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': 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: 74053164
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.224.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '224.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': 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: 74053165
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 4, 'counter': 495, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8546.336.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '336.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '336.149', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 149, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 336, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_{28}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 74053166
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 4, 'counter': 496, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8546.336.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: 74053167
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 4, 'counter': 497, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8546.336.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '336.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '336.149', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 149, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 336, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_{28}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053168
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 2, 'counter': 498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.336.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: 74053169
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 2, 'counter': 499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.336.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: 74053172
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.336.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: 74053173
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.336.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: 74053174
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.336.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 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: 74053175
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.336.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 74053176
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 448, 'characteristic': False, 'core_order': 2, 'counter': 504, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8546.336.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: 74053177
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 2, 'counter': 505, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8546.336.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: 74053178
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 506, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8546.336.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: 74053179
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 507, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8546.336.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053180
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 508, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8546.336.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053181
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 509, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8546.336.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74053183
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 1, 'counter': 510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.336.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 74053184
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.336.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 74053185
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.336.o1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.o1.a2', 'outer_equivalence': False, 'perfect': False, '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: 74053186
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.336.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 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: 74053187
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8546.336.p1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.p1.a2', 'outer_equivalence': False, 'perfect': False, '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: 74053188
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 3, 'counter': 515, 'cyclic': True, 'direct': False, 'hall': 3, 'label': '1344.8546.448.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': '448.1201', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1201, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 448, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{56}:C_2^2', '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: 74053189
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': True, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': True, 'core_order': 2, 'counter': 516, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8546.672.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '672.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '672.1141', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1141, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 672, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6\\times D_{28}', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'U2'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74053190
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': False, 'core_order': 1, 'counter': 517, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8546.672.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: 74053191
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 1, 'counter': 518, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8546.672.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: 74053192
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 1, 'counter': 519, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8546.672.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: 74053194
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 520, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8546.672.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: 74053195
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 521, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8546.672.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: 74053196
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 522, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8546.672.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.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': 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: 74053197
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 523, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8546.672.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.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': 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: 74053198
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8546', 'ambient_counter': 8546, 'ambient_order': 1344, 'ambient_tex': 'D_{56}:D_6', 'central': True, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': True, 'core_order': 1, 'counter': 524, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1344.8546.1344.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': '1344.8546', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8546, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1344, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{56}:D_6', '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: 74052935
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.n1.a1', '16.p1.a1', '16.p1.a2'], 'contains': ['64.a1.a1', '96.d1.a1', '224.d1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [2, 448, 192], 'label': '1344.8546.32.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052936
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.p1.a1', '16.p1.a2'], 'contains': ['64.a1.a1', '96.e1.a1', '224.e1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [4, 192, 448], 'label': '1344.8546.32.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bd1.a1', 'old_label': '32.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052977
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a2', '24.h1.a1'], 'contains': ['96.b1.a1', '96.f1.a1', '96.f1.b1', '336.o1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [1009, 192, 76], 'label': '1344.8546.48.o1.a2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.ba1.a1', 'old_label': '48.o1.a2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.o1.a2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052978
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '48.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.a1', '24.q1.a1'], 'contains': ['96.d1.a1', '96.e1.a1', '96.g1.a1', '336.p1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [2, 192, 4], 'label': '1344.8546.48.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.t1.a1', 'old_label': '48.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052979
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '48.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.a2', '24.q1.a1'], 'contains': ['96.d1.a1', '96.e1.a1', '96.g1.a1', '336.p1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [674, 192, 4], 'label': '1344.8546.48.p1.a2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.t1.a1', 'old_label': '48.p1.a2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.p1.a2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053080
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '96.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '48.e1.a1', '48.n1.a1', '48.p1.a1', '48.p1.a2'], 'contains': ['192.a1.a1', '672.d1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [2, 192], 'label': '1344.8546.96.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '96.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053081
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '96.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '48.f1.a1', '48.p1.a1', '48.p1.a2'], 'contains': ['192.a1.a1', '672.e1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [4, 192], 'label': '1344.8546.96.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bd1.a1', 'old_label': '96.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053164
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '224.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1.a1', '112.j1.a1', '112.p1.a1', '112.p1.a2'], 'contains': ['448.a1.a1', '672.g1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [6, 448], 'label': '1344.8546.224.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.s1.a1', 'old_label': '224.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053183
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '336.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.n1.a1', '112.n1.a1', '168.c1.a1'], 'contains': ['672.b1.a1', '672.c1.a1', '672.d1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [1009, 2], 'label': '1344.8546.336.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '336.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053184
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '336.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '28.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.a1', '112.o1.a1', '168.e1.a1'], 'contains': ['672.b1.a1', '672.f1.a1', '672.f1.b1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [337, 76], 'label': '1344.8546.336.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.j1.a1', 'old_label': '336.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053185
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '336.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '28.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.a2', '112.o1.a2', '168.e1.a1'], 'contains': ['672.b1.a1', '672.f1.a1', '672.f1.b1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [1009, 76], 'label': '1344.8546.336.o1.a2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.j1.a1', 'old_label': '336.o1.a2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.o1.a2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053186
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '336.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1.a1', '112.p1.a1', '168.n1.a1'], 'contains': ['672.d1.a1', '672.e1.a1', '672.g1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': None, 'generators': [2, 4], 'label': '1344.8546.336.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.r1.a1', 'old_label': '336.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053187
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '336.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1.a2', '112.p1.a2', '168.n1.a1'], 'contains': ['672.d1.a1', '672.e1.a1', '672.g1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': None, 'generators': [674, 4], 'label': '1344.8546.336.p1.a2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.r1.a1', 'old_label': '336.p1.a2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.p1.a2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052726
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['1344.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1', '2.h1.a1', '2.h1.b1', '2.i1.a1', '2.i1.b1', '2.j1.a1', '2.j1.b1', '2.k1.a1', '2.k1.b1', '3.a1.a1', '7.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 1008, 448, 4, 672, 192, 2, 168], 'label': '1344.8546.1.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1', '2.h1.a1', '2.h1.b1', '2.i1.a1', '2.i1.b1', '2.j1.a1', '2.j1.b1', '2.k1.a1', '2.k1.b1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052727
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '2.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['672.d1.a1', '672.g1.a1', '672.b1.a1', '672.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.h1.a1', '4.i1.b1', '4.k1.a1', '4.p1.b1', '4.q1.b1', '4.t1.b1', '4.w1.b1', '6.h1.b1', '14.h1.b1'], 'core': '2.h1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [3, 448, 168, 1008, 4, 192, 672], 'label': '1344.8546.2.h1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.h1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.h1.a1', '4.i1.b1', '4.k1.a1', '4.p1.b1', '4.q1.b1', '4.t1.b1', '4.w1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.h1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.h1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052728
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.x1.a1', '4.bb1.a1'], 'contains': ['16.b1.a1', '16.h1.a1', '16.m1.a1', '24.l1.a1', '56.n1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1011, 672, 448, 4, 192], 'label': '1344.8546.8.t1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.t1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.t1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052729
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.y1.a1', '4.bc1.a1'], 'contains': ['16.b1.a1', '16.i1.a1', '16.l1.a1', '24.m1.a1', '56.o1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [125, 672, 448, 974, 192], 'label': '1344.8546.8.u1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.u1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.u1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052730
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.b1', '4.y1.a1', '4.bc1.a1'], 'contains': ['16.b1.a1', '16.i1.b1', '16.l1.b1', '24.m1.b1', '56.o1.b1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1011, 672, 448, 76, 192], 'label': '1344.8546.8.u1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.u1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.u1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052731
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '4.x1.a1', '4.bb1.a1'], 'contains': ['16.b1.a1', '16.j1.a1', '16.k1.a1', '24.n1.a1', '56.p1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [53, 672, 448, 6, 192], 'label': '1344.8546.8.v1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.v1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.v1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052732
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '4.x1.a1', '4.bd1.a1'], 'contains': ['16.c1.a1', '16.h1.a1', '16.j1.a1', '16.p1.a1', '16.p1.a2', '24.q1.a1', '56.q1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [2, 672, 448, 4, 192], 'label': '1344.8546.8.w1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.w1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.w1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052733
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '4.y1.a1', '4.be1.a1'], 'contains': ['16.c1.a1', '16.i1.a1', '16.l1.b1', '24.r1.a1', '56.r1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [77, 672, 448, 2, 192], 'label': '1344.8546.8.x1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.x1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.x1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052734
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.b1', '4.y1.a1', '4.be1.a1'], 'contains': ['16.c1.a1', '16.i1.b1', '16.l1.a1', '24.r1.b1', '56.r1.b1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [2, 672, 448, 76, 192], 'label': '1344.8546.8.x1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.x1.b1', 'projective_image': None, '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': None}
  • id: 74052735
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1', '4.x1.a1', '4.bd1.a1'], 'contains': ['16.c1.a1', '16.k1.a1', '16.m1.a1', '24.u1.a1', '56.s1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [5, 672, 448, 2, 192], 'label': '1344.8546.8.y1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.y1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.y1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052736
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '4.z1.a1', '4.bb1.a1'], 'contains': ['16.g1.a1', '16.h1.a1', '16.j1.a1', '24.v1.a1', '56.t1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [338, 672, 448, 4, 192], 'label': '1344.8546.8.z1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.z1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.z1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052737
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.bb1.a1', '4.bd1.a1'], 'contains': ['16.e1.a1', '16.h1.a1', '16.k1.a1', '24.w1.a1', '56.u1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 448, 672, 4, 192], 'label': '1344.8546.8.ba1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.ba1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ba1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052738
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '2.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['672.e1.a1', '672.f1.b1', '672.d1.a1', '672.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.i1.a1', '4.j1.a1', '4.k1.a1', '4.r1.a1', '4.s1.a1', '4.u1.a1', '4.v1.a1', '6.i1.a1', '14.i1.a1'], 'core': '2.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [5, 448, 168, 336, 6, 192, 672], 'label': '1344.8546.2.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.i1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.i1.a1', '4.j1.a1', '4.k1.a1', '4.r1.a1', '4.s1.a1', '4.u1.a1', '4.v1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052739
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.z1.a1', '4.bd1.a1'], 'contains': ['16.f1.a1', '16.h1.a1', '16.m1.a1', '24.x1.a1', '56.v1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [3, 672, 448, 4, 192], 'label': '1344.8546.8.bb1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052740
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.ba1.a1', '4.be1.a1'], 'contains': ['16.f1.a1', '16.i1.a1', '16.l1.a1', '24.y1.a1', '56.x1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [77, 672, 448, 974, 192], 'label': '1344.8546.8.bc1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052741
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.b1', '4.ba1.a1', '4.be1.a1'], 'contains': ['16.f1.a1', '16.i1.b1', '16.l1.b1', '24.y1.b1', '56.x1.b1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [3, 672, 448, 76, 192], 'label': '1344.8546.8.bc1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bc1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bc1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052742
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '4.ba1.a1', '4.bc1.a1'], 'contains': ['16.g1.a1', '16.i1.a1', '16.l1.b1', '24.z1.a1', '56.y1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [77, 672, 448, 338, 192], 'label': '1344.8546.8.bd1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052743
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.b1', '4.ba1.a1', '4.bc1.a1'], 'contains': ['16.g1.a1', '16.i1.b1', '16.l1.a1', '24.z1.b1', '56.y1.b1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [338, 672, 448, 76, 192], 'label': '1344.8546.8.bd1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bd1.b1', 'projective_image': None, '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': None}
  • id: 74052744
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.bc1.a1', '4.be1.a1'], 'contains': ['16.e1.a1', '16.i1.a1', '16.i1.b1', '24.ba1.a1', '56.ba1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 448, 672, 76, 192], 'label': '1344.8546.8.be1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.be1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.be1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052745
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.bb1.a1', '4.bd1.a1'], 'contains': ['16.e1.a1', '16.j1.a1', '16.m1.a1', '24.bb1.a1', '56.bb1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 672, 448, 6, 192], 'label': '1344.8546.8.bf1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bf1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bf1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052746
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '4.z1.a1', '4.bd1.a1'], 'contains': ['16.f1.a1', '16.j1.a1', '16.k1.a1', '24.bc1.a1', '56.bc1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [5, 672, 448, 6, 192], 'label': '1344.8546.8.bg1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bg1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bg1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052747
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.bc1.a1', '4.be1.a1'], 'contains': ['16.e1.a1', '16.l1.a1', '16.l1.b1', '24.bh1.a1', '56.bh1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 672, 448, 974, 192], 'label': '1344.8546.8.bh1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bh1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bh1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052748
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1', '4.z1.a1', '4.bb1.a1'], 'contains': ['16.g1.a1', '16.k1.a1', '16.m1.a1', '24.bi1.a1', '56.bi1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [5, 672, 448, 338, 192], 'label': '1344.8546.8.bi1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bi1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bi1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052749
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '2.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['672.e1.a1', '672.d1.a1', '672.b1.a1', '672.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.i1.b1', '4.j1.a1', '4.k1.b1', '4.r1.b1', '4.s1.b1', '4.u1.b1', '4.v1.b1', '6.i1.b1', '14.i1.b1'], 'core': '2.i1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 448, 76, 336, 730, 192, 672], 'label': '1344.8546.2.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.i1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.i1.b1', '4.j1.a1', '4.k1.b1', '4.r1.b1', '4.s1.b1', '4.u1.b1', '4.v1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052750
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1', '6.b1.a1', '6.e1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.d1.a1', '24.g1.a1', '24.w1.a1', '84.f1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 336, 672, 4, 192], 'label': '1344.8546.12.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.b1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '24.b1.a1', '24.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052751
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.c1.a1', 'complements': ['112.p1.a1', '112.p1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.a1.a1', '6.c1.a1', '6.f1.a1'], 'contains': ['24.a1.a1', '24.c1.a1', '24.c1.b1', '24.h1.a1', '24.ba1.a1', '84.h1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 336, 672, 76, 192], 'label': '1344.8546.12.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.c1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '24.c1.a1', '24.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052752
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.d1.a1', 'complements': ['112.p1.a1', '112.p1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.a1.a1', '6.d1.a1', '6.g1.a1'], 'contains': ['24.a1.a1', '24.e1.a1', '24.e1.b1', '84.a1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 192, 336, 168, 672], 'label': '1344.8546.12.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.f1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '24.e1.a1', '24.e1.b1', '84.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052753
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.f1.a1', 'complements': ['112.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.p1.a1', '6.a1.a1', '6.h1.a1', '6.j1.a1'], 'contains': ['24.b1.a1', '24.c1.a1', '24.e1.b1', '84.x1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 336, 672, 4, 192], 'label': '1344.8546.12.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1.a1', 'normal_contained_in': ['4.p1.a1', '6.a1.a1'], 'normal_contains': ['24.b1.a1', '24.c1.a1', '24.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052754
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.f1.a1', 'complements': ['112.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.p1.b1', '6.a1.a1', '6.h1.b1', '6.j1.b1'], 'contains': ['24.b1.a1', '24.c1.b1', '24.e1.a1', '84.x1.b1'], 'core': '12.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [4, 1008, 672, 168, 192], 'label': '1344.8546.12.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1.b1', 'normal_contained_in': ['4.p1.b1', '6.a1.a1'], 'normal_contains': ['24.b1.a1', '24.c1.b1', '24.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052755
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.f1.a1', 'complements': ['112.p1.a1', '112.p1.a2', '112.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.s1.a1', '6.a1.a1', '6.i1.a1', '6.k1.a1'], 'contains': ['24.c1.a1', '24.d1.a1', '24.e1.a1', '84.ba1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [5, 336, 672, 168, 192], 'label': '1344.8546.12.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1.a1', 'normal_contained_in': ['4.s1.a1', '6.a1.a1'], 'normal_contains': ['24.c1.a1', '24.d1.a1', '24.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052756
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.f1.a1', 'complements': ['112.p1.a1', '112.p1.a2', '112.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.s1.b1', '6.a1.a1', '6.i1.b1', '6.k1.b1'], 'contains': ['24.c1.b1', '24.d1.a1', '24.e1.b1', '84.ba1.b1'], 'core': '12.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 336, 672, 76, 192], 'label': '1344.8546.12.e1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1.b1', 'normal_contained_in': ['4.s1.b1', '6.a1.a1'], 'normal_contains': ['24.c1.b1', '24.d1.a1', '24.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.e1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052757
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.x1.a1', '6.b1.a1'], 'contains': ['24.f1.a1', '24.g1.a1', '24.i1.a1', '24.l1.a1', '24.n1.a1', '24.q1.a1', '24.u1.a1', '84.b1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1009, 4, 672, 2, 192], 'label': '1344.8546.12.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052758
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.y1.a1', '6.c1.a1'], 'contains': ['24.f1.a1', '24.h1.a1', '24.k1.a1', '24.m1.a1', '24.m1.b1', '24.r1.a1', '24.r1.b1', '84.c1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1009, 76, 672, 2, 192], 'label': '1344.8546.12.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052759
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.a1', '6.c1.a1', '6.d1.a1'], 'contains': ['24.a1.a1', '24.f1.a1', '24.j1.a1', '24.o1.a1', '24.p1.a1', '24.s1.a1', '24.t1.a1', '84.d1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 336, 192, 2, 672], 'label': '1344.8546.12.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052760
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '2.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['672.f1.b1', '672.b1.a1', '672.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.l1.a1', '4.m1.a1', '4.o1.b1', '4.p1.a1', '4.q1.b1', '4.r1.a1', '4.u1.b1', '6.j1.a1', '14.j1.a1'], 'core': '2.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 448, 4, 336, 2, 192, 672], 'label': '1344.8546.2.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.j1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.l1.a1', '4.m1.a1', '4.o1.b1', '4.p1.a1', '4.q1.b1', '4.r1.a1', '4.u1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052761
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.z1.a1', '6.b1.a1'], 'contains': ['24.g1.a1', '24.i1.a1', '24.j1.a1', '24.v1.a1', '24.x1.a1', '24.bc1.a1', '24.bi1.a1', '84.e1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1009, 4, 672, 338, 192], 'label': '1344.8546.12.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052762
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.ba1.a1', '6.c1.a1'], 'contains': ['24.h1.a1', '24.j1.a1', '24.k1.a1', '24.y1.a1', '24.y1.b1', '24.z1.a1', '24.z1.b1', '84.g1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1009, 76, 672, 338, 192], 'label': '1344.8546.12.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052763
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.b1.a1', '6.f1.a1', '6.g1.a1'], 'contains': ['24.a1.a1', '24.i1.a1', '24.bb1.a1', '24.bd1.a1', '24.bf1.a1', '84.i1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 336, 672, 6, 192], 'label': '1344.8546.12.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052764
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.c1.a1', '6.e1.a1', '6.g1.a1'], 'contains': ['24.a1.a1', '24.k1.a1', '24.be1.a1', '24.be1.b1', '24.bh1.a1', '84.j1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 336, 672, 974, 192], 'label': '1344.8546.12.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052765
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.d1.a1', '6.e1.a1', '6.f1.a1'], 'contains': ['24.a1.a1', '24.bg1.a1', '24.bg1.b1', '84.k1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 192, 336, 730, 672], 'label': '1344.8546.12.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052766
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bb1.a1', '6.b1.a1'], 'contains': ['24.l1.a1', '24.n1.a1', '24.p1.a1', '24.v1.a1', '24.w1.a1', '24.bb1.a1', '24.bi1.a1', '84.l1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 4, 672, 338, 192], 'label': '1344.8546.12.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052767
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.b1.a1', '6.h1.a1', '6.h1.b1'], 'contains': ['24.b1.a1', '24.l1.a1', '24.o1.a1', '24.x1.a1', '24.bf1.a1', '84.m1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [3, 336, 672, 4, 192], 'label': '1344.8546.12.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052768
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.c1.a1', '6.h1.a1', '6.i1.a1'], 'contains': ['24.c1.a1', '24.m1.a1', '24.o1.a1', '24.y1.a1', '24.be1.a1', '84.n1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [77, 336, 672, 974, 192], 'label': '1344.8546.12.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052769
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.b1', '6.c1.a1', '6.h1.b1', '6.i1.b1'], 'contains': ['24.c1.b1', '24.m1.b1', '24.o1.a1', '24.y1.b1', '24.be1.b1', '84.n1.b1'], 'core': '24.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [3, 336, 672, 76, 192], 'label': '1344.8546.12.p1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.p1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.p1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052770
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bc1.a1', '6.c1.a1'], 'contains': ['24.m1.a1', '24.m1.b1', '24.p1.a1', '24.z1.a1', '24.z1.b1', '24.ba1.a1', '24.bh1.a1', '84.o1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 76, 672, 338, 192], 'label': '1344.8546.12.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052771
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '2.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['672.b1.a1', '672.f1.a1', '672.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.l1.a1', '4.m1.b1', '4.o1.a1', '4.p1.b1', '4.q1.a1', '4.r1.b1', '4.u1.a1', '6.j1.b1', '14.j1.b1'], 'core': '2.j1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [2, 448, 168, 1008, 4, 192, 672], 'label': '1344.8546.2.j1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.j1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.l1.a1', '4.m1.b1', '4.o1.a1', '4.p1.b1', '4.q1.a1', '4.r1.b1', '4.u1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.j1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.j1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052772
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '6.b1.a1', '6.i1.a1', '6.i1.b1'], 'contains': ['24.d1.a1', '24.n1.a1', '24.o1.a1', '24.bc1.a1', '24.bd1.a1', '84.p1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [5, 336, 672, 6, 192], 'label': '1344.8546.12.r1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.r1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.r1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052773
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '6.d1.a1', '6.h1.b1', '6.i1.a1'], 'contains': ['24.e1.a1', '24.o1.a1', '24.bg1.b1', '84.q1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [3, 192, 336, 168, 672], 'label': '1344.8546.12.s1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.s1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.s1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052774
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.s1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.b1', '6.d1.a1', '6.h1.a1', '6.i1.b1'], 'contains': ['24.e1.b1', '24.o1.a1', '24.bg1.a1', '84.q1.b1'], 'core': '24.e1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [169, 192, 336, 730, 672], 'label': '1344.8546.12.s1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.s1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.s1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052775
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bd1.a1', '6.b1.a1'], 'contains': ['24.q1.a1', '24.t1.a1', '24.u1.a1', '24.w1.a1', '24.x1.a1', '24.bb1.a1', '24.bc1.a1', '84.r1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 4, 672, 2, 192], 'label': '1344.8546.12.t1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.t1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.t1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052776
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '6.b1.a1', '6.j1.a1', '6.j1.b1'], 'contains': ['24.b1.a1', '24.q1.a1', '24.s1.a1', '24.v1.a1', '24.bd1.a1', '84.s1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2, 336, 672, 4, 192], 'label': '1344.8546.12.u1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.u1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.u1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052777
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '6.c1.a1', '6.j1.a1', '6.k1.a1'], 'contains': ['24.c1.a1', '24.r1.a1', '24.s1.a1', '24.z1.a1', '24.be1.b1', '84.t1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [77, 336, 672, 2, 192], 'label': '1344.8546.12.v1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.v1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.v1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052778
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.b1', '6.c1.a1', '6.j1.b1', '6.k1.b1'], 'contains': ['24.c1.b1', '24.r1.b1', '24.s1.a1', '24.z1.b1', '24.be1.a1', '84.t1.b1'], 'core': '24.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2, 336, 672, 76, 192], 'label': '1344.8546.12.v1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.v1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.v1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052779
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.be1.a1', '6.c1.a1'], 'contains': ['24.r1.a1', '24.r1.b1', '24.t1.a1', '24.y1.a1', '24.y1.b1', '24.ba1.a1', '24.bh1.a1', '84.u1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 76, 672, 2, 192], 'label': '1344.8546.12.w1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.w1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.w1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052780
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1', '6.b1.a1', '6.k1.a1', '6.k1.b1'], 'contains': ['24.d1.a1', '24.s1.a1', '24.u1.a1', '24.bf1.a1', '24.bi1.a1', '84.v1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [5, 336, 672, 2, 192], 'label': '1344.8546.12.x1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.x1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052781
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.o1.a1', '6.d1.a1', '6.j1.b1', '6.k1.a1'], 'contains': ['24.e1.a1', '24.s1.a1', '24.bg1.a1', '84.w1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2, 192, 336, 168, 672], 'label': '1344.8546.12.y1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.y1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.y1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052782
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '2.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['672.e1.a1', '672.f1.b1', '672.g1.a1', '672.b1.a1', '672.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.m1.a1', '4.n1.a1', '4.o1.a1', '4.s1.a1', '4.t1.a1', '4.v1.b1', '4.w1.b1', '6.k1.a1', '14.k1.a1'], 'core': '2.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [5, 448, 168, 336, 2, 192, 672], 'label': '1344.8546.2.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.k1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.m1.a1', '4.n1.a1', '4.o1.a1', '4.s1.a1', '4.t1.a1', '4.v1.b1', '4.w1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052783
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.o1.b1', '6.d1.a1', '6.j1.a1', '6.k1.b1'], 'contains': ['24.e1.b1', '24.s1.a1', '24.bg1.b1', '84.w1.b1'], 'core': '24.e1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [169, 192, 336, 2, 672], 'label': '1344.8546.12.y1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.o1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.y1.b1', 'projective_image': None, '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': None}
  • id: 74052784
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '6.e1.a1', '6.h1.a1', '6.j1.b1'], 'contains': ['24.b1.a1', '24.be1.a1', '24.bg1.a1', '84.y1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [730, 336, 672, 4, 192], 'label': '1344.8546.12.z1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.z1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.z1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052785
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.b1', '6.e1.a1', '6.h1.b1', '6.j1.a1'], 'contains': ['24.b1.a1', '24.be1.b1', '24.bg1.b1', '84.y1.b1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [731, 336, 672, 4, 192], 'label': '1344.8546.12.z1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.z1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.z1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052786
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.r1.a1', '6.f1.a1', '6.i1.a1', '6.j1.a1'], 'contains': ['24.c1.a1', '24.bd1.a1', '24.bg1.b1', '84.z1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [77, 336, 672, 6, 192], 'label': '1344.8546.12.ba1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.ba1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ba1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052787
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.r1.b1', '6.f1.a1', '6.i1.b1', '6.j1.b1'], 'contains': ['24.c1.b1', '24.bd1.a1', '24.bg1.a1', '84.z1.b1'], 'core': '24.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [730, 336, 672, 76, 192], 'label': '1344.8546.12.ba1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.r1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.ba1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ba1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052788
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1', '6.f1.a1', '6.h1.a1', '6.k1.a1'], 'contains': ['24.c1.a1', '24.bf1.a1', '24.bg1.a1', '84.bb1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [77, 336, 672, 730, 192], 'label': '1344.8546.12.bb1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052789
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.t1.b1', '6.f1.a1', '6.h1.b1', '6.k1.b1'], 'contains': ['24.c1.b1', '24.bf1.a1', '24.bg1.b1', '84.bb1.b1'], 'core': '24.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [731, 336, 672, 76, 192], 'label': '1344.8546.12.bb1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.t1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bb1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bb1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052790
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.u1.a1', '6.g1.a1', '6.i1.a1', '6.j1.b1'], 'contains': ['24.e1.a1', '24.bd1.a1', '24.be1.a1', '84.bc1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6, 336, 672, 168, 192], 'label': '1344.8546.12.bc1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052791
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.u1.b1', '6.g1.a1', '6.i1.b1', '6.j1.a1'], 'contains': ['24.e1.b1', '24.bd1.a1', '24.be1.b1', '84.bc1.b1'], 'core': '24.e1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [169, 336, 672, 6, 192], 'label': '1344.8546.12.bc1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.u1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bc1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bc1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052792
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.v1.a1', '6.e1.a1', '6.i1.a1', '6.k1.b1'], 'contains': ['24.d1.a1', '24.be1.a1', '24.bg1.b1', '84.bd1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [5, 1008, 672, 974, 192], 'label': '1344.8546.12.bd1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052793
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '2.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['672.e1.a1', '672.g1.a1', '672.b1.a1', '672.f1.a1', '672.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.m1.b1', '4.n1.a1', '4.o1.b1', '4.s1.b1', '4.t1.b1', '4.v1.a1', '4.w1.a1', '6.k1.b1', '14.k1.b1'], 'core': '2.k1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 448, 76, 336, 2, 192, 672], 'label': '1344.8546.2.k1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.k1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.m1.b1', '4.n1.a1', '4.o1.b1', '4.s1.b1', '4.t1.b1', '4.v1.a1', '4.w1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.k1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.k1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052794
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.v1.b1', '6.e1.a1', '6.i1.b1', '6.k1.a1'], 'contains': ['24.d1.a1', '24.be1.b1', '24.bg1.a1', '84.bd1.b1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [5, 1008, 672, 730, 192], 'label': '1344.8546.12.bd1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.v1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bd1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bd1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052795
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.w1.a1', '6.g1.a1', '6.h1.a1', '6.k1.b1'], 'contains': ['24.e1.b1', '24.be1.a1', '24.bf1.a1', '84.be1.a1'], 'core': '24.e1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [169, 336, 672, 974, 192], 'label': '1344.8546.12.be1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.be1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.be1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052796
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '12.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.w1.b1', '6.g1.a1', '6.h1.b1', '6.k1.a1'], 'contains': ['24.e1.a1', '24.be1.b1', '24.bf1.a1', '84.be1.b1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7, 1008, 672, 168, 192], 'label': '1344.8546.12.be1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.be1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.be1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052797
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '14.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1.a1', 'complements': ['96.e1.a1', '96.f1.b1', '96.g1.a1', '96.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '7.a1.a1'], 'contains': ['28.a1.a1', '28.b1.a1', '28.c1.a1', '28.d1.a1', '28.d1.b1', '28.e1.a1', '28.e1.b1', '42.c1.a1'], 'core': '14.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 448, 672, 2, 168, 336], 'label': '1344.8546.14.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '14.a1.a1', 'normal_contained_in': ['2.c1.a1'], 'normal_contains': ['28.a1.a1', '28.b1.a1', '28.c1.a1', '28.d1.a1', '28.d1.b1', '28.e1.a1', '28.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '14.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052798
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '14.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '7.a1.a1'], 'contains': ['28.a1.a1', '28.f1.a1', '28.h1.a1', '28.i1.a1', '28.l1.a1', '28.n1.a1', '28.o1.a1', '28.r1.a1', '28.s1.a1', '28.t1.a1', '28.w1.a1', '42.a1.a1'], 'core': '28.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 448, 672, 2, 4, 336], 'label': '1344.8546.14.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052799
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '14.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '7.a1.a1'], 'contains': ['28.a1.a1', '28.g1.a1', '28.j1.a1', '28.k1.a1', '28.m1.a1', '28.p1.a1', '28.p1.b1', '28.q1.a1', '28.u1.a1', '28.u1.b1', '28.v1.a1', '42.b1.a1'], 'core': '28.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 448, 672, 2, 76, 336], 'label': '1344.8546.14.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052800
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '14.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '224.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '7.a1.a1'], 'contains': ['28.b1.a1', '28.i1.a1', '28.k1.a1', '28.x1.a1', '28.x1.b1', '28.ba1.a1', '28.ba1.b1', '42.d1.a1'], 'core': '28.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 672, 1008, 4, 168, 448], 'label': '1344.8546.14.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052801
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '14.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '7.a1.a1'], 'contains': ['28.c1.a1', '28.i1.a1', '28.m1.a1', '28.y1.a1', '28.y1.b1', '28.bd1.a1', '28.bd1.b1', '42.e1.a1'], 'core': '28.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 448, 672, 730, 4, 336], 'label': '1344.8546.14.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052802
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '14.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '7.a1.a1'], 'contains': ['28.c1.a1', '28.k1.a1', '28.l1.a1', '28.z1.a1', '28.z1.b1', '28.bb1.a1', '28.bb1.b1', '42.f1.a1'], 'core': '28.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 448, 672, 730, 76, 336], 'label': '1344.8546.14.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052803
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '14.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '7.a1.a1'], 'contains': ['28.b1.a1', '28.l1.a1', '28.m1.a1', '28.bc1.a1', '28.bc1.b1', '28.be1.a1', '28.be1.b1', '42.g1.a1'], 'core': '28.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 448, 672, 6, 168, 336], 'label': '1344.8546.14.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052804
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.c1.a1', '6.d1.a1', '6.e1.a1', '6.f1.a1', '6.g1.a1', '6.h1.a1', '6.h1.b1', '6.i1.a1', '6.i1.b1', '6.j1.a1', '6.j1.b1', '6.k1.a1', '6.k1.b1', '21.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 672, 4, 168, 2, 192, 1008], 'label': '1344.8546.3.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '3.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052805
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '14.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.h1.a1', '7.a1.a1'], 'contains': ['28.d1.b1', '28.o1.a1', '28.p1.a1', '28.x1.a1', '28.y1.a1', '28.bb1.a1', '28.be1.a1', '42.h1.a1'], 'core': '28.d1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [169, 448, 672, 730, 4, 336], 'label': '1344.8546.14.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052806
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '14.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.h1.b1', '7.a1.a1'], 'contains': ['28.d1.a1', '28.o1.a1', '28.p1.b1', '28.x1.b1', '28.y1.b1', '28.bb1.b1', '28.be1.b1', '42.h1.b1'], 'core': '28.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [3, 448, 672, 4, 168, 1008], 'label': '1344.8546.14.h1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.h1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.h1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052807
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '14.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.i1.a1', '7.a1.a1'], 'contains': ['28.d1.a1', '28.p1.a1', '28.r1.a1', '28.z1.a1', '28.ba1.a1', '28.bc1.a1', '28.bd1.a1', '42.i1.a1'], 'core': '28.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [5, 448, 672, 6, 168, 336], 'label': '1344.8546.14.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052808
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '14.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.i1.b1', '7.a1.a1'], 'contains': ['28.d1.b1', '28.p1.b1', '28.r1.a1', '28.z1.b1', '28.ba1.b1', '28.bc1.b1', '28.bd1.b1', '42.i1.b1'], 'core': '28.d1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [169, 448, 672, 730, 76, 336], 'label': '1344.8546.14.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052809
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '14.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.j1.a1', '7.a1.a1'], 'contains': ['28.e1.b1', '28.t1.a1', '28.u1.a1', '28.x1.a1', '28.y1.b1', '28.z1.a1', '28.bc1.b1', '42.j1.a1'], 'core': '28.e1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [169, 448, 672, 2, 4, 336], 'label': '1344.8546.14.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052810
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '14.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.j1.b1', '7.a1.a1'], 'contains': ['28.e1.a1', '28.t1.a1', '28.u1.b1', '28.x1.b1', '28.y1.a1', '28.z1.b1', '28.bc1.a1', '42.j1.b1'], 'core': '28.e1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [2, 448, 672, 4, 168, 1008], 'label': '1344.8546.14.j1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.j1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.j1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052811
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '14.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.k1.a1', '7.a1.a1'], 'contains': ['28.e1.a1', '28.u1.a1', '28.w1.a1', '28.ba1.a1', '28.bb1.a1', '28.bd1.b1', '28.be1.b1', '42.k1.a1'], 'core': '28.e1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [5, 448, 672, 2, 168, 336], 'label': '1344.8546.14.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052812
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '14.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.k1.b1', '7.a1.a1'], 'contains': ['28.e1.b1', '28.u1.b1', '28.w1.a1', '28.ba1.b1', '28.bb1.b1', '28.bd1.a1', '28.be1.a1', '42.k1.b1'], 'core': '28.e1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [169, 448, 672, 2, 76, 336], 'label': '1344.8546.14.k1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.k1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.k1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.k1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052813
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.p1.a1', '8.q1.a1', '8.r1.a1', '8.s1.a1'], 'contains': ['32.a1.a1', '32.b1.a1', '48.a1.a1', '112.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1009, 448, 192, 672], 'label': '1344.8546.16.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1'], 'normal_contains': ['32.a1.a1', '48.a1.a1', '112.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052814
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.d1.a1', '8.e1.a1', '8.t1.a1', '8.u1.a1', '8.u1.b1', '8.v1.a1'], 'contains': ['32.a1.a1', '32.c1.a1', '48.d1.a1', '112.b1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1011, 192, 448, 672], 'label': '1344.8546.16.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1', '8.e1.a1', '8.d1.a1'], 'normal_contains': ['32.a1.a1', '112.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052834
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '16.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.w1.a1'], 'contains': ['32.d1.a1', '32.e1.a1', '32.g1.a1', '48.p1.a2', '112.p1.a2'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [674, 448, 192, 4], 'label': '1344.8546.16.p1.a2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bd1.a1', 'old_label': '16.p1.a2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.p1.a2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052815
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.d1.a1', '8.e1.a1', '8.f1.a1', '8.g1.a1', '12.h1.a1', '28.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 448, 336, 192, 2, 672], 'label': '1344.8546.4.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.e1.a1', '8.d1.a1', '8.g1.a1', '8.f1.a1', '28.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052816
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.f1.a1', '8.g1.a1', '8.w1.a1', '8.x1.a1', '8.x1.b1', '8.y1.a1'], 'contains': ['32.a1.a1', '32.d1.a1', '48.e1.a1', '112.c1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [2, 192, 448, 672], 'label': '1344.8546.16.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.a1.a1', '8.g1.a1', '8.f1.a1'], 'normal_contains': ['32.a1.a1', '112.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052817
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.d1.a1', '8.f1.a1', '8.h1.a1', '8.i1.a1', '8.i1.b1', '8.j1.a1', '8.k1.a1', '8.l1.a1', '8.l1.b1', '8.m1.a1', '8.n1.a1', '8.n1.b1', '8.o1.a1', '8.o1.b1'], 'contains': ['32.a1.a1', '48.b1.a1', '112.d1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [336, 192, 672, 448], 'label': '1344.8546.16.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.a1', 'normal_contained_in': ['8.b1.a1', '8.d1.a1', '8.f1.a1', '8.h1.a1', '8.i1.a1', '8.i1.b1', '8.j1.a1', '8.k1.a1', '8.m1.a1', '8.l1.a1', '8.l1.b1', '8.n1.a1', '8.n1.b1', '8.o1.a1', '8.o1.b1'], 'normal_contains': ['32.a1.a1', '48.b1.a1', '112.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052818
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.e1.a1', '8.g1.a1', '8.ba1.a1', '8.be1.a1', '8.bf1.a1', '8.bh1.a1'], 'contains': ['32.a1.a1', '48.c1.a1', '112.e1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 192, 672, 448], 'label': '1344.8546.16.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.e1.a1', 'normal_contained_in': ['8.b1.a1', '8.e1.a1', '8.g1.a1'], 'normal_contains': ['32.a1.a1', '48.c1.a1', '112.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052819
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.d1.a1', '8.g1.a1', '8.bb1.a1', '8.bc1.a1', '8.bc1.b1', '8.bg1.a1'], 'contains': ['32.a1.a1', '48.i1.a1', '112.f1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [3, 672, 448, 192], 'label': '1344.8546.16.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.f1.a1', 'normal_contained_in': ['8.c1.a1', '8.d1.a1', '8.g1.a1'], 'normal_contains': ['32.a1.a1', '112.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052820
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.e1.a1', '8.f1.a1', '8.z1.a1', '8.bd1.a1', '8.bd1.b1', '8.bi1.a1'], 'contains': ['32.a1.a1', '48.j1.a1', '112.g1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [338, 672, 448, 192], 'label': '1344.8546.16.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.g1.a1', 'normal_contained_in': ['8.c1.a1', '8.e1.a1', '8.f1.a1'], 'normal_contains': ['32.a1.a1', '112.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052821
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.p1.a1', '8.t1.a1', '8.w1.a1', '8.z1.a1', '8.ba1.a1', '8.bb1.a1'], 'contains': ['32.a1.a1', '32.e1.a1', '48.f1.a1', '112.h1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [4, 448, 192, 672], 'label': '1344.8546.16.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052822
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.q1.a1', '8.u1.a1', '8.x1.a1', '8.bc1.a1', '8.bd1.a1', '8.be1.a1'], 'contains': ['32.a1.a1', '32.f1.a1', '48.g1.a1', '112.i1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [77, 448, 192, 672], 'label': '1344.8546.16.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052823
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.b1', '8.q1.a1', '8.u1.b1', '8.x1.b1', '8.bc1.b1', '8.bd1.b1', '8.be1.a1'], 'contains': ['32.a1.a1', '32.f1.b1', '48.g1.b1', '112.i1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [76, 448, 192, 672], 'label': '1344.8546.16.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052824
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.r1.a1', '8.v1.a1', '8.w1.a1', '8.z1.a1', '8.bf1.a1', '8.bg1.a1'], 'contains': ['32.a1.a1', '32.g1.a1', '48.h1.a1', '112.j1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [6, 448, 192, 672], 'label': '1344.8546.16.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052825
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.p1.a1', '8.v1.a1', '8.y1.a1', '8.ba1.a1', '8.bg1.a1', '8.bi1.a1'], 'contains': ['32.a1.a1', '48.k1.a1', '112.k1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [5, 672, 192, 448], 'label': '1344.8546.16.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052826
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.b1.a1', '8.h1.a1', '8.k1.a1', '8.p1.a1', '8.ba1.a1', '12.a1.a1', '28.i1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 192, 336, 448, 4, 672], 'label': '1344.8546.4.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.b1.a1', '8.h1.a1', '8.k1.a1', '12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052827
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '8.s1.a1', '8.u1.a1', '8.x1.b1', '8.bc1.a1', '8.bd1.b1', '8.bh1.a1'], 'contains': ['32.a1.a1', '48.l1.a1', '112.l1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [974, 448, 192, 672], 'label': '1344.8546.16.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052828
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.b1', '8.s1.a1', '8.u1.b1', '8.x1.a1', '8.bc1.b1', '8.bd1.a1', '8.bh1.a1'], 'contains': ['32.a1.a1', '48.l1.b1', '112.l1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [975, 448, 192, 672], 'label': '1344.8546.16.l1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.l1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052829
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '8.r1.a1', '8.t1.a1', '8.y1.a1', '8.bb1.a1', '8.bf1.a1', '8.bi1.a1'], 'contains': ['32.a1.a1', '48.m1.a1', '112.m1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [7, 448, 192, 672], 'label': '1344.8546.16.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052830
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '16.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1'], 'contains': ['32.b1.a1', '32.c1.a1', '32.d1.a1', '48.n1.a1', '112.n1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [1009, 192, 448, 2], 'label': '1344.8546.16.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052831
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '16.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1'], 'contains': ['32.b1.a1', '32.f1.a1', '32.f1.b1', '48.o1.a1', '112.o1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [337, 448, 192, 76], 'label': '1344.8546.16.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.ba1.a1', 'old_label': '16.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052832
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '16.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1'], 'contains': ['32.b1.a1', '32.f1.a1', '32.f1.b1', '48.o1.a2', '112.o1.a2'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [1009, 448, 192, 76], 'label': '1344.8546.16.o1.a2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.ba1.a1', 'old_label': '16.o1.a2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.o1.a2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052833
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '16.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.w1.a1'], 'contains': ['32.d1.a1', '32.e1.a1', '32.g1.a1', '48.p1.a1', '112.p1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [2, 448, 192, 4], 'label': '1344.8546.16.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bd1.a1', 'old_label': '16.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052835
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '21.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '7.a1.a1'], 'contains': ['42.a1.a1', '42.b1.a1', '42.c1.a1', '42.d1.a1', '42.e1.a1', '42.f1.a1', '42.g1.a1', '42.h1.a1', '42.h1.b1', '42.i1.a1', '42.i1.b1', '42.j1.a1', '42.j1.b1', '42.k1.a1', '42.k1.b1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [1, 2, 4, 168], 'label': '1344.8546.21.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '21.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '21.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052836
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1', '12.h1.a1', '12.k1.a1', '12.l1.a1', '12.m1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.c1.a1', '168.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 192, 672, 336], 'label': '1344.8546.24.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.b1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1'], 'normal_contains': ['48.a1.a1', '48.c1.a1', '48.b1.a1', '168.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052837
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '2.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': ['672.f1.b1', '672.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.d1.a1', '4.h1.a1', '4.j1.a1', '4.l1.a1', '4.n1.a1', '4.x1.a1', '4.z1.a1', '4.bb1.a1', '4.bd1.a1', '6.b1.a1', '14.b1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 448, 4, 336, 2, 192, 672], 'label': '1344.8546.2.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.d1.a1', '4.h1.a1', '4.j1.a1', '4.l1.a1', '4.n1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052838
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': ['336.p1.a1', '336.p1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'contains': ['8.b1.a1', '8.i1.a1', '8.i1.b1', '8.q1.a1', '8.be1.a1', '12.b1.a1', '28.k1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 192, 336, 448, 76, 672], 'label': '1344.8546.4.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'normal_contains': ['8.b1.a1', '8.i1.a1', '8.i1.b1', '12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052839
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.a1.a1', '12.d1.a1', '12.d1.b1', '12.o1.a1', '12.u1.a1', '12.z1.a1', '12.z1.b1'], 'contains': ['48.b1.a1', '48.f1.a1', '168.v1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [4, 672, 192, 336], 'label': '1344.8546.24.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.h1.a1', '12.a1.a1', '12.d1.a1', '12.d1.b1'], 'normal_contains': ['48.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052840
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '12.b1.a1', '12.d1.a1', '12.e1.a1', '12.p1.a1', '12.v1.a1', '12.ba1.a1', '12.bb1.a1'], 'contains': ['48.b1.a1', '48.g1.a1', '168.y1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [77, 672, 192, 336], 'label': '1344.8546.24.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1.a1', 'normal_contained_in': ['8.i1.a1', '12.b1.a1', '12.d1.a1', '12.e1.a1'], 'normal_contains': ['48.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052841
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.i1.b1', '12.b1.a1', '12.d1.b1', '12.e1.b1', '12.p1.b1', '12.v1.b1', '12.ba1.b1', '12.bb1.b1'], 'contains': ['48.b1.a1', '48.g1.b1', '168.y1.b1'], 'core': '24.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [76, 672, 192, 336], 'label': '1344.8546.24.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1.b1', 'normal_contained_in': ['8.i1.b1', '12.b1.a1', '12.d1.b1', '12.e1.b1'], 'normal_contains': ['48.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052842
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '12.a1.a1', '12.e1.a1', '12.e1.b1', '12.r1.a1', '12.x1.a1', '12.bd1.a1', '12.bd1.b1'], 'contains': ['48.b1.a1', '48.k1.a1', '168.bd1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [5, 672, 192, 336], 'label': '1344.8546.24.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1.a1', 'normal_contained_in': ['8.k1.a1', '12.a1.a1', '12.e1.a1', '12.e1.b1'], 'normal_contains': ['48.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052843
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.k1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '12.c1.a1', '12.d1.b1', '12.e1.a1', '12.s1.a1', '12.y1.a1', '12.bc1.a1', '12.be1.b1'], 'contains': ['48.b1.a1', '168.b1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [168, 336, 672, 192], 'label': '1344.8546.24.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.e1.a1', 'normal_contained_in': ['8.n1.a1', '12.c1.a1', '12.d1.b1', '12.e1.a1'], 'normal_contains': ['48.b1.a1', '168.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052844
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.k1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.n1.b1', '12.c1.a1', '12.d1.a1', '12.e1.b1', '12.s1.b1', '12.y1.b1', '12.bc1.b1', '12.be1.a1'], 'contains': ['48.b1.a1', '168.b1.b1'], 'core': '24.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 336, 672, 192], 'label': '1344.8546.24.e1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.e1.b1', 'normal_contained_in': ['8.n1.b1', '12.c1.a1', '12.d1.a1', '12.e1.b1'], 'normal_contains': ['48.b1.a1', '168.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.e1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052845
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.f1.a1', '12.g1.a1', '12.h1.a1'], 'contains': ['48.a1.a1', '48.d1.a1', '48.e1.a1', '48.n1.a1', '168.c1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1009, 672, 192, 2], 'label': '1344.8546.24.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052846
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '12.a1.a1', '12.f1.a1', '12.i1.a1'], 'contains': ['48.a1.a1', '48.f1.a1', '48.k1.a1', '168.d1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1009, 672, 192, 4], 'label': '1344.8546.24.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052847
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '12.b1.a1', '12.g1.a1', '12.j1.a1'], 'contains': ['48.a1.a1', '48.g1.a1', '48.g1.b1', '48.o1.a1', '48.o1.a2', '168.e1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1009, 672, 192, 76], 'label': '1344.8546.24.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052848
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.r1.a1', '12.f1.a1', '12.i1.a1', '12.k1.a1'], 'contains': ['48.a1.a1', '48.h1.a1', '48.m1.a1', '168.f1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1009, 672, 192, 6], 'label': '1344.8546.24.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052849
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.j1.a1', '8.m1.a1', '8.r1.a1', '8.bf1.a1', '12.k1.a1', '28.l1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 192, 336, 672, 6, 448], 'label': '1344.8546.4.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1', '8.j1.a1', '8.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052850
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.h1.a1', '12.i1.a1', '12.j1.a1'], 'contains': ['48.a1.a1', '48.i1.a1', '48.j1.a1', '168.g1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1009, 192, 672, 338], 'label': '1344.8546.24.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052851
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.a1', '12.g1.a1', '12.j1.a1', '12.l1.a1'], 'contains': ['48.a1.a1', '48.l1.a1', '48.l1.b1', '168.h1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1009, 672, 192, 974], 'label': '1344.8546.24.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052852
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.t1.a1', '12.f1.a1', '12.n1.a1', '12.o1.a1'], 'contains': ['48.d1.a1', '48.f1.a1', '48.m1.a1', '168.i1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1011, 672, 192, 4], 'label': '1344.8546.24.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052853
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.u1.a1', '12.g1.a1', '12.p1.a1', '12.q1.a1'], 'contains': ['48.d1.a1', '48.g1.a1', '48.l1.a1', '168.j1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [125, 672, 192, 974], 'label': '1344.8546.24.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052854
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.u1.b1', '12.g1.a1', '12.p1.b1', '12.q1.a1'], 'contains': ['48.d1.a1', '48.g1.b1', '48.l1.b1', '168.j1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1011, 672, 192, 76], 'label': '1344.8546.24.m1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.m1.b1', 'projective_image': None, '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': None}
  • id: 74052855
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1.a1', '12.f1.a1', '12.n1.a1', '12.r1.a1'], 'contains': ['48.d1.a1', '48.h1.a1', '48.k1.a1', '168.k1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53, 672, 192, 6], 'label': '1344.8546.24.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052856
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.h1.a1', '12.o1.a1', '12.p1.a1', '12.p1.b1', '12.r1.a1', '12.s1.a1', '12.s1.b1'], 'contains': ['48.b1.a1', '48.d1.a1', '48.i1.a1', '168.l1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [3, 192, 672, 336], 'label': '1344.8546.24.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052857
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.h1.a1', '12.n1.a1', '12.q1.a1'], 'contains': ['48.c1.a1', '48.d1.a1', '48.j1.a1', '168.m1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 192, 672, 338], 'label': '1344.8546.24.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052858
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.w1.a1', '12.f1.a1', '12.t1.a1', '12.u1.a1'], 'contains': ['48.e1.a1', '48.f1.a1', '48.h1.a1', '48.p1.a1', '48.p1.a2', '168.n1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [2, 672, 192, 4], 'label': '1344.8546.24.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052859
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.x1.a1', '12.g1.a1', '12.v1.a1', '12.w1.a1'], 'contains': ['48.e1.a1', '48.g1.a1', '48.l1.b1', '168.o1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [77, 672, 192, 2], 'label': '1344.8546.24.r1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.r1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052860
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': ['336.p1.a1', '336.p1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.l1.a1', '8.l1.b1', '8.s1.a1', '8.bh1.a1', '12.l1.a1', '28.m1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 192, 336, 672, 974, 448], 'label': '1344.8546.4.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1', '8.l1.a1', '8.l1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052861
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.x1.b1', '12.g1.a1', '12.v1.b1', '12.w1.a1'], 'contains': ['48.e1.a1', '48.g1.b1', '48.l1.a1', '168.o1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [2, 672, 192, 76], 'label': '1344.8546.24.r1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.r1.b1', 'projective_image': None, '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': None}
  • id: 74052862
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.h1.a1', '12.u1.a1', '12.v1.a1', '12.v1.b1', '12.x1.a1', '12.y1.a1', '12.y1.b1'], 'contains': ['48.b1.a1', '48.e1.a1', '48.j1.a1', '168.p1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2, 192, 672, 336], 'label': '1344.8546.24.s1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.s1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.s1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052863
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '12.h1.a1', '12.t1.a1', '12.w1.a1'], 'contains': ['48.c1.a1', '48.e1.a1', '48.i1.a1', '168.q1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 192, 672, 2], 'label': '1344.8546.24.t1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.t1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.t1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052864
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.y1.a1', '12.f1.a1', '12.t1.a1', '12.x1.a1'], 'contains': ['48.e1.a1', '48.k1.a1', '48.m1.a1', '168.r1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [5, 672, 192, 2], 'label': '1344.8546.24.u1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.u1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.u1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052865
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.z1.a1', '12.i1.a1', '12.n1.a1', '12.u1.a1'], 'contains': ['48.f1.a1', '48.h1.a1', '48.j1.a1', '168.s1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [338, 672, 192, 4], 'label': '1344.8546.24.v1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.v1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.v1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052866
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ba1.a1', '12.a1.a1', '12.n1.a1', '12.t1.a1'], 'contains': ['48.c1.a1', '48.f1.a1', '48.k1.a1', '168.t1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 672, 192, 4], 'label': '1344.8546.24.w1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.w1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.w1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052867
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bb1.a1', '12.i1.a1', '12.o1.a1', '12.t1.a1'], 'contains': ['48.f1.a1', '48.i1.a1', '48.m1.a1', '168.u1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [3, 672, 192, 4], 'label': '1344.8546.24.x1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.x1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.x1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052868
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bc1.a1', '12.j1.a1', '12.p1.a1', '12.w1.a1'], 'contains': ['48.g1.a1', '48.i1.a1', '48.l1.a1', '168.w1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [77, 672, 192, 974], 'label': '1344.8546.24.y1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.y1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.y1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052869
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bc1.b1', '12.j1.a1', '12.p1.b1', '12.w1.a1'], 'contains': ['48.g1.b1', '48.i1.a1', '48.l1.b1', '168.w1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [3, 672, 192, 76], 'label': '1344.8546.24.y1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.y1.b1', 'projective_image': None, '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': None}
  • id: 74052870
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.a1', '12.j1.a1', '12.q1.a1', '12.v1.a1'], 'contains': ['48.g1.a1', '48.j1.a1', '48.l1.b1', '168.x1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [77, 672, 192, 338], 'label': '1344.8546.24.z1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.z1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.z1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052871
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1.a1', 'complements': ['336.p1.a1', '336.p1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.n1.a1', '8.n1.b1', '12.c1.a1', '28.b1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 672, 448, 192, 168, 336], 'label': '1344.8546.4.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1', '8.n1.a1', '8.n1.b1', '12.c1.a1', '28.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052872
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.b1', '12.j1.a1', '12.q1.a1', '12.v1.b1'], 'contains': ['48.g1.b1', '48.j1.a1', '48.l1.a1', '168.x1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [338, 672, 192, 76], 'label': '1344.8546.24.z1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.z1.b1', 'projective_image': None, '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': None}
  • id: 74052873
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.be1.a1', '12.b1.a1', '12.q1.a1', '12.w1.a1'], 'contains': ['48.c1.a1', '48.g1.a1', '48.g1.b1', '168.z1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 672, 192, 76], 'label': '1344.8546.24.ba1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.ba1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ba1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052874
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bf1.a1', '12.k1.a1', '12.n1.a1', '12.t1.a1'], 'contains': ['48.c1.a1', '48.h1.a1', '48.m1.a1', '168.ba1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 672, 192, 6], 'label': '1344.8546.24.bb1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.bb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052875
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bg1.a1', '12.i1.a1', '12.r1.a1', '12.t1.a1'], 'contains': ['48.h1.a1', '48.i1.a1', '48.k1.a1', '168.bb1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [5, 672, 192, 6], 'label': '1344.8546.24.bc1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.bc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052876
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '12.k1.a1', '12.r1.a1', '12.u1.a1', '12.ba1.a1', '12.ba1.b1', '12.bc1.a1', '12.bc1.b1'], 'contains': ['48.b1.a1', '48.h1.a1', '168.bc1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6, 672, 192, 336], 'label': '1344.8546.24.bd1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052877
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '12.l1.a1', '12.p1.a1', '12.v1.b1', '12.z1.a1', '12.bc1.a1', '12.bd1.a1', '12.be1.a1'], 'contains': ['48.b1.a1', '48.l1.a1', '168.be1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [974, 672, 192, 336], 'label': '1344.8546.24.be1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.be1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.be1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052878
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.b1', '12.l1.a1', '12.p1.b1', '12.v1.a1', '12.z1.b1', '12.bc1.b1', '12.bd1.b1', '12.be1.b1'], 'contains': ['48.b1.a1', '48.l1.b1', '168.be1.b1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [975, 672, 192, 336], 'label': '1344.8546.24.be1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.be1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.be1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052879
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '12.k1.a1', '12.o1.a1', '12.x1.a1', '12.bb1.a1', '12.bb1.b1', '12.be1.a1', '12.be1.b1'], 'contains': ['48.b1.a1', '48.m1.a1', '168.bf1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7, 672, 192, 336], 'label': '1344.8546.24.bf1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bf1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bf1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052880
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.s1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '12.m1.a1', '12.s1.b1', '12.y1.a1', '12.z1.a1', '12.ba1.b1', '12.bb1.a1', '12.bd1.b1'], 'contains': ['48.b1.a1', '168.bg1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [730, 336, 672, 192], 'label': '1344.8546.24.bg1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bg1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bg1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052881
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.b1', '12.m1.a1', '12.s1.a1', '12.y1.b1', '12.z1.b1', '12.ba1.a1', '12.bb1.b1', '12.bd1.a1'], 'contains': ['48.b1.a1', '168.bg1.b1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [731, 336, 672, 192], 'label': '1344.8546.24.bg1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.o1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bg1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bg1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052882
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1.a1', 'complements': ['336.p1.a1', '336.p1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'contains': ['8.b1.a1', '8.o1.a1', '8.o1.b1', '12.m1.a1', '28.c1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 448, 192, 336, 730, 672], 'label': '1344.8546.4.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'normal_contains': ['8.b1.a1', '8.o1.a1', '8.o1.b1', '28.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052883
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bh1.a1', '12.l1.a1', '12.q1.a1', '12.w1.a1'], 'contains': ['48.c1.a1', '48.l1.a1', '48.l1.b1', '168.bh1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 672, 192, 974], 'label': '1344.8546.24.bh1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.bh1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bh1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052884
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '24.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bi1.a1', '12.i1.a1', '12.n1.a1', '12.x1.a1'], 'contains': ['48.j1.a1', '48.k1.a1', '48.m1.a1', '168.bi1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [5, 672, 192, 338], 'label': '1344.8546.24.bi1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.bi1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bi1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052885
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '14.a1.a1', '14.b1.a1', '14.c1.a1'], 'contains': ['56.a1.a1', '56.b1.a1', '56.c1.a1', '56.d1.a1', '56.e1.a1', '56.f1.a1', '56.g1.a1', '84.d1.a1'], 'core': '28.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 448, 2, 336, 672], 'label': '1344.8546.28.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.a1.a1', 'normal_contained_in': ['4.a1.a1', '14.a1.a1'], 'normal_contains': ['56.a1.a1', '56.b1.a1', '56.c1.a1', '56.e1.a1', '56.d1.a1', '56.g1.a1', '56.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '28.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052886
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1.a1', 'complements': ['48.p1.a1', '48.p1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '14.a1.a1', '14.d1.a1', '14.g1.a1'], 'contains': ['56.b1.a1', '56.h1.a1', '56.h1.b1', '84.a1.a1'], 'core': '28.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 672, 168, 448, 336], 'label': '1344.8546.28.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.b1.a1', 'normal_contained_in': ['4.f1.a1', '14.a1.a1'], 'normal_contains': ['56.b1.a1', '56.h1.a1', '56.h1.b1', '84.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '28.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052887
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1.a1', 'complements': ['48.p1.a1', '48.p1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '14.a1.a1', '14.e1.a1', '14.f1.a1'], 'contains': ['56.b1.a1', '56.i1.a1', '56.i1.b1', '84.k1.a1'], 'core': '28.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 448, 730, 336, 672], 'label': '1344.8546.28.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.c1.a1', 'normal_contained_in': ['4.g1.a1', '14.a1.a1'], 'normal_contains': ['56.b1.a1', '56.i1.a1', '56.i1.b1'], 'normalizer': '1.a1.a1', 'old_label': '28.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052888
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1.a1', 'complements': ['48.p1.a1', '48.p1.a2', '48.o1.a1', '48.o1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '14.a1.a1', '14.h1.b1', '14.i1.a1'], 'contains': ['56.d1.a1', '56.h1.a1', '56.i1.b1', '84.q1.a1'], 'core': '28.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [3, 448, 168, 336, 672], 'label': '1344.8546.28.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.d1.a1', 'normal_contained_in': ['4.k1.a1', '14.a1.a1'], 'normal_contains': ['56.d1.a1', '56.h1.a1', '56.i1.b1'], 'normalizer': '1.a1.a1', 'old_label': '28.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052889
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1.b1', 'complements': ['48.p1.a1', '48.p1.a2', '48.o1.a2', '48.o1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.k1.b1', '14.a1.a1', '14.h1.a1', '14.i1.b1'], 'contains': ['56.d1.a1', '56.h1.b1', '56.i1.a1', '84.q1.b1'], 'core': '28.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 448, 730, 336, 672], 'label': '1344.8546.28.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.d1.b1', 'normal_contained_in': ['4.k1.b1', '14.a1.a1'], 'normal_contains': ['56.d1.a1', '56.h1.b1', '56.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '28.d1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.d1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052890
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1.a1', 'complements': ['48.o1.a1', '48.o1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['4.o1.a1', '14.a1.a1', '14.j1.b1', '14.k1.a1'], 'contains': ['56.f1.a1', '56.h1.a1', '56.i1.a1', '84.w1.a1'], 'core': '28.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [2, 448, 168, 336, 672], 'label': '1344.8546.28.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.e1.a1', 'normal_contained_in': ['4.o1.a1', '14.a1.a1'], 'normal_contains': ['56.f1.a1', '56.h1.a1', '56.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '28.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052891
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1.a1', 'complements': ['48.o1.a2', '48.o1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.o1.b1', '14.a1.a1', '14.j1.a1', '14.k1.b1'], 'contains': ['56.f1.a1', '56.h1.b1', '56.i1.b1', '84.w1.b1'], 'core': '28.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 448, 2, 336, 672], 'label': '1344.8546.28.e1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.e1.b1', 'normal_contained_in': ['4.o1.b1', '14.a1.a1'], 'normal_contains': ['56.f1.a1', '56.h1.b1', '56.i1.b1'], 'normalizer': '1.a1.a1', 'old_label': '28.e1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.e1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052892
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.x1.a1', '14.b1.a1'], 'contains': ['56.a1.a1', '56.j1.a1', '56.l1.a1', '56.n1.a1', '56.p1.a1', '56.q1.a1', '56.s1.a1', '84.b1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1009, 448, 2, 4, 672], 'label': '1344.8546.28.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '28.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052893
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': ['336.o1.a1', '336.o1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.h1.a1', '2.h1.b1'], 'contains': ['8.d1.a1', '8.h1.a1', '8.m1.a1', '8.t1.a1', '8.bb1.a1', '12.o1.a1', '28.o1.a1'], 'core': '4.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [3, 192, 336, 672, 4, 448], 'label': '1344.8546.4.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': ['2.a1.a1', '2.h1.a1', '2.h1.b1'], 'normal_contains': ['8.d1.a1', '8.h1.a1', '8.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052894
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.y1.a1', '14.c1.a1'], 'contains': ['56.a1.a1', '56.k1.a1', '56.m1.a1', '56.o1.a1', '56.o1.b1', '56.r1.a1', '56.r1.b1', '84.c1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1009, 448, 2, 76, 672], 'label': '1344.8546.28.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '28.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052895
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.z1.a1', '14.b1.a1'], 'contains': ['56.c1.a1', '56.j1.a1', '56.l1.a1', '56.t1.a1', '56.v1.a1', '56.bc1.a1', '56.bi1.a1', '84.e1.a1'], 'core': '56.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1009, 448, 338, 4, 672], 'label': '1344.8546.28.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '28.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052896
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '14.b1.a1', '14.d1.a1', '14.e1.a1'], 'contains': ['56.b1.a1', '56.j1.a1', '56.u1.a1', '56.w1.a1', '56.be1.a1', '84.f1.a1'], 'core': '56.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 672, 4, 336, 448], 'label': '1344.8546.28.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052897
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.ba1.a1', '14.c1.a1'], 'contains': ['56.c1.a1', '56.k1.a1', '56.m1.a1', '56.x1.a1', '56.x1.b1', '56.y1.a1', '56.y1.b1', '84.g1.a1'], 'core': '56.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1009, 448, 338, 76, 672], 'label': '1344.8546.28.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '28.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052898
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '14.c1.a1', '14.d1.a1', '14.f1.a1'], 'contains': ['56.b1.a1', '56.k1.a1', '56.z1.a1', '56.z1.b1', '56.ba1.a1', '84.h1.a1'], 'core': '56.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 672, 76, 336, 448], 'label': '1344.8546.28.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052899
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '14.b1.a1', '14.f1.a1', '14.g1.a1'], 'contains': ['56.b1.a1', '56.l1.a1', '56.bb1.a1', '56.bd1.a1', '56.bg1.a1', '84.i1.a1'], 'core': '56.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 448, 6, 336, 672], 'label': '1344.8546.28.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052900
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '14.c1.a1', '14.e1.a1', '14.g1.a1'], 'contains': ['56.b1.a1', '56.m1.a1', '56.bf1.a1', '56.bf1.b1', '56.bh1.a1', '84.j1.a1'], 'core': '56.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 448, 974, 336, 672], 'label': '1344.8546.28.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052901
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bb1.a1', '14.b1.a1'], 'contains': ['56.e1.a1', '56.n1.a1', '56.p1.a1', '56.t1.a1', '56.u1.a1', '56.bb1.a1', '56.bi1.a1', '84.l1.a1'], 'core': '56.e1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1, 448, 338, 4, 672], 'label': '1344.8546.28.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '28.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052902
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '14.b1.a1', '14.h1.a1', '14.h1.b1'], 'contains': ['56.d1.a1', '56.n1.a1', '56.v1.a1', '56.w1.a1', '56.bg1.a1', '84.m1.a1'], 'core': '56.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [3, 448, 4, 336, 672], 'label': '1344.8546.28.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052903
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '14.c1.a1', '14.h1.a1', '14.i1.a1'], 'contains': ['56.d1.a1', '56.o1.a1', '56.x1.a1', '56.z1.a1', '56.bf1.a1', '84.n1.a1'], 'core': '56.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [77, 448, 974, 336, 672], 'label': '1344.8546.28.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052904
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': ['336.p1.a1', '336.p1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.h1.a1', '2.i1.a1'], 'contains': ['8.d1.a1', '8.i1.a1', '8.l1.a1', '8.u1.a1', '8.bc1.a1', '12.p1.a1', '28.p1.a1'], 'core': '4.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [77, 192, 336, 672, 974, 448], 'label': '1344.8546.4.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.a1', 'normal_contained_in': ['2.b1.a1', '2.h1.a1', '2.i1.a1'], 'normal_contains': ['8.d1.a1', '8.i1.a1', '8.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052905
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.b1', '14.c1.a1', '14.h1.b1', '14.i1.b1'], 'contains': ['56.d1.a1', '56.o1.b1', '56.x1.b1', '56.z1.b1', '56.bf1.b1', '84.n1.b1'], 'core': '56.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [3, 448, 76, 336, 672], 'label': '1344.8546.28.p1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.p1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.p1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052906
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bc1.a1', '14.c1.a1'], 'contains': ['56.e1.a1', '56.o1.a1', '56.o1.b1', '56.y1.a1', '56.y1.b1', '56.ba1.a1', '56.bh1.a1', '84.o1.a1'], 'core': '56.e1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1, 448, 338, 76, 672], 'label': '1344.8546.28.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '28.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052907
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '14.b1.a1', '14.i1.a1', '14.i1.b1'], 'contains': ['56.d1.a1', '56.p1.a1', '56.bc1.a1', '56.bd1.a1', '56.be1.a1', '84.p1.a1'], 'core': '56.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [5, 448, 6, 336, 672], 'label': '1344.8546.28.r1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.r1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.r1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052908
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bd1.a1', '14.b1.a1'], 'contains': ['56.g1.a1', '56.q1.a1', '56.s1.a1', '56.u1.a1', '56.v1.a1', '56.bb1.a1', '56.bc1.a1', '84.r1.a1'], 'core': '56.g1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1, 448, 2, 4, 672], 'label': '1344.8546.28.s1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '28.s1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.s1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052909
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '14.b1.a1', '14.j1.a1', '14.j1.b1'], 'contains': ['56.f1.a1', '56.q1.a1', '56.t1.a1', '56.w1.a1', '56.bd1.a1', '84.s1.a1'], 'core': '56.f1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [2, 448, 4, 336, 672], 'label': '1344.8546.28.t1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.t1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.t1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052910
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '14.c1.a1', '14.j1.a1', '14.k1.a1'], 'contains': ['56.f1.a1', '56.r1.a1', '56.y1.a1', '56.z1.a1', '56.bf1.b1', '84.t1.a1'], 'core': '56.f1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [77, 448, 2, 336, 672], 'label': '1344.8546.28.u1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.u1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.u1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052911
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.b1', '14.c1.a1', '14.j1.b1', '14.k1.b1'], 'contains': ['56.f1.a1', '56.r1.b1', '56.y1.b1', '56.z1.b1', '56.bf1.a1', '84.t1.b1'], 'core': '56.f1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [2, 448, 76, 336, 672], 'label': '1344.8546.28.u1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.u1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.u1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052912
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.be1.a1', '14.c1.a1'], 'contains': ['56.g1.a1', '56.r1.a1', '56.r1.b1', '56.x1.a1', '56.x1.b1', '56.ba1.a1', '56.bh1.a1', '84.u1.a1'], 'core': '56.g1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1, 448, 2, 76, 672], 'label': '1344.8546.28.v1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '28.v1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.v1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052934
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.n1.a1'], 'contains': ['64.a1.a1', '96.c1.a1', '224.c1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1011, 448, 192], 'label': '1344.8546.32.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052913
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1', '14.b1.a1', '14.k1.a1', '14.k1.b1'], 'contains': ['56.f1.a1', '56.s1.a1', '56.be1.a1', '56.bg1.a1', '56.bi1.a1', '84.v1.a1'], 'core': '56.f1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [5, 448, 2, 336, 672], 'label': '1344.8546.28.w1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.w1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.w1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052914
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '224.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.p1.a1', '14.d1.a1', '14.h1.a1', '14.j1.a1'], 'contains': ['56.h1.b1', '56.w1.a1', '56.z1.a1', '84.x1.a1'], 'core': '56.h1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [169, 672, 4, 448, 336], 'label': '1344.8546.28.x1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.x1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.x1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052915
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': ['336.p1.a1', '336.p1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.h1.b1', '2.i1.b1'], 'contains': ['8.d1.a1', '8.i1.b1', '8.l1.b1', '8.u1.b1', '8.bc1.b1', '12.p1.b1', '28.p1.b1'], 'core': '4.i1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [3, 192, 336, 672, 76, 448], 'label': '1344.8546.4.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.b1', 'normal_contained_in': ['2.b1.a1', '2.h1.b1', '2.i1.b1'], 'normal_contains': ['8.d1.a1', '8.i1.b1', '8.l1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052916
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '224.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.p1.b1', '14.d1.a1', '14.h1.b1', '14.j1.b1'], 'contains': ['56.h1.a1', '56.w1.a1', '56.z1.b1', '84.x1.b1'], 'core': '56.h1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [4, 672, 168, 448, 1008], 'label': '1344.8546.28.x1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.p1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.x1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.x1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052917
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '14.e1.a1', '14.h1.a1', '14.j1.b1'], 'contains': ['56.i1.a1', '56.w1.a1', '56.bf1.a1', '84.y1.a1'], 'core': '56.i1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [730, 448, 4, 336, 672], 'label': '1344.8546.28.y1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.y1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.y1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052918
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.b1', '14.e1.a1', '14.h1.b1', '14.j1.a1'], 'contains': ['56.i1.b1', '56.w1.a1', '56.bf1.b1', '84.y1.b1'], 'core': '56.i1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [731, 448, 4, 336, 672], 'label': '1344.8546.28.y1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.y1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.y1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052919
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.r1.a1', '14.f1.a1', '14.i1.a1', '14.j1.a1'], 'contains': ['56.i1.b1', '56.z1.a1', '56.bd1.a1', '84.z1.a1'], 'core': '56.i1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [845, 448, 6, 1008, 672], 'label': '1344.8546.28.z1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.z1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.z1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052920
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.r1.b1', '14.f1.a1', '14.i1.b1', '14.j1.b1'], 'contains': ['56.i1.a1', '56.z1.b1', '56.bd1.a1', '84.z1.b1'], 'core': '56.i1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [730, 448, 76, 336, 672], 'label': '1344.8546.28.z1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.r1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.z1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.z1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052921
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '224.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.s1.a1', '14.d1.a1', '14.i1.a1', '14.k1.a1'], 'contains': ['56.h1.a1', '56.z1.a1', '56.be1.a1', '84.ba1.a1'], 'core': '56.h1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [5, 672, 168, 448, 336], 'label': '1344.8546.28.ba1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.ba1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.ba1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052922
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '224.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.s1.b1', '14.d1.a1', '14.i1.b1', '14.k1.b1'], 'contains': ['56.h1.b1', '56.z1.b1', '56.be1.a1', '84.ba1.b1'], 'core': '56.h1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [169, 672, 76, 448, 336], 'label': '1344.8546.28.ba1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.s1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.ba1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.ba1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052923
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1', '14.f1.a1', '14.h1.a1', '14.k1.a1'], 'contains': ['56.i1.a1', '56.z1.a1', '56.bg1.a1', '84.bb1.a1'], 'core': '56.i1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [77, 448, 730, 336, 672], 'label': '1344.8546.28.bb1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.bb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.bb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052924
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.t1.b1', '14.f1.a1', '14.h1.b1', '14.k1.b1'], 'contains': ['56.i1.b1', '56.z1.b1', '56.bg1.a1', '84.bb1.b1'], 'core': '56.i1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [731, 448, 76, 336, 672], 'label': '1344.8546.28.bb1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.t1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.bb1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.bb1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052925
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.u1.a1', '14.g1.a1', '14.i1.a1', '14.j1.b1'], 'contains': ['56.h1.a1', '56.bd1.a1', '56.bf1.a1', '84.bc1.a1'], 'core': '56.h1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [6, 448, 168, 336, 672], 'label': '1344.8546.28.bc1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.bc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.bc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052926
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': ['336.o1.a1', '336.o1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.i1.a1', '2.i1.b1'], 'contains': ['8.d1.a1', '8.j1.a1', '8.k1.a1', '8.v1.a1', '8.bg1.a1', '12.r1.a1', '28.r1.a1'], 'core': '4.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [5, 192, 336, 672, 6, 448], 'label': '1344.8546.4.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.a1', 'normal_contained_in': ['2.a1.a1', '2.i1.a1', '2.i1.b1'], 'normal_contains': ['8.d1.a1', '8.j1.a1', '8.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052927
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.u1.b1', '14.g1.a1', '14.i1.b1', '14.j1.a1'], 'contains': ['56.h1.b1', '56.bd1.a1', '56.bf1.b1', '84.bc1.b1'], 'core': '56.h1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [169, 448, 6, 336, 672], 'label': '1344.8546.28.bc1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.u1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.bc1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.bc1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052928
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.v1.a1', '14.e1.a1', '14.i1.a1', '14.k1.b1'], 'contains': ['56.i1.b1', '56.be1.a1', '56.bf1.a1', '84.bd1.a1'], 'core': '56.i1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [581, 448, 974, 336, 672], 'label': '1344.8546.28.bd1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.bd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.bd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052929
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.v1.b1', '14.e1.a1', '14.i1.b1', '14.k1.a1'], 'contains': ['56.i1.a1', '56.be1.a1', '56.bf1.b1', '84.bd1.b1'], 'core': '56.i1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [5, 448, 730, 1008, 672], 'label': '1344.8546.28.bd1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.v1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.bd1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.bd1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052930
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.w1.a1', '14.g1.a1', '14.h1.a1', '14.k1.b1'], 'contains': ['56.h1.b1', '56.bf1.a1', '56.bg1.a1', '84.be1.a1'], 'core': '56.h1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [169, 448, 974, 336, 672], 'label': '1344.8546.28.be1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.be1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.be1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052931
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '28.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.w1.b1', '14.g1.a1', '14.h1.b1', '14.k1.a1'], 'contains': ['56.h1.a1', '56.bf1.b1', '56.bg1.a1', '84.be1.b1'], 'core': '56.h1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [7, 448, 168, 1008, 672], 'label': '1344.8546.28.be1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.be1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.be1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052932
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.d1.a1', '16.e1.a1', '16.f1.a1', '16.g1.a1', '16.h1.a1', '16.i1.a1', '16.i1.b1', '16.j1.a1', '16.k1.a1', '16.l1.a1', '16.l1.b1', '16.m1.a1'], 'contains': ['64.a1.a1', '96.a1.a1', '224.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [672, 192, 448], 'label': '1344.8546.32.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.e1.a1', '16.d1.a1', '16.f1.a1', '16.g1.a1'], 'normal_contains': ['64.a1.a1', '96.a1.a1', '224.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052933
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.n1.a1', '16.o1.a1', '16.o1.a2'], 'contains': ['64.a1.a1', '96.b1.a1', '224.b1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1009, 192, 448], 'label': '1344.8546.32.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052937
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1.a1', 'complements': ['336.p1.a1', '336.p1.a2', '336.o1.a1', '336.o1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.h1.b1', '2.i1.a1'], 'contains': ['8.d1.a1', '8.n1.a1', '8.o1.b1', '12.s1.a1', '28.d1.a1'], 'core': '4.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [3, 448, 192, 336, 168, 672], 'label': '1344.8546.4.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': ['2.c1.a1', '2.h1.b1', '2.i1.a1'], 'normal_contains': ['8.d1.a1', '8.n1.a1', '8.o1.b1', '28.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052938
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.o1.a1', '16.o1.a2'], 'contains': ['64.a1.a1', '96.f1.a1', '224.f1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [77, 192, 448], 'label': '1344.8546.32.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.ba1.a1', 'old_label': '32.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052939
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.b1', '16.o1.a1', '16.o1.a2'], 'contains': ['64.a1.a1', '96.f1.b1', '224.f1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [76, 192, 448], 'label': '1344.8546.32.f1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.ba1.a1', 'old_label': '32.f1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.f1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052940
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '32.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '16.p1.a1', '16.p1.a2'], 'contains': ['64.a1.a1', '96.g1.a1', '224.g1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [6, 192, 448], 'label': '1344.8546.32.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bd1.a1', 'old_label': '32.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052941
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '42.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '14.b1.a1', '21.a1.a1'], 'contains': ['84.b1.a1', '84.d1.a1', '84.e1.a1', '84.f1.a1', '84.i1.a1', '84.l1.a1', '84.m1.a1', '84.p1.a1', '84.r1.a1', '84.s1.a1', '84.v1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [1, 2, 4, 336], 'label': '1344.8546.42.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052942
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '42.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '14.c1.a1', '21.a1.a1'], 'contains': ['84.c1.a1', '84.d1.a1', '84.g1.a1', '84.h1.a1', '84.j1.a1', '84.n1.a1', '84.n1.b1', '84.o1.a1', '84.t1.a1', '84.t1.b1', '84.u1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [1, 2, 76, 336], 'label': '1344.8546.42.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052943
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '42.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '14.a1.a1', '21.a1.a1'], 'contains': ['84.a1.a1', '84.d1.a1', '84.k1.a1', '84.q1.a1', '84.q1.b1', '84.w1.a1', '84.w1.b1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 2, 168], 'label': '1344.8546.42.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '14.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '42.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052944
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '42.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '14.d1.a1', '21.a1.a1'], 'contains': ['84.a1.a1', '84.f1.a1', '84.h1.a1', '84.x1.a1', '84.x1.b1', '84.ba1.a1', '84.ba1.b1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 4, 168], 'label': '1344.8546.42.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '42.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052945
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '42.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '14.e1.a1', '21.a1.a1'], 'contains': ['84.f1.a1', '84.j1.a1', '84.k1.a1', '84.y1.a1', '84.y1.b1', '84.bd1.a1', '84.bd1.b1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [1, 730, 4], 'label': '1344.8546.42.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052946
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '42.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '14.f1.a1', '21.a1.a1'], 'contains': ['84.h1.a1', '84.i1.a1', '84.k1.a1', '84.z1.a1', '84.z1.b1', '84.bb1.a1', '84.bb1.b1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [1, 730, 76], 'label': '1344.8546.42.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052947
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '42.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '14.g1.a1', '21.a1.a1'], 'contains': ['84.a1.a1', '84.i1.a1', '84.j1.a1', '84.bc1.a1', '84.bc1.b1', '84.be1.a1', '84.be1.b1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [1, 6, 168], 'label': '1344.8546.42.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052948
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '2.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': ['672.e1.a1', '672.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '4.e1.a1', '4.i1.a1', '4.i1.b1', '4.m1.a1', '4.m1.b1', '4.y1.a1', '4.ba1.a1', '4.bc1.a1', '4.be1.a1', '6.c1.a1', '14.c1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 448, 76, 336, 2, 192, 672], 'label': '1344.8546.2.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.c1.a1', '4.e1.a1', '4.i1.a1', '4.i1.b1', '4.m1.a1', '4.m1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052949
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1.b1', 'complements': ['336.p1.a1', '336.p1.a2', '336.o1.a2', '336.o1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.h1.a1', '2.i1.b1'], 'contains': ['8.d1.a1', '8.n1.b1', '8.o1.a1', '12.s1.b1', '28.d1.b1'], 'core': '4.k1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 448, 192, 336, 730, 672], 'label': '1344.8546.4.k1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.b1', 'normal_contained_in': ['2.c1.a1', '2.h1.a1', '2.i1.b1'], 'normal_contains': ['8.d1.a1', '8.n1.b1', '8.o1.a1', '28.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.k1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.k1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052950
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '42.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '14.h1.a1', '21.a1.a1'], 'contains': ['84.m1.a1', '84.n1.a1', '84.q1.b1', '84.x1.a1', '84.y1.a1', '84.bb1.a1', '84.be1.a1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [169, 730, 4], 'label': '1344.8546.42.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052951
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '42.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.b1', '14.h1.b1', '21.a1.a1'], 'contains': ['84.m1.a1', '84.n1.b1', '84.q1.a1', '84.x1.b1', '84.y1.b1', '84.bb1.b1', '84.be1.b1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [3, 4, 168], 'label': '1344.8546.42.h1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.h1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.h1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052952
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '42.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '14.i1.a1', '21.a1.a1'], 'contains': ['84.n1.a1', '84.p1.a1', '84.q1.a1', '84.z1.a1', '84.ba1.a1', '84.bc1.a1', '84.bd1.a1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [5, 6, 168], 'label': '1344.8546.42.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052953
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '42.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.b1', '14.i1.b1', '21.a1.a1'], 'contains': ['84.n1.b1', '84.p1.a1', '84.q1.b1', '84.z1.b1', '84.ba1.b1', '84.bc1.b1', '84.bd1.b1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [169, 730, 76], 'label': '1344.8546.42.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052954
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '42.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1.a1', '14.j1.a1', '21.a1.a1'], 'contains': ['84.s1.a1', '84.t1.a1', '84.w1.b1', '84.x1.a1', '84.y1.b1', '84.z1.a1', '84.bc1.b1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [169, 2, 4], 'label': '1344.8546.42.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052955
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '42.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1.b1', '14.j1.b1', '21.a1.a1'], 'contains': ['84.s1.a1', '84.t1.b1', '84.w1.a1', '84.x1.b1', '84.y1.a1', '84.z1.b1', '84.bc1.a1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [2, 4, 168], 'label': '1344.8546.42.j1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.j1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.j1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052956
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '42.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1.a1', '14.k1.a1', '21.a1.a1'], 'contains': ['84.t1.a1', '84.v1.a1', '84.w1.a1', '84.ba1.a1', '84.bb1.a1', '84.bd1.b1', '84.be1.b1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [5, 2, 168], 'label': '1344.8546.42.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052957
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '42.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1.b1', '14.k1.b1', '21.a1.a1'], 'contains': ['84.t1.b1', '84.v1.a1', '84.w1.b1', '84.ba1.b1', '84.bb1.b1', '84.bd1.a1', '84.be1.a1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [169, 2, 76], 'label': '1344.8546.42.k1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.k1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.k1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.k1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052958
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '48.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.f1.a1', '24.g1.a1', '24.h1.a1', '24.i1.a1', '24.j1.a1', '24.k1.a1'], 'contains': ['96.a1.a1', '96.b1.a1', '336.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1009, 192, 672], 'label': '1344.8546.48.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1'], 'normal_contains': ['96.a1.a1', '336.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052959
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1', '24.c1.b1', '24.d1.a1', '24.e1.a1', '24.e1.b1', '24.o1.a1', '24.s1.a1', '24.bd1.a1', '24.be1.a1', '24.be1.b1', '24.bf1.a1', '24.bg1.a1', '24.bg1.b1'], 'contains': ['96.a1.a1', '336.b1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [336, 672, 192], 'label': '1344.8546.48.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1.a1', 'normal_contained_in': ['16.d1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1', '24.c1.b1', '24.d1.a1', '24.e1.a1', '24.e1.b1'], 'normal_contains': ['96.a1.a1', '336.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052960
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': ['336.o1.a1', '336.o1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.j1.a1', '2.j1.b1'], 'contains': ['8.f1.a1', '8.h1.a1', '8.j1.a1', '8.w1.a1', '8.z1.a1', '12.u1.a1', '28.t1.a1'], 'core': '4.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [2, 192, 336, 672, 4, 448], 'label': '1344.8546.4.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': ['2.a1.a1', '2.j1.a1', '2.j1.b1'], 'normal_contains': ['8.f1.a1', '8.h1.a1', '8.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052961
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '24.a1.a1', '24.p1.a1', '24.t1.a1', '24.w1.a1', '24.ba1.a1', '24.bb1.a1', '24.bh1.a1'], 'contains': ['96.a1.a1', '336.c1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 672, 192], 'label': '1344.8546.48.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1.a1', 'normal_contained_in': ['16.e1.a1', '24.a1.a1'], 'normal_contains': ['96.a1.a1', '336.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052962
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.f1.a1', '24.l1.a1', '24.m1.a1', '24.m1.b1', '24.n1.a1', '24.o1.a1', '24.p1.a1'], 'contains': ['96.a1.a1', '96.c1.a1', '336.d1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1011, 192, 672], 'label': '1344.8546.48.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052963
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.f1.a1', '24.q1.a1', '24.r1.a1', '24.r1.b1', '24.s1.a1', '24.t1.a1', '24.u1.a1'], 'contains': ['96.a1.a1', '96.d1.a1', '336.e1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2, 192, 672], 'label': '1344.8546.48.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052964
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '24.b1.a1', '24.g1.a1', '24.l1.a1', '24.q1.a1', '24.v1.a1', '24.w1.a1', '24.x1.a1'], 'contains': ['96.a1.a1', '96.e1.a1', '336.f1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [4, 192, 672], 'label': '1344.8546.48.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '48.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052965
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '24.c1.a1', '24.h1.a1', '24.m1.a1', '24.r1.a1', '24.y1.a1', '24.z1.a1', '24.ba1.a1'], 'contains': ['96.a1.a1', '96.f1.a1', '336.g1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [77, 192, 672], 'label': '1344.8546.48.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052966
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.b1', '24.c1.b1', '24.h1.a1', '24.m1.b1', '24.r1.b1', '24.y1.b1', '24.z1.b1', '24.ba1.a1'], 'contains': ['96.a1.a1', '96.f1.b1', '336.g1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [76, 192, 672], 'label': '1344.8546.48.g1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.g1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052967
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '24.i1.a1', '24.n1.a1', '24.q1.a1', '24.v1.a1', '24.bb1.a1', '24.bc1.a1', '24.bd1.a1'], 'contains': ['96.a1.a1', '96.g1.a1', '336.h1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6, 192, 672], 'label': '1344.8546.48.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052968
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '24.j1.a1', '24.o1.a1', '24.t1.a1', '24.x1.a1', '24.y1.a1', '24.y1.b1', '24.bc1.a1'], 'contains': ['96.a1.a1', '336.i1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [3, 672, 192], 'label': '1344.8546.48.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052969
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '24.j1.a1', '24.p1.a1', '24.s1.a1', '24.v1.a1', '24.z1.a1', '24.z1.b1', '24.bi1.a1'], 'contains': ['96.a1.a1', '336.j1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [338, 672, 192], 'label': '1344.8546.48.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052970
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '24.d1.a1', '24.g1.a1', '24.n1.a1', '24.u1.a1', '24.w1.a1', '24.bc1.a1', '24.bi1.a1'], 'contains': ['96.a1.a1', '336.k1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [5, 192, 672], 'label': '1344.8546.48.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '48.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052971
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.j1.a1', '2.k1.a1'], 'contains': ['8.f1.a1', '8.i1.a1', '8.l1.b1', '8.x1.a1', '8.bd1.a1', '12.v1.a1', '28.u1.a1'], 'core': '4.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [77, 192, 336, 672, 2, 448], 'label': '1344.8546.4.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': ['2.b1.a1', '2.j1.a1', '2.k1.a1'], 'normal_contains': ['8.f1.a1', '8.i1.a1', '8.l1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052972
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '24.k1.a1', '24.m1.a1', '24.r1.b1', '24.y1.a1', '24.z1.b1', '24.be1.a1', '24.bh1.a1'], 'contains': ['96.a1.a1', '336.l1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [974, 192, 672], 'label': '1344.8546.48.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '48.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052973
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.b1', '24.k1.a1', '24.m1.b1', '24.r1.a1', '24.y1.b1', '24.z1.a1', '24.be1.b1', '24.bh1.a1'], 'contains': ['96.a1.a1', '336.l1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [975, 192, 672], 'label': '1344.8546.48.l1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '48.l1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052974
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.a1', '24.i1.a1', '24.l1.a1', '24.u1.a1', '24.x1.a1', '24.bb1.a1', '24.bf1.a1', '24.bi1.a1'], 'contains': ['96.a1.a1', '336.m1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7, 192, 672], 'label': '1344.8546.48.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052975
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '48.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '24.f1.a1'], 'contains': ['96.b1.a1', '96.c1.a1', '96.d1.a1', '336.n1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [1009, 192, 2], 'label': '1344.8546.48.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '48.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052976
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a1', '24.h1.a1'], 'contains': ['96.b1.a1', '96.f1.a1', '96.f1.b1', '336.o1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [337, 192, 76], 'label': '1344.8546.48.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.ba1.a1', 'old_label': '48.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052980
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '28.a1.a1', '28.f1.a1', '28.g1.a1'], 'contains': ['112.a1.a1', '112.b1.a1', '112.c1.a1', '112.n1.a1', '168.c1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1009, 2, 672, 448], 'label': '1344.8546.56.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.a1.a1', 'normal_contained_in': ['8.a1.a1', '28.a1.a1'], 'normal_contains': ['112.a1.a1', '112.b1.a1', '112.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '56.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052981
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '28.a1.a1', '28.b1.a1', '28.c1.a1', '28.i1.a1', '28.k1.a1', '28.l1.a1', '28.m1.a1'], 'contains': ['112.a1.a1', '112.d1.a1', '112.e1.a1', '168.a1.a1'], 'core': '56.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 336, 448, 672], 'label': '1344.8546.56.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.b1.a1', 'normal_contained_in': ['8.b1.a1', '28.a1.a1', '28.b1.a1', '28.c1.a1'], 'normal_contains': ['112.a1.a1', '112.e1.a1', '112.d1.a1', '168.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '56.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052982
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.j1.b1', '2.k1.b1'], 'contains': ['8.f1.a1', '8.i1.b1', '8.l1.a1', '8.x1.b1', '8.bd1.b1', '12.v1.b1', '28.u1.b1'], 'core': '4.m1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [2, 192, 336, 672, 76, 448], 'label': '1344.8546.4.m1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.b1', 'normal_contained_in': ['2.b1.a1', '2.j1.b1', '2.k1.b1'], 'normal_contains': ['8.f1.a1', '8.i1.b1', '8.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.m1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.m1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052983
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '28.a1.a1', '28.h1.a1', '28.j1.a1'], 'contains': ['112.a1.a1', '112.f1.a1', '112.g1.a1', '168.g1.a1'], 'core': '56.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1009, 338, 672, 448], 'label': '1344.8546.56.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.c1.a1', 'normal_contained_in': ['8.c1.a1', '28.a1.a1'], 'normal_contains': ['112.a1.a1', '112.f1.a1', '112.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '56.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052984
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '28.a1.a1', '28.d1.a1', '28.d1.b1', '28.o1.a1', '28.p1.a1', '28.p1.b1', '28.r1.a1'], 'contains': ['112.b1.a1', '112.d1.a1', '112.f1.a1', '168.l1.a1'], 'core': '56.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [3, 336, 672, 448], 'label': '1344.8546.56.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.d1.a1', 'normal_contained_in': ['8.d1.a1', '28.a1.a1', '28.d1.a1', '28.d1.b1'], 'normal_contains': ['112.b1.a1', '112.d1.a1', '112.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '56.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052985
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '28.a1.a1', '28.n1.a1', '28.q1.a1'], 'contains': ['112.b1.a1', '112.e1.a1', '112.g1.a1', '168.m1.a1'], 'core': '56.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 338, 672, 448], 'label': '1344.8546.56.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.e1.a1', 'normal_contained_in': ['8.e1.a1', '28.a1.a1'], 'normal_contains': ['112.b1.a1', '112.e1.a1', '112.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '56.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052986
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '28.a1.a1', '28.e1.a1', '28.e1.b1', '28.t1.a1', '28.u1.a1', '28.u1.b1', '28.w1.a1'], 'contains': ['112.c1.a1', '112.d1.a1', '112.g1.a1', '168.p1.a1'], 'core': '56.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [2, 336, 672, 448], 'label': '1344.8546.56.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.f1.a1', 'normal_contained_in': ['8.f1.a1', '28.a1.a1', '28.e1.a1', '28.e1.b1'], 'normal_contains': ['112.c1.a1', '112.d1.a1', '112.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '56.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052987
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '28.a1.a1', '28.s1.a1', '28.v1.a1'], 'contains': ['112.c1.a1', '112.e1.a1', '112.f1.a1', '168.q1.a1'], 'core': '56.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 2, 672, 448], 'label': '1344.8546.56.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.g1.a1', 'normal_contained_in': ['8.g1.a1', '28.a1.a1'], 'normal_contains': ['112.c1.a1', '112.e1.a1', '112.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '56.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052988
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.n1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '28.b1.a1', '28.d1.a1', '28.e1.a1', '28.x1.b1', '28.ba1.a1', '28.bc1.a1', '28.be1.b1'], 'contains': ['112.d1.a1', '168.b1.a1'], 'core': '56.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [168, 448, 336, 672], 'label': '1344.8546.56.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.h1.a1', 'normal_contained_in': ['8.n1.a1', '28.b1.a1', '28.d1.a1', '28.e1.a1'], 'normal_contains': ['112.d1.a1', '168.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '56.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052989
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.n1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.n1.b1', '28.b1.a1', '28.d1.b1', '28.e1.b1', '28.x1.a1', '28.ba1.b1', '28.bc1.b1', '28.be1.a1'], 'contains': ['112.d1.a1', '168.b1.b1'], 'core': '56.h1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 448, 336, 672], 'label': '1344.8546.56.h1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.h1.b1', 'normal_contained_in': ['8.n1.b1', '28.b1.a1', '28.d1.b1', '28.e1.b1'], 'normal_contains': ['112.d1.a1', '168.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '56.h1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.h1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052990
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '28.c1.a1', '28.d1.b1', '28.e1.a1', '28.y1.a1', '28.z1.b1', '28.bb1.a1', '28.bd1.b1'], 'contains': ['112.d1.a1', '168.bg1.a1'], 'core': '56.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [730, 336, 672, 448], 'label': '1344.8546.56.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.i1.a1', 'normal_contained_in': ['8.o1.a1', '28.c1.a1', '28.d1.b1', '28.e1.a1'], 'normal_contains': ['112.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '56.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052991
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.o1.b1', '28.c1.a1', '28.d1.a1', '28.e1.b1', '28.y1.b1', '28.z1.a1', '28.bb1.b1', '28.bd1.a1'], 'contains': ['112.d1.a1', '168.bg1.b1'], 'core': '56.i1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [731, 336, 672, 448], 'label': '1344.8546.56.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.i1.b1', 'normal_contained_in': ['8.o1.b1', '28.c1.a1', '28.d1.a1', '28.e1.b1'], 'normal_contains': ['112.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '56.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052992
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '28.f1.a1', '28.h1.a1', '28.i1.a1'], 'contains': ['112.a1.a1', '112.h1.a1', '112.k1.a1', '168.d1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1009, 4, 448, 672], 'label': '1344.8546.56.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052993
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': ['336.o1.a1', '336.o1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.k1.a1', '2.k1.b1'], 'contains': ['8.f1.a1', '8.k1.a1', '8.m1.a1', '8.y1.a1', '8.bi1.a1', '12.x1.a1', '28.w1.a1'], 'core': '4.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [5, 192, 336, 672, 2, 448], 'label': '1344.8546.4.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': ['2.a1.a1', '2.k1.a1', '2.k1.b1'], 'normal_contains': ['8.f1.a1', '8.k1.a1', '8.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052994
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '28.g1.a1', '28.j1.a1', '28.k1.a1'], 'contains': ['112.a1.a1', '112.i1.a1', '112.i1.b1', '112.o1.a1', '112.o1.a2', '168.e1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1009, 76, 672, 448], 'label': '1344.8546.56.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '56.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052995
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.r1.a1', '28.f1.a1', '28.h1.a1', '28.l1.a1'], 'contains': ['112.a1.a1', '112.j1.a1', '112.m1.a1', '168.f1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1009, 6, 672, 448], 'label': '1344.8546.56.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052996
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.a1', '28.g1.a1', '28.j1.a1', '28.m1.a1'], 'contains': ['112.a1.a1', '112.l1.a1', '112.l1.b1', '168.h1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1009, 974, 672, 448], 'label': '1344.8546.56.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '56.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052997
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.t1.a1', '28.f1.a1', '28.n1.a1', '28.o1.a1'], 'contains': ['112.b1.a1', '112.h1.a1', '112.m1.a1', '168.i1.a1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1011, 4, 672, 448], 'label': '1344.8546.56.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052998
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.u1.a1', '28.g1.a1', '28.p1.a1', '28.q1.a1'], 'contains': ['112.b1.a1', '112.i1.a1', '112.l1.a1', '168.j1.a1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1085, 974, 672, 448], 'label': '1344.8546.56.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '56.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052999
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.u1.b1', '28.g1.a1', '28.p1.b1', '28.q1.a1'], 'contains': ['112.b1.a1', '112.i1.b1', '112.l1.b1', '168.j1.b1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1011, 76, 672, 448], 'label': '1344.8546.56.o1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '56.o1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.o1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053000
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1.a1', '28.f1.a1', '28.n1.a1', '28.r1.a1'], 'contains': ['112.b1.a1', '112.j1.a1', '112.k1.a1', '168.k1.a1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1013, 6, 672, 448], 'label': '1344.8546.56.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053001
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.w1.a1', '28.f1.a1', '28.s1.a1', '28.t1.a1'], 'contains': ['112.c1.a1', '112.h1.a1', '112.j1.a1', '112.p1.a1', '112.p1.a2', '168.n1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [2, 4, 672, 448], 'label': '1344.8546.56.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053002
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.x1.a1', '28.g1.a1', '28.u1.a1', '28.v1.a1'], 'contains': ['112.c1.a1', '112.i1.a1', '112.l1.b1', '168.o1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [77, 2, 672, 448], 'label': '1344.8546.56.r1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '56.r1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.r1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053003
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.x1.b1', '28.g1.a1', '28.u1.b1', '28.v1.a1'], 'contains': ['112.c1.a1', '112.i1.b1', '112.l1.a1', '168.o1.b1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [2, 76, 672, 448], 'label': '1344.8546.56.r1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '56.r1.b1', 'projective_image': None, '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': None}
  • id: 74053004
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1.a1', 'complements': ['336.o1.a1', '336.o1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.j1.b1', '2.k1.a1'], 'contains': ['8.f1.a1', '8.n1.a1', '8.o1.a1', '12.y1.a1', '28.e1.a1'], 'core': '4.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [2, 448, 192, 336, 168, 672], 'label': '1344.8546.4.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.o1.a1', 'normal_contained_in': ['2.c1.a1', '2.j1.b1', '2.k1.a1'], 'normal_contains': ['8.f1.a1', '8.n1.a1', '8.o1.a1', '28.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053005
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.y1.a1', '28.f1.a1', '28.s1.a1', '28.w1.a1'], 'contains': ['112.c1.a1', '112.k1.a1', '112.m1.a1', '168.r1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [5, 2, 672, 448], 'label': '1344.8546.56.s1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.s1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.s1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053006
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.z1.a1', '28.h1.a1', '28.n1.a1', '28.t1.a1'], 'contains': ['112.g1.a1', '112.h1.a1', '112.j1.a1', '168.s1.a1'], 'core': '112.g1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [338, 4, 672, 448], 'label': '1344.8546.56.t1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.t1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.t1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053007
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ba1.a1', '28.i1.a1', '28.n1.a1', '28.s1.a1'], 'contains': ['112.e1.a1', '112.h1.a1', '112.k1.a1', '168.t1.a1'], 'core': '112.e1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1, 4, 448, 672], 'label': '1344.8546.56.u1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.u1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.u1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053008
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bb1.a1', '28.h1.a1', '28.o1.a1', '28.s1.a1'], 'contains': ['112.f1.a1', '112.h1.a1', '112.m1.a1', '168.u1.a1'], 'core': '112.f1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [3, 4, 672, 448], 'label': '1344.8546.56.v1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.v1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.v1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053009
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '28.i1.a1', '28.o1.a1', '28.t1.a1', '28.x1.a1', '28.x1.b1', '28.y1.a1', '28.y1.b1'], 'contains': ['112.d1.a1', '112.h1.a1', '168.v1.a1'], 'core': '112.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [4, 336, 448, 672], 'label': '1344.8546.56.w1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.w1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.w1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053010
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bc1.a1', '28.j1.a1', '28.p1.a1', '28.v1.a1'], 'contains': ['112.f1.a1', '112.i1.a1', '112.l1.a1', '168.w1.a1'], 'core': '112.f1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [77, 974, 672, 448], 'label': '1344.8546.56.x1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '56.x1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.x1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053011
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bc1.b1', '28.j1.a1', '28.p1.b1', '28.v1.a1'], 'contains': ['112.f1.a1', '112.i1.b1', '112.l1.b1', '168.w1.b1'], 'core': '112.f1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [3, 76, 672, 448], 'label': '1344.8546.56.x1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '56.x1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.x1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053012
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.a1', '28.j1.a1', '28.q1.a1', '28.u1.a1'], 'contains': ['112.g1.a1', '112.i1.a1', '112.l1.b1', '168.x1.a1'], 'core': '112.g1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [77, 338, 672, 448], 'label': '1344.8546.56.y1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '56.y1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.y1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053013
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.b1', '28.j1.a1', '28.q1.a1', '28.u1.b1'], 'contains': ['112.g1.a1', '112.i1.b1', '112.l1.a1', '168.x1.b1'], 'core': '112.g1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [338, 76, 672, 448], 'label': '1344.8546.56.y1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '56.y1.b1', 'projective_image': None, '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': None}
  • id: 74053014
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '28.k1.a1', '28.p1.a1', '28.u1.a1', '28.x1.a1', '28.z1.a1', '28.ba1.a1', '28.bb1.a1'], 'contains': ['112.d1.a1', '112.i1.a1', '168.y1.a1'], 'core': '112.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [77, 336, 448, 672], 'label': '1344.8546.56.z1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.z1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.z1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053015
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1.a1', 'complements': ['336.o1.a2', '336.o1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.j1.a1', '2.k1.b1'], 'contains': ['8.f1.a1', '8.n1.b1', '8.o1.b1', '12.y1.b1', '28.e1.b1'], 'core': '4.o1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 448, 192, 336, 2, 672], 'label': '1344.8546.4.o1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.o1.b1', 'normal_contained_in': ['2.c1.a1', '2.j1.a1', '2.k1.b1'], 'normal_contains': ['8.f1.a1', '8.n1.b1', '8.o1.b1', '28.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.o1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.o1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053016
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.b1', '28.k1.a1', '28.p1.b1', '28.u1.b1', '28.x1.b1', '28.z1.b1', '28.ba1.b1', '28.bb1.b1'], 'contains': ['112.d1.a1', '112.i1.b1', '168.y1.b1'], 'core': '112.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [76, 336, 448, 672], 'label': '1344.8546.56.z1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.z1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.z1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053017
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.be1.a1', '28.k1.a1', '28.q1.a1', '28.v1.a1'], 'contains': ['112.e1.a1', '112.i1.a1', '112.i1.b1', '168.z1.a1'], 'core': '112.e1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1, 76, 448, 672], 'label': '1344.8546.56.ba1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '56.ba1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.ba1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053018
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bf1.a1', '28.l1.a1', '28.n1.a1', '28.s1.a1'], 'contains': ['112.e1.a1', '112.j1.a1', '112.m1.a1', '168.ba1.a1'], 'core': '112.e1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1, 6, 672, 448], 'label': '1344.8546.56.bb1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.bb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.bb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053019
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bg1.a1', '28.h1.a1', '28.r1.a1', '28.s1.a1'], 'contains': ['112.f1.a1', '112.j1.a1', '112.k1.a1', '168.bb1.a1'], 'core': '112.f1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [5, 6, 672, 448], 'label': '1344.8546.56.bc1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.bc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.bc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053020
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '28.l1.a1', '28.r1.a1', '28.t1.a1', '28.z1.a1', '28.z1.b1', '28.bc1.a1', '28.bc1.b1'], 'contains': ['112.d1.a1', '112.j1.a1', '168.bc1.a1'], 'core': '112.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [6, 336, 672, 448], 'label': '1344.8546.56.bd1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.bd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.bd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053021
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '28.i1.a1', '28.r1.a1', '28.w1.a1', '28.ba1.a1', '28.ba1.b1', '28.bd1.a1', '28.bd1.b1'], 'contains': ['112.d1.a1', '112.k1.a1', '168.bd1.a1'], 'core': '112.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [5, 336, 448, 672], 'label': '1344.8546.56.be1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.be1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.be1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053022
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '28.m1.a1', '28.p1.a1', '28.u1.b1', '28.y1.a1', '28.bc1.a1', '28.bd1.a1', '28.be1.a1'], 'contains': ['112.d1.a1', '112.l1.a1', '168.be1.a1'], 'core': '112.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [974, 336, 672, 448], 'label': '1344.8546.56.bf1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.bf1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.bf1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053023
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.b1', '28.m1.a1', '28.p1.b1', '28.u1.a1', '28.y1.b1', '28.bc1.b1', '28.bd1.b1', '28.be1.b1'], 'contains': ['112.d1.a1', '112.l1.b1', '168.be1.b1'], 'core': '112.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [975, 336, 672, 448], 'label': '1344.8546.56.bf1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.bf1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.bf1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053024
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '28.l1.a1', '28.o1.a1', '28.w1.a1', '28.bb1.a1', '28.bb1.b1', '28.be1.a1', '28.be1.b1'], 'contains': ['112.d1.a1', '112.m1.a1', '168.bf1.a1'], 'core': '112.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [7, 336, 672, 448], 'label': '1344.8546.56.bg1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.bg1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.bg1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053025
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bh1.a1', '28.m1.a1', '28.q1.a1', '28.v1.a1'], 'contains': ['112.e1.a1', '112.l1.a1', '112.l1.b1', '168.bh1.a1'], 'core': '112.e1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1, 974, 672, 448], 'label': '1344.8546.56.bh1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '56.bh1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.bh1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053026
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '224.a1.a1', 'complements': ['336.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.h1.a1', '2.j1.a1'], 'contains': ['8.h1.a1', '8.i1.a1', '8.n1.b1', '12.d1.a1', '28.x1.a1'], 'core': '4.p1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 192, 448, 336, 4, 672], 'label': '1344.8546.4.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.p1.a1', 'normal_contained_in': ['2.d1.a1', '2.h1.a1', '2.j1.a1'], 'normal_contains': ['8.h1.a1', '8.i1.a1', '8.n1.b1', '12.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053027
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '56.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bi1.a1', '28.h1.a1', '28.n1.a1', '28.w1.a1'], 'contains': ['112.g1.a1', '112.k1.a1', '112.m1.a1', '168.bi1.a1'], 'core': '112.g1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [5, 338, 672, 448], 'label': '1344.8546.56.bi1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.bi1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.bi1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053028
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.f1.a1', 'complements': ['21.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '32.d1.a1', '32.e1.a1', '32.f1.a1', '32.f1.b1', '32.g1.a1'], 'contains': ['192.a1.a1', '448.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [448, 192], 'label': '1344.8546.64.a1.a1', 'mobius_quo': None, 'mobius_sub': None, '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': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053029
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.d1.a1', 'complements': ['16.p1.a1', '16.p1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '28.b1.a1', '42.c1.a1', '42.d1.a1', '42.g1.a1'], 'contains': ['168.a1.a1', '168.b1.a1', '168.b1.b1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 168], 'label': '1344.8546.84.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '84.a1.a1', 'normal_contained_in': ['12.c1.a1', '28.b1.a1'], 'normal_contains': ['168.a1.a1', '168.b1.a1', '168.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '84.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053030
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '28.f1.a1', '42.a1.a1'], 'contains': ['168.c1.a1', '168.d1.a1', '168.f1.a1', '168.i1.a1', '168.k1.a1', '168.n1.a1', '168.r1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [1009, 2, 4], 'label': '1344.8546.84.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '84.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053031
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '28.g1.a1', '42.b1.a1'], 'contains': ['168.c1.a1', '168.e1.a1', '168.h1.a1', '168.j1.a1', '168.j1.b1', '168.o1.a1', '168.o1.b1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [1009, 2, 76], 'label': '1344.8546.84.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.b1.a1', 'old_label': '84.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053032
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '28.a1.a1', '42.a1.a1', '42.b1.a1', '42.c1.a1'], 'contains': ['168.a1.a1', '168.c1.a1', '168.g1.a1', '168.l1.a1', '168.m1.a1', '168.p1.a1', '168.q1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 2, 336], 'label': '1344.8546.84.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '84.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053033
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '28.h1.a1', '42.a1.a1'], 'contains': ['168.d1.a1', '168.f1.a1', '168.g1.a1', '168.s1.a1', '168.u1.a1', '168.bb1.a1', '168.bi1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [1009, 338, 4], 'label': '1344.8546.84.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '84.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053034
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '28.i1.a1', '42.a1.a1', '42.d1.a1', '42.e1.a1'], 'contains': ['168.a1.a1', '168.d1.a1', '168.t1.a1', '168.v1.a1', '168.bd1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 4, 336], 'label': '1344.8546.84.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '84.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053035
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '28.j1.a1', '42.b1.a1'], 'contains': ['168.e1.a1', '168.g1.a1', '168.h1.a1', '168.w1.a1', '168.w1.b1', '168.x1.a1', '168.x1.b1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [1009, 338, 76], 'label': '1344.8546.84.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.b1.a1', 'old_label': '84.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053036
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '28.k1.a1', '42.b1.a1', '42.d1.a1', '42.f1.a1'], 'contains': ['168.a1.a1', '168.e1.a1', '168.y1.a1', '168.y1.b1', '168.z1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 76, 336], 'label': '1344.8546.84.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '84.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053037
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '224.a1.a1', 'complements': ['336.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.h1.b1', '2.j1.b1'], 'contains': ['8.h1.a1', '8.i1.b1', '8.n1.a1', '12.d1.b1', '28.x1.b1'], 'core': '4.p1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [4, 192, 448, 1008, 168, 672], 'label': '1344.8546.4.p1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.p1.b1', 'normal_contained_in': ['2.d1.a1', '2.h1.b1', '2.j1.b1'], 'normal_contains': ['8.h1.a1', '8.i1.b1', '8.n1.a1', '12.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.p1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.p1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053038
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '28.l1.a1', '42.a1.a1', '42.f1.a1', '42.g1.a1'], 'contains': ['168.a1.a1', '168.f1.a1', '168.ba1.a1', '168.bc1.a1', '168.bf1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [1, 6, 336], 'label': '1344.8546.84.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053039
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '28.m1.a1', '42.b1.a1', '42.e1.a1', '42.g1.a1'], 'contains': ['168.a1.a1', '168.h1.a1', '168.be1.a1', '168.be1.b1', '168.bh1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [1, 974, 336], 'label': '1344.8546.84.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053040
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '28.c1.a1', '42.c1.a1', '42.e1.a1', '42.f1.a1'], 'contains': ['168.a1.a1', '168.bg1.a1', '168.bg1.b1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 730], 'label': '1344.8546.84.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '84.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053041
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '28.n1.a1', '42.a1.a1'], 'contains': ['168.i1.a1', '168.k1.a1', '168.m1.a1', '168.s1.a1', '168.t1.a1', '168.ba1.a1', '168.bi1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [1, 338, 4], 'label': '1344.8546.84.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '84.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053042
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '28.o1.a1', '42.a1.a1', '42.h1.a1', '42.h1.b1'], 'contains': ['168.i1.a1', '168.l1.a1', '168.u1.a1', '168.v1.a1', '168.bf1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [3, 4, 336], 'label': '1344.8546.84.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053043
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1.a1', '28.p1.a1', '42.b1.a1', '42.h1.a1', '42.i1.a1'], 'contains': ['168.j1.a1', '168.l1.a1', '168.w1.a1', '168.y1.a1', '168.be1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [77, 974, 336], 'label': '1344.8546.84.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053044
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1.b1', '28.p1.b1', '42.b1.a1', '42.h1.b1', '42.i1.b1'], 'contains': ['168.j1.b1', '168.l1.a1', '168.w1.b1', '168.y1.b1', '168.be1.b1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [3, 76, 336], 'label': '1344.8546.84.n1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.n1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.n1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053045
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1', '28.q1.a1', '42.b1.a1'], 'contains': ['168.j1.a1', '168.j1.b1', '168.m1.a1', '168.x1.a1', '168.x1.b1', '168.z1.a1', '168.bh1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [1, 338, 76], 'label': '1344.8546.84.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.b1.a1', 'old_label': '84.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053046
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1.a1', '28.r1.a1', '42.a1.a1', '42.i1.a1', '42.i1.b1'], 'contains': ['168.k1.a1', '168.l1.a1', '168.bb1.a1', '168.bc1.a1', '168.bd1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [5, 6, 336], 'label': '1344.8546.84.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053047
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1.a1', '28.d1.a1', '42.c1.a1', '42.h1.b1', '42.i1.a1'], 'contains': ['168.b1.a1', '168.l1.a1', '168.bg1.b1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [3, 168], 'label': '1344.8546.84.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '84.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053048
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['336.o1.a1', '336.o1.a2', '336.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.h1.a1', '2.j1.b1'], 'contains': ['8.h1.a1', '8.l1.a1', '8.o1.a1', '12.z1.a1', '28.y1.a1'], 'core': '4.q1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [730, 192, 336, 672, 4, 448], 'label': '1344.8546.4.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.a1', 'normal_contained_in': ['2.e1.a1', '2.h1.a1', '2.j1.b1'], 'normal_contains': ['8.h1.a1', '8.l1.a1', '8.o1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053049
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.s1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1.b1', '28.d1.b1', '42.c1.a1', '42.h1.a1', '42.i1.b1'], 'contains': ['168.b1.b1', '168.l1.a1', '168.bg1.a1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [169, 730], 'label': '1344.8546.84.q1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '84.q1.b1', 'projective_image': None, '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': None}
  • id: 74053050
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1.a1', '28.s1.a1', '42.a1.a1'], 'contains': ['168.n1.a1', '168.q1.a1', '168.r1.a1', '168.t1.a1', '168.u1.a1', '168.ba1.a1', '168.bb1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [1, 2, 4], 'label': '1344.8546.84.r1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '84.r1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.r1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053051
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.u1.a1', '28.t1.a1', '42.a1.a1', '42.j1.a1', '42.j1.b1'], 'contains': ['168.n1.a1', '168.p1.a1', '168.s1.a1', '168.v1.a1', '168.bc1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [2, 4, 336], 'label': '1344.8546.84.s1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.s1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.s1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053052
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1.a1', '28.u1.a1', '42.b1.a1', '42.j1.a1', '42.k1.a1'], 'contains': ['168.o1.a1', '168.p1.a1', '168.x1.a1', '168.y1.a1', '168.be1.b1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [77, 2, 336], 'label': '1344.8546.84.t1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.t1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.t1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053053
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1.b1', '28.u1.b1', '42.b1.a1', '42.j1.b1', '42.k1.b1'], 'contains': ['168.o1.b1', '168.p1.a1', '168.x1.b1', '168.y1.b1', '168.be1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [2, 76, 336], 'label': '1344.8546.84.t1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.t1.b1', 'projective_image': None, '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': None}
  • id: 74053054
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.w1.a1', '28.v1.a1', '42.b1.a1'], 'contains': ['168.o1.a1', '168.o1.b1', '168.q1.a1', '168.w1.a1', '168.w1.b1', '168.z1.a1', '168.bh1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [1, 2, 76], 'label': '1344.8546.84.u1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.b1.a1', 'old_label': '84.u1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.u1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053055
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.x1.a1', '28.w1.a1', '42.a1.a1', '42.k1.a1', '42.k1.b1'], 'contains': ['168.p1.a1', '168.r1.a1', '168.bd1.a1', '168.bf1.a1', '168.bi1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [5, 2, 336], 'label': '1344.8546.84.v1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.v1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.v1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053056
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.y1.a1', '28.e1.a1', '42.c1.a1', '42.j1.b1', '42.k1.a1'], 'contains': ['168.b1.a1', '168.p1.a1', '168.bg1.a1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2, 168], 'label': '1344.8546.84.w1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '84.w1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.w1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053057
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.y1.b1', '28.e1.b1', '42.c1.a1', '42.j1.a1', '42.k1.b1'], 'contains': ['168.b1.b1', '168.p1.a1', '168.bg1.b1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [169, 2], 'label': '1344.8546.84.w1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '84.w1.b1', 'projective_image': None, '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': None}
  • id: 74053058
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '28.x1.a1', '42.d1.a1', '42.h1.a1', '42.j1.a1'], 'contains': ['168.b1.b1', '168.v1.a1', '168.y1.a1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [169, 4], 'label': '1344.8546.84.x1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '84.x1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.x1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053121
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '56.p1.a1', '84.b1.a1', '84.l1.a1', '84.p1.a1'], 'contains': ['336.d1.a1', '336.h1.a1', '336.k1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [1013, 6], 'label': '1344.8546.168.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '168.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053059
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '2.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1.a1', 'complements': ['672.e1.a1', '672.f1.b1', '672.g1.a1', '672.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.f1.a1', '4.g1.a1', '4.k1.a1', '4.k1.b1', '4.o1.a1', '4.o1.b1', '6.d1.a1', '14.a1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 672, 168, 192, 2, 448, 336], 'label': '1344.8546.2.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.f1.a1', '4.g1.a1', '4.k1.a1', '4.k1.b1', '4.o1.a1', '4.o1.b1', '14.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053060
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['336.o1.a2', '336.o1.a1', '336.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.h1.b1', '2.j1.a1'], 'contains': ['8.h1.a1', '8.l1.b1', '8.o1.b1', '12.z1.b1', '28.y1.b1'], 'core': '4.q1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [731, 192, 336, 672, 4, 448], 'label': '1344.8546.4.q1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.b1', 'normal_contained_in': ['2.e1.a1', '2.h1.b1', '2.j1.a1'], 'normal_contains': ['8.h1.a1', '8.l1.b1', '8.o1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.q1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.q1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053061
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.b1', '28.x1.b1', '42.d1.a1', '42.h1.b1', '42.j1.b1'], 'contains': ['168.b1.a1', '168.v1.a1', '168.y1.b1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [4, 168], 'label': '1344.8546.84.x1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '84.x1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.x1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053062
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.z1.a1', '28.y1.a1', '42.e1.a1', '42.h1.a1', '42.j1.b1'], 'contains': ['168.v1.a1', '168.be1.a1', '168.bg1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [730, 4], 'label': '1344.8546.84.y1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.y1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.y1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053063
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.z1.b1', '28.y1.b1', '42.e1.a1', '42.h1.b1', '42.j1.a1'], 'contains': ['168.v1.a1', '168.be1.b1', '168.bg1.b1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [731, 4], 'label': '1344.8546.84.y1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.y1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.y1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053064
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ba1.a1', '28.z1.a1', '42.f1.a1', '42.i1.a1', '42.j1.a1'], 'contains': ['168.y1.a1', '168.bc1.a1', '168.bg1.b1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [845, 6], 'label': '1344.8546.84.z1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.z1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.z1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053065
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ba1.b1', '28.z1.b1', '42.f1.a1', '42.i1.b1', '42.j1.b1'], 'contains': ['168.y1.b1', '168.bc1.a1', '168.bg1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [730, 76], 'label': '1344.8546.84.z1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.r1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.z1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.z1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053066
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '28.ba1.a1', '42.d1.a1', '42.i1.a1', '42.k1.a1'], 'contains': ['168.b1.a1', '168.y1.a1', '168.bd1.a1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [5, 168], 'label': '1344.8546.84.ba1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '84.ba1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.ba1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053067
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.b1', '28.ba1.b1', '42.d1.a1', '42.i1.b1', '42.k1.b1'], 'contains': ['168.b1.b1', '168.y1.b1', '168.bd1.a1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [169, 76], 'label': '1344.8546.84.ba1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '84.ba1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.ba1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053068
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bb1.a1', '28.bb1.a1', '42.f1.a1', '42.h1.a1', '42.k1.a1'], 'contains': ['168.y1.a1', '168.bf1.a1', '168.bg1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [77, 730], 'label': '1344.8546.84.bb1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.bb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.bb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053069
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bb1.b1', '28.bb1.b1', '42.f1.a1', '42.h1.b1', '42.k1.b1'], 'contains': ['168.y1.b1', '168.bf1.a1', '168.bg1.b1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [731, 76], 'label': '1344.8546.84.bb1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.t1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.bb1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.bb1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053070
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bc1.a1', '28.bc1.a1', '42.g1.a1', '42.i1.a1', '42.j1.b1'], 'contains': ['168.b1.a1', '168.bc1.a1', '168.be1.a1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [6, 168], 'label': '1344.8546.84.bc1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.bc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.bc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053071
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['336.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.i1.a1', '2.j1.a1'], 'contains': ['8.i1.a1', '8.j1.a1', '8.o1.b1', '12.ba1.a1', '28.z1.a1'], 'core': '4.r1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [77, 192, 336, 672, 6, 448], 'label': '1344.8546.4.r1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.r1.a1', 'normal_contained_in': ['2.f1.a1', '2.i1.a1', '2.j1.a1'], 'normal_contains': ['8.i1.a1', '8.j1.a1', '8.o1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.r1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.r1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053072
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bc1.b1', '28.bc1.b1', '42.g1.a1', '42.i1.b1', '42.j1.a1'], 'contains': ['168.b1.b1', '168.bc1.a1', '168.be1.b1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [169, 6], 'label': '1344.8546.84.bc1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.u1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.bc1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.bc1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053073
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bd1.a1', '28.bd1.a1', '42.e1.a1', '42.i1.a1', '42.k1.b1'], 'contains': ['168.bd1.a1', '168.be1.a1', '168.bg1.b1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [581, 974], 'label': '1344.8546.84.bd1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.bd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.bd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053074
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bd1.b1', '28.bd1.b1', '42.e1.a1', '42.i1.b1', '42.k1.a1'], 'contains': ['168.bd1.a1', '168.be1.b1', '168.bg1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [5, 730], 'label': '1344.8546.84.bd1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.v1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.bd1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.bd1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053075
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.be1.a1', '28.be1.a1', '42.g1.a1', '42.h1.a1', '42.k1.b1'], 'contains': ['168.b1.b1', '168.be1.a1', '168.bf1.a1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [169, 974], 'label': '1344.8546.84.be1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.be1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.be1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053076
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '84.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.be1.b1', '28.be1.b1', '42.g1.a1', '42.h1.b1', '42.k1.a1'], 'contains': ['168.b1.a1', '168.be1.b1', '168.bf1.a1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [7, 168], 'label': '1344.8546.84.be1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.be1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.be1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053077
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '96.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.a1.a1', '48.b1.a1', '48.c1.a1', '48.d1.a1', '48.e1.a1', '48.f1.a1', '48.g1.a1', '48.g1.b1', '48.h1.a1', '48.i1.a1', '48.j1.a1', '48.k1.a1', '48.l1.a1', '48.l1.b1', '48.m1.a1'], 'contains': ['192.a1.a1', '672.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [672, 192], 'label': '1344.8546.96.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.a1.a1', 'normal_contained_in': ['32.a1.a1', '48.a1.a1', '48.c1.a1', '48.b1.a1'], 'normal_contains': ['192.a1.a1', '672.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053078
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '96.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '48.a1.a1', '48.n1.a1', '48.o1.a1', '48.o1.a2'], 'contains': ['192.a1.a1', '672.b1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1009, 192], 'label': '1344.8546.96.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '96.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053079
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '96.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '48.d1.a1', '48.n1.a1'], 'contains': ['192.a1.a1', '672.c1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1011, 192], 'label': '1344.8546.96.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '96.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053082
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['336.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.i1.b1', '2.j1.b1'], 'contains': ['8.i1.b1', '8.j1.a1', '8.o1.a1', '12.ba1.b1', '28.z1.b1'], 'core': '4.r1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [730, 192, 336, 672, 76, 448], 'label': '1344.8546.4.r1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.r1.b1', 'normal_contained_in': ['2.f1.a1', '2.i1.b1', '2.j1.b1'], 'normal_contains': ['8.i1.b1', '8.j1.a1', '8.o1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.r1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.r1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053083
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '96.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '48.g1.a1', '48.o1.a1', '48.o1.a2'], 'contains': ['192.a1.a1', '672.f1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [77, 192], 'label': '1344.8546.96.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.ba1.a1', 'old_label': '96.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053084
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '96.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.b1', '48.g1.b1', '48.o1.a1', '48.o1.a2'], 'contains': ['192.a1.a1', '672.f1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [76, 192], 'label': '1344.8546.96.f1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.ba1.a1', 'old_label': '96.f1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.f1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053085
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '96.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1.a1', '48.h1.a1', '48.p1.a1', '48.p1.a2'], 'contains': ['192.a1.a1', '672.g1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [6, 192], 'label': '1344.8546.96.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.t1.a1', 'old_label': '96.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053086
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '112.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '56.a1.a1', '56.b1.a1', '56.c1.a1', '56.j1.a1', '56.k1.a1', '56.l1.a1', '56.m1.a1'], 'contains': ['224.a1.a1', '224.b1.a1', '336.a1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1009, 672, 448], 'label': '1344.8546.112.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.a1.a1', 'normal_contained_in': ['16.a1.a1', '56.a1.a1', '56.b1.a1', '56.c1.a1'], 'normal_contains': ['224.a1.a1', '336.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '112.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053087
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '112.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '56.a1.a1', '56.d1.a1', '56.e1.a1', '56.n1.a1', '56.o1.a1', '56.o1.b1', '56.p1.a1'], 'contains': ['224.a1.a1', '224.c1.a1', '336.d1.a1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1011, 672, 448], 'label': '1344.8546.112.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.b1.a1', 'normal_contained_in': ['16.b1.a1', '56.a1.a1', '56.e1.a1', '56.d1.a1'], 'normal_contains': ['224.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '112.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053088
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '112.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '56.a1.a1', '56.f1.a1', '56.g1.a1', '56.q1.a1', '56.r1.a1', '56.r1.b1', '56.s1.a1'], 'contains': ['224.a1.a1', '224.d1.a1', '336.e1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [2, 672, 448], 'label': '1344.8546.112.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.c1.a1', 'normal_contained_in': ['16.c1.a1', '56.a1.a1', '56.g1.a1', '56.f1.a1'], 'normal_contains': ['224.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '112.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053089
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '112.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '56.b1.a1', '56.d1.a1', '56.f1.a1', '56.h1.a1', '56.h1.b1', '56.i1.a1', '56.i1.b1', '56.w1.a1', '56.z1.a1', '56.z1.b1', '56.bd1.a1', '56.be1.a1', '56.bf1.a1', '56.bf1.b1', '56.bg1.a1'], 'contains': ['224.a1.a1', '336.b1.a1'], 'core': '112.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [336, 448, 672], 'label': '1344.8546.112.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.d1.a1', 'normal_contained_in': ['16.d1.a1', '56.b1.a1', '56.d1.a1', '56.f1.a1', '56.h1.a1', '56.h1.b1', '56.i1.a1', '56.i1.b1'], 'normal_contains': ['224.a1.a1', '336.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '112.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053090
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '112.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '56.b1.a1', '56.e1.a1', '56.g1.a1', '56.u1.a1', '56.ba1.a1', '56.bb1.a1', '56.bh1.a1'], 'contains': ['224.a1.a1', '336.c1.a1'], 'core': '112.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 448, 672], 'label': '1344.8546.112.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.e1.a1', 'normal_contained_in': ['16.e1.a1', '56.b1.a1', '56.e1.a1', '56.g1.a1'], 'normal_contains': ['224.a1.a1', '336.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '112.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053091
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '112.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '56.c1.a1', '56.d1.a1', '56.g1.a1', '56.v1.a1', '56.x1.a1', '56.x1.b1', '56.bc1.a1'], 'contains': ['224.a1.a1', '336.i1.a1'], 'core': '112.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [3, 672, 448], 'label': '1344.8546.112.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.f1.a1', 'normal_contained_in': ['16.f1.a1', '56.c1.a1', '56.d1.a1', '56.g1.a1'], 'normal_contains': ['224.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '112.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053092
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '112.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '56.c1.a1', '56.e1.a1', '56.f1.a1', '56.t1.a1', '56.y1.a1', '56.y1.b1', '56.bi1.a1'], 'contains': ['224.a1.a1', '336.j1.a1'], 'core': '112.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [338, 672, 448], 'label': '1344.8546.112.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.g1.a1', 'normal_contained_in': ['16.g1.a1', '56.c1.a1', '56.e1.a1', '56.f1.a1'], 'normal_contains': ['224.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '112.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053093
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '224.a1.a1', 'complements': ['336.p1.a1', '336.p1.a2', '336.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.i1.a1', '2.k1.a1'], 'contains': ['8.i1.a1', '8.k1.a1', '8.n1.a1', '12.e1.a1', '28.ba1.a1'], 'core': '4.s1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [5, 192, 448, 336, 168, 672], 'label': '1344.8546.4.s1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.s1.a1', 'normal_contained_in': ['2.d1.a1', '2.i1.a1', '2.k1.a1'], 'normal_contains': ['8.i1.a1', '8.k1.a1', '8.n1.a1', '12.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.s1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.s1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053094
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '112.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '56.j1.a1', '56.n1.a1', '56.q1.a1', '56.t1.a1', '56.u1.a1', '56.v1.a1', '56.w1.a1'], 'contains': ['224.a1.a1', '224.e1.a1', '336.f1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [4, 672, 448], 'label': '1344.8546.112.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '112.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053095
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '112.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '56.k1.a1', '56.o1.a1', '56.r1.a1', '56.x1.a1', '56.y1.a1', '56.z1.a1', '56.ba1.a1'], 'contains': ['224.a1.a1', '224.f1.a1', '336.g1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [77, 672, 448], 'label': '1344.8546.112.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '112.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053096
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '112.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.b1', '56.k1.a1', '56.o1.b1', '56.r1.b1', '56.x1.b1', '56.y1.b1', '56.z1.b1', '56.ba1.a1'], 'contains': ['224.a1.a1', '224.f1.b1', '336.g1.b1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [76, 672, 448], 'label': '1344.8546.112.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '112.i1.b1', 'projective_image': None, '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': None}
  • id: 74053097
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '112.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '56.l1.a1', '56.p1.a1', '56.q1.a1', '56.t1.a1', '56.bb1.a1', '56.bc1.a1', '56.bd1.a1'], 'contains': ['224.a1.a1', '224.g1.a1', '336.h1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [6, 672, 448], 'label': '1344.8546.112.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '112.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053098
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '112.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '56.j1.a1', '56.p1.a1', '56.s1.a1', '56.u1.a1', '56.bc1.a1', '56.be1.a1', '56.bi1.a1'], 'contains': ['224.a1.a1', '336.k1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [5, 448, 672], 'label': '1344.8546.112.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '112.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053099
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '112.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '56.m1.a1', '56.o1.a1', '56.r1.b1', '56.x1.a1', '56.y1.b1', '56.bf1.a1', '56.bh1.a1'], 'contains': ['224.a1.a1', '336.l1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [974, 672, 448], 'label': '1344.8546.112.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '112.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053100
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '112.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.b1', '56.m1.a1', '56.o1.b1', '56.r1.a1', '56.x1.b1', '56.y1.a1', '56.bf1.b1', '56.bh1.a1'], 'contains': ['224.a1.a1', '336.l1.b1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [975, 672, 448], 'label': '1344.8546.112.l1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '112.l1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.l1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053101
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '112.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.a1', '56.l1.a1', '56.n1.a1', '56.s1.a1', '56.v1.a1', '56.bb1.a1', '56.bg1.a1', '56.bi1.a1'], 'contains': ['224.a1.a1', '336.m1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [7, 672, 448], 'label': '1344.8546.112.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '112.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053102
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '112.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '56.a1.a1'], 'contains': ['224.b1.a1', '224.c1.a1', '224.d1.a1', '336.n1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [1009, 2, 448], 'label': '1344.8546.112.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '112.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053103
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '112.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a1', '56.k1.a1'], 'contains': ['224.b1.a1', '224.f1.a1', '224.f1.b1', '336.o1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [337, 76, 448], 'label': '1344.8546.112.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.j1.a1', 'old_label': '112.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053104
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '224.a1.a1', 'complements': ['336.p1.a1', '336.p1.a2', '336.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.i1.b1', '2.k1.b1'], 'contains': ['8.i1.b1', '8.k1.a1', '8.n1.b1', '12.e1.b1', '28.ba1.b1'], 'core': '4.s1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 192, 448, 336, 76, 672], 'label': '1344.8546.4.s1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.s1.b1', 'normal_contained_in': ['2.d1.a1', '2.i1.b1', '2.k1.b1'], 'normal_contains': ['8.i1.b1', '8.k1.a1', '8.n1.b1', '12.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.s1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.s1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053105
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '112.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a2', '56.k1.a1'], 'contains': ['224.b1.a1', '224.f1.a1', '224.f1.b1', '336.o1.a2'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [1009, 76, 448], 'label': '1344.8546.112.o1.a2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.j1.a1', 'old_label': '112.o1.a2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.o1.a2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053106
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '112.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.a1', '56.q1.a1'], 'contains': ['224.d1.a1', '224.e1.a1', '224.g1.a1', '336.p1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [2, 4, 448], 'label': '1344.8546.112.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.s1.a1', 'old_label': '112.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053107
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '112.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.a2', '56.q1.a1'], 'contains': ['224.d1.a1', '224.e1.a1', '224.g1.a1', '336.p1.a2'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [674, 4, 448], 'label': '1344.8546.112.p1.a2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.s1.a1', 'old_label': '112.p1.a2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.p1.a2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053108
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '56.b1.a1', '84.a1.a1', '84.d1.a1', '84.f1.a1', '84.h1.a1', '84.i1.a1', '84.j1.a1', '84.k1.a1'], 'contains': ['336.a1.a1', '336.b1.a1', '336.c1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 336], 'label': '1344.8546.168.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '168.a1.a1', 'normal_contained_in': ['24.a1.a1', '56.b1.a1', '84.a1.a1'], 'normal_contains': ['336.a1.a1', '336.c1.a1', '336.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '168.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053109
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.k1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '56.h1.a1', '84.a1.a1', '84.q1.a1', '84.w1.a1', '84.x1.b1', '84.ba1.a1', '84.bc1.a1', '84.be1.b1'], 'contains': ['336.b1.a1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [168], 'label': '1344.8546.168.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '168.b1.a1', 'normal_contained_in': ['24.e1.a1', '56.h1.a1', '84.a1.a1'], 'normal_contains': ['336.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '168.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053110
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.k1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.e1.b1', '56.h1.b1', '84.a1.a1', '84.q1.b1', '84.w1.b1', '84.x1.a1', '84.ba1.b1', '84.bc1.b1', '84.be1.a1'], 'contains': ['336.b1.a1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169], 'label': '1344.8546.168.b1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '168.b1.b1', 'normal_contained_in': ['24.e1.b1', '56.h1.b1', '84.a1.a1'], 'normal_contains': ['336.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '168.b1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.b1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053111
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '56.a1.a1', '84.b1.a1', '84.c1.a1', '84.d1.a1'], 'contains': ['336.a1.a1', '336.d1.a1', '336.e1.a1', '336.n1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1009, 2, 672], 'label': '1344.8546.168.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '168.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053112
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '56.j1.a1', '84.b1.a1', '84.e1.a1', '84.f1.a1'], 'contains': ['336.a1.a1', '336.f1.a1', '336.k1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1009, 4], 'label': '1344.8546.168.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '168.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053113
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '28.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '56.k1.a1', '84.c1.a1', '84.g1.a1', '84.h1.a1'], 'contains': ['336.a1.a1', '336.g1.a1', '336.g1.b1', '336.o1.a1', '336.o1.a2'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1009, 76, 672], 'label': '1344.8546.168.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '168.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053114
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '56.l1.a1', '84.b1.a1', '84.e1.a1', '84.i1.a1'], 'contains': ['336.a1.a1', '336.h1.a1', '336.m1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [1009, 6], 'label': '1344.8546.168.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '168.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053115
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['336.p1.a1', '336.p1.a2', '336.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.h1.a1', '2.k1.a1'], 'contains': ['8.i1.a1', '8.m1.a1', '8.o1.a1', '12.bb1.a1', '28.bb1.a1'], 'core': '4.t1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [77, 192, 336, 672, 730, 448], 'label': '1344.8546.4.t1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.t1.a1', 'normal_contained_in': ['2.f1.a1', '2.h1.a1', '2.k1.a1'], 'normal_contains': ['8.i1.a1', '8.m1.a1', '8.o1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.t1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.t1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053116
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '56.c1.a1', '84.d1.a1', '84.e1.a1', '84.g1.a1'], 'contains': ['336.a1.a1', '336.i1.a1', '336.j1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1009, 338], 'label': '1344.8546.168.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '168.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053117
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '56.m1.a1', '84.c1.a1', '84.g1.a1', '84.j1.a1'], 'contains': ['336.a1.a1', '336.l1.a1', '336.l1.b1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [1009, 974], 'label': '1344.8546.168.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.b1.a1', 'old_label': '168.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053118
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '56.n1.a1', '84.b1.a1', '84.l1.a1', '84.m1.a1'], 'contains': ['336.d1.a1', '336.f1.a1', '336.m1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [1011, 4], 'label': '1344.8546.168.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '168.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053119
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '56.o1.a1', '84.c1.a1', '84.n1.a1', '84.o1.a1'], 'contains': ['336.d1.a1', '336.g1.a1', '336.l1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [1085, 974], 'label': '1344.8546.168.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.b1.a1', 'old_label': '168.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053120
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.b1', '56.o1.b1', '84.c1.a1', '84.n1.b1', '84.o1.a1'], 'contains': ['336.d1.a1', '336.g1.b1', '336.l1.b1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [1011, 76], 'label': '1344.8546.168.j1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.b1.a1', 'old_label': '168.j1.b1', 'projective_image': None, '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': None}
  • id: 74053122
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '56.d1.a1', '84.d1.a1', '84.m1.a1', '84.n1.a1', '84.n1.b1', '84.p1.a1', '84.q1.a1', '84.q1.b1'], 'contains': ['336.b1.a1', '336.d1.a1', '336.i1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [3, 336], 'label': '1344.8546.168.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '168.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053123
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.a1', '56.e1.a1', '84.d1.a1', '84.l1.a1', '84.o1.a1'], 'contains': ['336.c1.a1', '336.d1.a1', '336.j1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 338], 'label': '1344.8546.168.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '168.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053124
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '56.q1.a1', '84.b1.a1', '84.r1.a1', '84.s1.a1'], 'contains': ['336.e1.a1', '336.f1.a1', '336.h1.a1', '336.p1.a1', '336.p1.a2'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [2, 4, 672], 'label': '1344.8546.168.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '168.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053125
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.r1.a1', '56.r1.a1', '84.c1.a1', '84.t1.a1', '84.u1.a1'], 'contains': ['336.e1.a1', '336.g1.a1', '336.l1.b1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [77, 2], 'label': '1344.8546.168.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.b1.a1', 'old_label': '168.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053126
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['336.p1.a1', '336.p1.a2', '336.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.h1.b1', '2.k1.b1'], 'contains': ['8.i1.b1', '8.m1.a1', '8.o1.b1', '12.bb1.b1', '28.bb1.b1'], 'core': '4.t1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [731, 192, 336, 672, 76, 448], 'label': '1344.8546.4.t1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.t1.b1', 'normal_contained_in': ['2.f1.a1', '2.h1.b1', '2.k1.b1'], 'normal_contains': ['8.i1.b1', '8.m1.a1', '8.o1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.t1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.t1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053127
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.r1.b1', '56.r1.b1', '84.c1.a1', '84.t1.b1', '84.u1.a1'], 'contains': ['336.e1.a1', '336.g1.b1', '336.l1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [2, 76], 'label': '1344.8546.168.o1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.b1.a1', 'old_label': '168.o1.b1', 'projective_image': None, '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': None}
  • id: 74053128
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.a1', '56.f1.a1', '84.d1.a1', '84.s1.a1', '84.t1.a1', '84.t1.b1', '84.v1.a1', '84.w1.a1', '84.w1.b1'], 'contains': ['336.b1.a1', '336.e1.a1', '336.j1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2, 336], 'label': '1344.8546.168.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '168.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053129
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1.a1', '56.g1.a1', '84.d1.a1', '84.r1.a1', '84.u1.a1'], 'contains': ['336.c1.a1', '336.e1.a1', '336.i1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 2], 'label': '1344.8546.168.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '168.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053130
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.u1.a1', '56.s1.a1', '84.b1.a1', '84.r1.a1', '84.v1.a1'], 'contains': ['336.e1.a1', '336.k1.a1', '336.m1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [5, 2], 'label': '1344.8546.168.r1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '168.r1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.r1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053131
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.v1.a1', '56.t1.a1', '84.e1.a1', '84.l1.a1', '84.s1.a1'], 'contains': ['336.f1.a1', '336.h1.a1', '336.j1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [338, 4], 'label': '1344.8546.168.s1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '168.s1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.s1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053132
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '28.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.w1.a1', '56.u1.a1', '84.f1.a1', '84.l1.a1', '84.r1.a1'], 'contains': ['336.c1.a1', '336.f1.a1', '336.k1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1, 4], 'label': '1344.8546.168.t1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '168.t1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.t1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053133
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.x1.a1', '56.v1.a1', '84.e1.a1', '84.m1.a1', '84.r1.a1'], 'contains': ['336.f1.a1', '336.i1.a1', '336.m1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [3, 4], 'label': '1344.8546.168.u1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '168.u1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.u1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053134
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '56.w1.a1', '84.f1.a1', '84.m1.a1', '84.s1.a1', '84.x1.a1', '84.x1.b1', '84.y1.a1', '84.y1.b1'], 'contains': ['336.b1.a1', '336.f1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [4, 336], 'label': '1344.8546.168.v1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '168.v1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.v1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053135
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1.a1', '56.x1.a1', '84.g1.a1', '84.n1.a1', '84.u1.a1'], 'contains': ['336.g1.a1', '336.i1.a1', '336.l1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [77, 974], 'label': '1344.8546.168.w1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.b1.a1', 'old_label': '168.w1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.w1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053136
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1.b1', '56.x1.b1', '84.g1.a1', '84.n1.b1', '84.u1.a1'], 'contains': ['336.g1.b1', '336.i1.a1', '336.l1.b1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [3, 76], 'label': '1344.8546.168.w1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.b1.a1', 'old_label': '168.w1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.w1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053137
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['336.o1.a1', '336.o1.a2', '336.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.i1.a1', '2.j1.b1'], 'contains': ['8.j1.a1', '8.l1.a1', '8.n1.a1', '12.bc1.a1', '28.bc1.a1'], 'core': '4.u1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [6, 192, 336, 672, 168, 448], 'label': '1344.8546.4.u1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.u1.a1', 'normal_contained_in': ['2.g1.a1', '2.i1.a1', '2.j1.b1'], 'normal_contains': ['8.j1.a1', '8.l1.a1', '8.n1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.u1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.u1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053138
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.z1.a1', '56.y1.a1', '84.g1.a1', '84.o1.a1', '84.t1.a1'], 'contains': ['336.g1.a1', '336.j1.a1', '336.l1.b1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [77, 338], 'label': '1344.8546.168.x1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.b1.a1', 'old_label': '168.x1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.x1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053139
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.z1.b1', '56.y1.b1', '84.g1.a1', '84.o1.a1', '84.t1.b1'], 'contains': ['336.g1.b1', '336.j1.a1', '336.l1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [338, 76], 'label': '1344.8546.168.x1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.b1.a1', 'old_label': '168.x1.b1', 'projective_image': None, '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': None}
  • id: 74053140
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '56.z1.a1', '84.h1.a1', '84.n1.a1', '84.t1.a1', '84.x1.a1', '84.z1.a1', '84.ba1.a1', '84.bb1.a1'], 'contains': ['336.b1.a1', '336.g1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [77, 336], 'label': '1344.8546.168.y1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '168.y1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.y1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053141
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.b1', '56.z1.b1', '84.h1.a1', '84.n1.b1', '84.t1.b1', '84.x1.b1', '84.z1.b1', '84.ba1.b1', '84.bb1.b1'], 'contains': ['336.b1.a1', '336.g1.b1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [76, 336], 'label': '1344.8546.168.y1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '168.y1.b1', 'projective_image': None, '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': None}
  • id: 74053142
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1.a1', '56.ba1.a1', '84.h1.a1', '84.o1.a1', '84.u1.a1'], 'contains': ['336.c1.a1', '336.g1.a1', '336.g1.b1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1, 76], 'label': '1344.8546.168.z1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '168.z1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.z1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053143
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bb1.a1', '56.bb1.a1', '84.i1.a1', '84.l1.a1', '84.r1.a1'], 'contains': ['336.c1.a1', '336.h1.a1', '336.m1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [1, 6], 'label': '1344.8546.168.ba1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '168.ba1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.ba1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053144
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bc1.a1', '56.bc1.a1', '84.e1.a1', '84.p1.a1', '84.r1.a1'], 'contains': ['336.h1.a1', '336.i1.a1', '336.k1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [5, 6], 'label': '1344.8546.168.bb1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '168.bb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053145
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bd1.a1', '56.bd1.a1', '84.i1.a1', '84.p1.a1', '84.s1.a1', '84.z1.a1', '84.z1.b1', '84.bc1.a1', '84.bc1.b1'], 'contains': ['336.b1.a1', '336.h1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [6, 336], 'label': '1344.8546.168.bc1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '168.bc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053146
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '56.be1.a1', '84.f1.a1', '84.p1.a1', '84.v1.a1', '84.ba1.a1', '84.ba1.b1', '84.bd1.a1', '84.bd1.b1'], 'contains': ['336.b1.a1', '336.k1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [5, 336], 'label': '1344.8546.168.bd1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '168.bd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053147
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.be1.a1', '56.bf1.a1', '84.j1.a1', '84.n1.a1', '84.t1.b1', '84.y1.a1', '84.bc1.a1', '84.bd1.a1', '84.be1.a1'], 'contains': ['336.b1.a1', '336.l1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [974, 336], 'label': '1344.8546.168.be1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '168.be1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.be1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053148
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['336.n1.a1', '336.o1.a2', '336.o1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.i1.b1', '2.j1.a1'], 'contains': ['8.j1.a1', '8.l1.b1', '8.n1.b1', '12.bc1.b1', '28.bc1.b1'], 'core': '4.u1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 192, 336, 672, 6, 448], 'label': '1344.8546.4.u1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.u1.b1', 'normal_contained_in': ['2.g1.a1', '2.i1.b1', '2.j1.a1'], 'normal_contains': ['8.j1.a1', '8.l1.b1', '8.n1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.u1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.u1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053149
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.be1.b1', '56.bf1.b1', '84.j1.a1', '84.n1.b1', '84.t1.a1', '84.y1.b1', '84.bc1.b1', '84.bd1.b1', '84.be1.b1'], 'contains': ['336.b1.a1', '336.l1.b1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [975, 336], 'label': '1344.8546.168.be1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '168.be1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.be1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053150
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bf1.a1', '56.bg1.a1', '84.i1.a1', '84.m1.a1', '84.v1.a1', '84.bb1.a1', '84.bb1.b1', '84.be1.a1', '84.be1.b1'], 'contains': ['336.b1.a1', '336.m1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [7, 336], 'label': '1344.8546.168.bf1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '168.bf1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bf1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053151
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.s1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bg1.a1', '56.i1.a1', '84.k1.a1', '84.q1.b1', '84.w1.a1', '84.y1.a1', '84.z1.b1', '84.bb1.a1', '84.bd1.b1'], 'contains': ['336.b1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [730], 'label': '1344.8546.168.bg1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '168.bg1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bg1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053152
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bg1.b1', '56.i1.b1', '84.k1.a1', '84.q1.a1', '84.w1.b1', '84.y1.b1', '84.z1.a1', '84.bb1.b1', '84.bd1.a1'], 'contains': ['336.b1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [731], 'label': '1344.8546.168.bg1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '168.bg1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bg1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053153
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bh1.a1', '56.bh1.a1', '84.j1.a1', '84.o1.a1', '84.u1.a1'], 'contains': ['336.c1.a1', '336.l1.a1', '336.l1.b1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [1, 974], 'label': '1344.8546.168.bh1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.b1.a1', 'old_label': '168.bh1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bh1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053154
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '168.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bi1.a1', '56.bi1.a1', '84.e1.a1', '84.l1.a1', '84.v1.a1'], 'contains': ['336.j1.a1', '336.k1.a1', '336.m1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [5, 338], 'label': '1344.8546.168.bi1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '168.bi1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bi1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053155
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '192.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.c1.a1', 'complements': ['7.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.a1.a1', '96.b1.a1', '96.c1.a1', '96.d1.a1', '96.e1.a1', '96.f1.a1', '96.f1.b1', '96.g1.a1'], 'contains': ['1344.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [192], 'label': '1344.8546.192.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1.a1', 'normal_contained_in': ['64.a1.a1', '96.a1.a1'], 'normal_contains': ['1344.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053156
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '224.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '112.a1.a1', '112.b1.a1', '112.c1.a1', '112.d1.a1', '112.e1.a1', '112.f1.a1', '112.g1.a1', '112.h1.a1', '112.i1.a1', '112.i1.b1', '112.j1.a1', '112.k1.a1', '112.l1.a1', '112.l1.b1', '112.m1.a1'], 'contains': ['448.a1.a1', '672.a1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [672, 448], 'label': '1344.8546.224.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '224.a1.a1', 'normal_contained_in': ['32.a1.a1', '112.a1.a1', '112.b1.a1', '112.c1.a1', '112.e1.a1', '112.d1.a1', '112.f1.a1', '112.g1.a1'], 'normal_contains': ['448.a1.a1', '672.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '224.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053157
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '224.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '112.a1.a1', '112.n1.a1', '112.o1.a1', '112.o1.a2'], 'contains': ['448.a1.a1', '672.b1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1009, 448], 'label': '1344.8546.224.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '224.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053158
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '224.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '112.b1.a1', '112.n1.a1'], 'contains': ['448.a1.a1', '672.c1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1011, 448], 'label': '1344.8546.224.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '224.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053159
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['336.p1.a1', '336.p1.a2', '336.o1.a1', '336.o1.a2', '336.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.i1.a1', '2.k1.b1'], 'contains': ['8.k1.a1', '8.l1.a1', '8.o1.b1', '12.bd1.a1', '28.bd1.a1'], 'core': '4.v1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [5, 192, 1008, 672, 974, 448], 'label': '1344.8546.4.v1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.v1.a1', 'normal_contained_in': ['2.e1.a1', '2.i1.a1', '2.k1.b1'], 'normal_contains': ['8.k1.a1', '8.l1.a1', '8.o1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.v1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.v1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053160
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '224.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '112.c1.a1', '112.n1.a1', '112.p1.a1', '112.p1.a2'], 'contains': ['448.a1.a1', '672.d1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [2, 448], 'label': '1344.8546.224.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '224.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053161
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '224.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '112.h1.a1', '112.p1.a1', '112.p1.a2'], 'contains': ['448.a1.a1', '672.e1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [4, 448], 'label': '1344.8546.224.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.s1.a1', 'old_label': '224.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053162
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '224.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '112.i1.a1', '112.o1.a1', '112.o1.a2'], 'contains': ['448.a1.a1', '672.f1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [77, 448], 'label': '1344.8546.224.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.j1.a1', 'old_label': '224.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053163
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '224.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.b1', '112.i1.b1', '112.o1.a1', '112.o1.a2'], 'contains': ['448.a1.a1', '672.f1.b1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [76, 448], 'label': '1344.8546.224.f1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.j1.a1', 'old_label': '224.f1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.f1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053165
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '336.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '112.a1.a1', '168.a1.a1', '168.c1.a1', '168.d1.a1', '168.e1.a1', '168.f1.a1', '168.g1.a1', '168.h1.a1'], 'contains': ['672.a1.a1', '672.b1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1009, 672], 'label': '1344.8546.336.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '336.a1.a1', 'normal_contained_in': ['48.a1.a1', '112.a1.a1', '168.a1.a1'], 'normal_contains': ['672.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '336.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053166
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '336.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '112.d1.a1', '168.a1.a1', '168.b1.a1', '168.b1.b1', '168.l1.a1', '168.p1.a1', '168.v1.a1', '168.y1.a1', '168.y1.b1', '168.bc1.a1', '168.bd1.a1', '168.be1.a1', '168.be1.b1', '168.bf1.a1', '168.bg1.a1', '168.bg1.b1'], 'contains': ['672.a1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [336], 'label': '1344.8546.336.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '336.b1.a1', 'normal_contained_in': ['48.b1.a1', '112.d1.a1', '168.a1.a1', '168.b1.a1', '168.b1.b1'], 'normal_contains': ['672.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '336.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053167
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '336.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '112.e1.a1', '168.a1.a1', '168.m1.a1', '168.q1.a1', '168.t1.a1', '168.z1.a1', '168.ba1.a1', '168.bh1.a1'], 'contains': ['672.a1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1], 'label': '1344.8546.336.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '336.c1.a1', 'normal_contained_in': ['48.c1.a1', '112.e1.a1', '168.a1.a1'], 'normal_contains': ['672.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '336.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053168
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '336.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '112.b1.a1', '168.c1.a1', '168.i1.a1', '168.j1.a1', '168.j1.b1', '168.k1.a1', '168.l1.a1', '168.m1.a1'], 'contains': ['672.a1.a1', '672.c1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1011, 672], 'label': '1344.8546.336.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '336.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053169
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '336.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '112.c1.a1', '168.c1.a1', '168.n1.a1', '168.o1.a1', '168.o1.b1', '168.p1.a1', '168.q1.a1', '168.r1.a1'], 'contains': ['672.a1.a1', '672.d1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2, 672], 'label': '1344.8546.336.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '336.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053170
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '2.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '224.a1.a1', 'complements': ['672.d1.a1', '672.g1.a1', '672.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.a1', '4.f1.a1', '4.p1.a1', '4.p1.b1', '4.s1.a1', '4.s1.b1', '6.a1.a1', '14.d1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 672, 168, 448, 4, 192, 1008], 'label': '1344.8546.2.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.c1.a1', '4.f1.a1', '4.p1.a1', '4.p1.b1', '4.s1.a1', '4.s1.b1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053171
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['336.p1.a1', '336.p1.a2', '336.n1.a1', '336.o1.a1', '336.o1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.i1.b1', '2.k1.a1'], 'contains': ['8.k1.a1', '8.l1.b1', '8.o1.a1', '12.bd1.b1', '28.bd1.b1'], 'core': '4.v1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [5, 192, 1008, 672, 730, 448], 'label': '1344.8546.4.v1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.v1.b1', 'normal_contained_in': ['2.e1.a1', '2.i1.b1', '2.k1.a1'], 'normal_contains': ['8.k1.a1', '8.l1.b1', '8.o1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.v1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.v1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053172
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '336.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '28.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '112.h1.a1', '168.d1.a1', '168.i1.a1', '168.n1.a1', '168.s1.a1', '168.t1.a1', '168.u1.a1', '168.v1.a1'], 'contains': ['672.a1.a1', '672.e1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [4, 672], 'label': '1344.8546.336.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '336.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053173
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '336.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '28.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '112.i1.a1', '168.e1.a1', '168.j1.a1', '168.o1.a1', '168.w1.a1', '168.x1.a1', '168.y1.a1', '168.z1.a1'], 'contains': ['672.a1.a1', '672.f1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [77, 672], 'label': '1344.8546.336.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '336.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053174
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '336.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '28.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.b1', '112.i1.b1', '168.e1.a1', '168.j1.b1', '168.o1.b1', '168.w1.b1', '168.x1.b1', '168.y1.b1', '168.z1.a1'], 'contains': ['672.a1.a1', '672.f1.b1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [76, 672], 'label': '1344.8546.336.g1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '336.g1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.g1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053175
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '336.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '112.j1.a1', '168.f1.a1', '168.k1.a1', '168.n1.a1', '168.s1.a1', '168.ba1.a1', '168.bb1.a1', '168.bc1.a1'], 'contains': ['672.a1.a1', '672.g1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [6, 672], 'label': '1344.8546.336.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '336.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053176
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '336.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '112.f1.a1', '168.g1.a1', '168.l1.a1', '168.q1.a1', '168.u1.a1', '168.w1.a1', '168.w1.b1', '168.bb1.a1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [3], 'label': '1344.8546.336.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '336.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053177
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '336.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '112.g1.a1', '168.g1.a1', '168.m1.a1', '168.p1.a1', '168.s1.a1', '168.x1.a1', '168.x1.b1', '168.bi1.a1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [338], 'label': '1344.8546.336.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '336.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053178
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '336.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '28.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.a1', '112.k1.a1', '168.d1.a1', '168.k1.a1', '168.r1.a1', '168.t1.a1', '168.bb1.a1', '168.bd1.a1', '168.bi1.a1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [5], 'label': '1344.8546.336.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '336.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053179
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '336.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.l1.a1', '112.l1.a1', '168.h1.a1', '168.j1.a1', '168.o1.b1', '168.w1.a1', '168.x1.b1', '168.be1.a1', '168.bh1.a1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [974], 'label': '1344.8546.336.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.b1.a1', 'old_label': '336.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053180
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '336.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.l1.b1', '112.l1.b1', '168.h1.a1', '168.j1.b1', '168.o1.a1', '168.w1.b1', '168.x1.a1', '168.be1.b1', '168.bh1.a1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [975], 'label': '1344.8546.336.l1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.b1.a1', 'old_label': '336.l1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.l1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053181
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '336.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.m1.a1', '112.m1.a1', '168.f1.a1', '168.i1.a1', '168.r1.a1', '168.u1.a1', '168.ba1.a1', '168.bf1.a1', '168.bi1.a1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [7], 'label': '1344.8546.336.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '336.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053182
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['336.p1.a1', '336.p1.a2', '336.o1.a2', '336.o1.a1', '336.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.h1.a1', '2.k1.b1'], 'contains': ['8.l1.a1', '8.m1.a1', '8.n1.b1', '12.be1.a1', '28.be1.a1'], 'core': '4.w1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 192, 336, 672, 974, 448], 'label': '1344.8546.4.w1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.a1', 'normal_contained_in': ['2.g1.a1', '2.h1.a1', '2.k1.b1'], 'normal_contains': ['8.m1.a1', '8.l1.a1', '8.n1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.w1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.w1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053188
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '448.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.d1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '224.a1.a1', '224.b1.a1', '224.c1.a1', '224.d1.a1', '224.e1.a1', '224.f1.a1', '224.f1.b1', '224.g1.a1'], 'contains': ['1344.a1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [448], 'label': '1344.8546.448.a1.a1', 'mobius_quo': None, 'mobius_sub': None, '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': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '448.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053189
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '672.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '224.a1.a1', '336.a1.a1', '336.b1.a1', '336.c1.a1', '336.d1.a1', '336.e1.a1', '336.f1.a1', '336.g1.a1', '336.g1.b1', '336.h1.a1', '336.i1.a1', '336.j1.a1', '336.k1.a1', '336.l1.a1', '336.l1.b1', '336.m1.a1'], 'contains': ['1344.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [672], 'label': '1344.8546.672.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '672.a1.a1', 'normal_contained_in': ['96.a1.a1', '224.a1.a1', '336.a1.a1', '336.c1.a1', '336.b1.a1'], 'normal_contains': ['1344.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '672.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053190
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '672.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1.a1', '224.b1.a1', '336.a1.a1', '336.n1.a1', '336.o1.a1', '336.o1.a2'], 'contains': ['1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1009], 'label': '1344.8546.672.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '336.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '672.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053191
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '672.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.c1.a1', '224.c1.a1', '336.d1.a1', '336.n1.a1'], 'contains': ['1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1011], 'label': '1344.8546.672.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '672.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053192
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '672.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.d1.a1', '224.d1.a1', '336.e1.a1', '336.n1.a1', '336.p1.a1', '336.p1.a2'], 'contains': ['1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [2], 'label': '1344.8546.672.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '672.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053193
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['336.p1.a1', '336.p1.a2', '336.o1.a2', '336.o1.a1', '336.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.h1.b1', '2.k1.a1'], 'contains': ['8.l1.b1', '8.m1.a1', '8.n1.a1', '12.be1.b1', '28.be1.b1'], 'core': '4.w1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [7, 192, 1008, 672, 168, 448], 'label': '1344.8546.4.w1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.b1', 'normal_contained_in': ['2.g1.a1', '2.h1.b1', '2.k1.a1'], 'normal_contains': ['8.m1.a1', '8.l1.b1', '8.n1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.w1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.w1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053194
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '672.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '28.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.e1.a1', '224.e1.a1', '336.f1.a1', '336.p1.a1', '336.p1.a2'], 'contains': ['1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [4], 'label': '1344.8546.672.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.s1.a1', 'old_label': '672.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053195
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '672.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '28.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.f1.a1', '224.f1.a1', '336.g1.a1', '336.o1.a1', '336.o1.a2'], 'contains': ['1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [77], 'label': '1344.8546.672.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.j1.a1', 'old_label': '672.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053196
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '672.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '28.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.f1.b1', '224.f1.b1', '336.g1.b1', '336.o1.a1', '336.o1.a2'], 'contains': ['1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [76], 'label': '1344.8546.672.f1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.j1.a1', 'old_label': '672.f1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.f1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053197
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '672.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.g1.a1', '224.g1.a1', '336.h1.a1', '336.p1.a1', '336.p1.a2'], 'contains': ['1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': None, 'generators': [6], 'label': '1344.8546.672.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.r1.a1', 'old_label': '672.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053198
    {'ambient': '1344.8546', '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.d1.a1', '672.e1.a1', '672.f1.a1', '672.f1.b1', '672.g1.a1'], 'contains': [], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [], 'label': '1344.8546.1344.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1344.a1.a1', 'normal_contained_in': ['192.a1.a1', '448.a1.a1', '672.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '1344.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1344.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053199
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.p1.a1', '8.r1.a1', '8.t1.a1', '8.v1.a1', '8.w1.a1', '8.y1.a1', '12.f1.a1', '28.f1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1009, 192, 4, 672, 2, 448], 'label': '1344.8546.4.x1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.x1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.x1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053200
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.a1.a1', '8.q1.a1', '8.s1.a1', '8.u1.a1', '8.u1.b1', '8.x1.a1', '8.x1.b1', '12.g1.a1', '28.g1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1009, 192, 76, 672, 2, 448], 'label': '1344.8546.4.y1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.y1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.y1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053201
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.c1.a1', '8.p1.a1', '8.r1.a1', '8.z1.a1', '8.bb1.a1', '8.bg1.a1', '8.bi1.a1', '12.i1.a1', '28.h1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1009, 192, 4, 672, 338, 448], 'label': '1344.8546.4.z1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.z1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.z1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053202
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.c1.a1', '8.q1.a1', '8.s1.a1', '8.bc1.a1', '8.bc1.b1', '8.bd1.a1', '8.bd1.b1', '12.j1.a1', '28.j1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1009, 192, 76, 672, 338, 448], 'label': '1344.8546.4.ba1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.ba1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.ba1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053203
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.e1.a1', '8.t1.a1', '8.v1.a1', '8.z1.a1', '8.ba1.a1', '8.bf1.a1', '8.bi1.a1', '12.n1.a1', '28.n1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 192, 4, 672, 338, 448], 'label': '1344.8546.4.bb1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.bb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053204
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.e1.a1', '8.u1.a1', '8.u1.b1', '8.bd1.a1', '8.bd1.b1', '8.be1.a1', '8.bh1.a1', '12.q1.a1', '28.q1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 192, 76, 672, 338, 448], 'label': '1344.8546.4.bc1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.bc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053205
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.g1.a1', '8.w1.a1', '8.y1.a1', '8.ba1.a1', '8.bb1.a1', '8.bf1.a1', '8.bg1.a1', '12.t1.a1', '28.s1.a1'], 'core': '8.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 192, 4, 672, 2, 448], 'label': '1344.8546.4.bd1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.bd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053206
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '2.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['672.f1.b1', '672.d1.a1', '672.g1.a1', '672.f1.a1', '672.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.e1.a1', '4.g1.a1', '4.q1.a1', '4.q1.b1', '4.v1.a1', '4.v1.b1', '6.e1.a1', '14.e1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 448, 4, 336, 730, 192, 672], 'label': '1344.8546.2.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.e1.a1', '4.g1.a1', '4.q1.a1', '4.q1.b1', '4.v1.a1', '4.v1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053207
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '4.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.g1.a1', '8.x1.a1', '8.x1.b1', '8.bc1.a1', '8.bc1.b1', '8.be1.a1', '8.bh1.a1', '12.w1.a1', '28.v1.a1'], 'core': '8.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 192, 76, 672, 2, 448], 'label': '1344.8546.4.be1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.be1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.be1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053208
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '6.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.f1.a1', 'complements': ['224.d1.a1', '224.g1.a1', '224.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.c1.a1', '12.d1.a1', '12.d1.b1', '12.e1.a1', '12.e1.b1', '42.d1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 192, 168, 1008, 4, 672], 'label': '1344.8546.6.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.d1.a1'], 'normal_contains': ['12.a1.a1', '12.b1.a1', '12.c1.a1', '12.d1.a1', '12.d1.b1', '12.e1.a1', '12.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053209
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.f1.a1', '12.h1.a1', '12.i1.a1', '12.k1.a1', '12.n1.a1', '12.o1.a1', '12.r1.a1', '12.t1.a1', '12.u1.a1', '12.x1.a1', '42.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 192, 4, 336, 2, 672], 'label': '1344.8546.6.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053210
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.g1.a1', '12.h1.a1', '12.j1.a1', '12.l1.a1', '12.p1.a1', '12.p1.b1', '12.q1.a1', '12.v1.a1', '12.v1.b1', '12.w1.a1', '42.b1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 192, 76, 336, 2, 672], 'label': '1344.8546.6.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053211
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.h1.a1', '12.m1.a1', '12.s1.a1', '12.s1.b1', '12.y1.a1', '12.y1.b1', '42.c1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 672, 168, 192, 2, 336], 'label': '1344.8546.6.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053212
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.l1.a1', '12.m1.a1', '12.z1.a1', '12.z1.b1', '12.bd1.a1', '12.bd1.b1', '42.e1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 192, 4, 336, 730, 672], 'label': '1344.8546.6.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053213
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.k1.a1', '12.m1.a1', '12.ba1.a1', '12.ba1.b1', '12.bb1.a1', '12.bb1.b1', '42.f1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 192, 76, 336, 730, 672], 'label': '1344.8546.6.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053214
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.k1.a1', '12.l1.a1', '12.bc1.a1', '12.bc1.b1', '12.be1.a1', '12.be1.b1', '42.g1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 192, 168, 336, 6, 672], 'label': '1344.8546.6.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053215
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.h1.a1', '3.a1.a1'], 'contains': ['12.d1.a1', '12.o1.a1', '12.p1.a1', '12.s1.b1', '12.z1.a1', '12.bb1.a1', '12.be1.a1', '42.h1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [169, 192, 4, 336, 730, 672], 'label': '1344.8546.6.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053216
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.h1.b1', '3.a1.a1'], 'contains': ['12.d1.b1', '12.o1.a1', '12.p1.b1', '12.s1.a1', '12.z1.b1', '12.bb1.b1', '12.be1.b1', '42.h1.b1'], 'core': '12.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [3, 192, 168, 1008, 4, 672], 'label': '1344.8546.6.h1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.h1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053217
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '2.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['672.e1.a1', '672.d1.a1', '672.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.d1.a1', '4.g1.a1', '4.r1.a1', '4.r1.b1', '4.t1.a1', '4.t1.b1', '6.f1.a1', '14.f1.a1'], 'core': '2.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 448, 76, 336, 730, 192, 672], 'label': '1344.8546.2.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.d1.a1', '4.g1.a1', '4.r1.a1', '4.r1.b1', '4.t1.a1', '4.t1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053218
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.i1.a1', '3.a1.a1'], 'contains': ['12.e1.a1', '12.p1.a1', '12.r1.a1', '12.s1.a1', '12.ba1.a1', '12.bc1.a1', '12.bd1.a1', '42.i1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [5, 192, 168, 336, 6, 672], 'label': '1344.8546.6.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053219
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.i1.b1', '3.a1.a1'], 'contains': ['12.e1.b1', '12.p1.b1', '12.r1.a1', '12.s1.b1', '12.ba1.b1', '12.bc1.b1', '12.bd1.b1', '42.i1.b1'], 'core': '12.e1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [169, 192, 76, 336, 730, 672], 'label': '1344.8546.6.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053220
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '6.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.j1.a1', '3.a1.a1'], 'contains': ['12.d1.a1', '12.u1.a1', '12.v1.a1', '12.y1.b1', '12.z1.b1', '12.ba1.a1', '12.bc1.b1', '42.j1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [169, 192, 4, 336, 2, 672], 'label': '1344.8546.6.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053221
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '6.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.j1.b1', '3.a1.a1'], 'contains': ['12.d1.b1', '12.u1.a1', '12.v1.b1', '12.y1.a1', '12.z1.a1', '12.ba1.b1', '12.bc1.a1', '42.j1.b1'], 'core': '12.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2, 192, 168, 1008, 4, 672], 'label': '1344.8546.6.j1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.j1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.j1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053222
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '6.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.k1.a1', '3.a1.a1'], 'contains': ['12.e1.a1', '12.v1.a1', '12.x1.a1', '12.y1.a1', '12.bb1.a1', '12.bd1.b1', '12.be1.b1', '42.k1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [5, 192, 168, 336, 2, 672], 'label': '1344.8546.6.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053223
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '6.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.k1.b1', '3.a1.a1'], 'contains': ['12.e1.b1', '12.v1.b1', '12.x1.a1', '12.y1.b1', '12.bb1.b1', '12.bd1.a1', '12.be1.a1', '42.k1.b1'], 'core': '12.e1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [169, 192, 76, 336, 2, 672], 'label': '1344.8546.6.k1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.k1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.k1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.k1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053224
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '7.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['14.a1.a1', '14.b1.a1', '14.c1.a1', '14.d1.a1', '14.e1.a1', '14.f1.a1', '14.g1.a1', '14.h1.a1', '14.h1.b1', '14.i1.a1', '14.i1.b1', '14.j1.a1', '14.j1.b1', '14.k1.a1', '14.k1.b1', '21.a1.a1'], 'core': '14.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 672, 1008, 2, 448, 4, 168], 'label': '1344.8546.7.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '7.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053225
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.x1.a1', '4.y1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.n1.a1', '24.f1.a1', '56.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1009, 672, 192, 2, 448], 'label': '1344.8546.8.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '56.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053226
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['16.a1.a1', '16.d1.a1', '16.e1.a1', '24.a1.a1', '56.b1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 448, 192, 336, 672], 'label': '1344.8546.8.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'normal_contains': ['16.a1.a1', '16.e1.a1', '16.d1.a1', '24.a1.a1', '56.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053227
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.z1.a1', '4.ba1.a1'], 'contains': ['16.a1.a1', '16.f1.a1', '16.g1.a1', '24.j1.a1', '56.c1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1009, 192, 672, 338, 448], 'label': '1344.8546.8.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '16.f1.a1', '16.g1.a1', '56.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053228
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '2.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['672.e1.a1', '672.f1.b1', '672.d1.a1', '672.f1.a1', '672.c1.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': None, 'generators': [1, 448, 168, 336, 6, 192, 672], 'label': '1344.8546.2.g1.a1', 'mobius_quo': None, 'mobius_sub': None, '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': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053229
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.h1.a1', '4.i1.a1', '4.i1.b1', '4.j1.a1', '4.k1.a1', '4.k1.b1'], 'contains': ['16.b1.a1', '16.d1.a1', '16.f1.a1', '24.o1.a1', '56.d1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [3, 192, 672, 336, 448], 'label': '1344.8546.8.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1.a1', 'normal_contained_in': ['4.a1.a1', '4.h1.a1', '4.i1.a1', '4.i1.b1', '4.j1.a1', '4.k1.a1', '4.k1.b1'], 'normal_contains': ['16.b1.a1', '16.d1.a1', '16.f1.a1', '56.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053230
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.bb1.a1', '4.bc1.a1'], 'contains': ['16.b1.a1', '16.e1.a1', '16.g1.a1', '24.p1.a1', '56.e1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 192, 672, 338, 448], 'label': '1344.8546.8.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.b1.a1', '16.e1.a1', '16.g1.a1', '56.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053231
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.l1.a1', '4.m1.a1', '4.m1.b1', '4.n1.a1', '4.o1.a1', '4.o1.b1'], 'contains': ['16.c1.a1', '16.d1.a1', '16.g1.a1', '24.s1.a1', '56.f1.a1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [2, 192, 672, 336, 448], 'label': '1344.8546.8.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1.a1', 'normal_contained_in': ['4.a1.a1', '4.l1.a1', '4.m1.a1', '4.m1.b1', '4.n1.a1', '4.o1.a1', '4.o1.b1'], 'normal_contains': ['16.c1.a1', '16.d1.a1', '16.g1.a1', '56.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053232
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.bd1.a1', '4.be1.a1'], 'contains': ['16.c1.a1', '16.e1.a1', '16.f1.a1', '24.t1.a1', '56.g1.a1'], 'core': '8.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 192, 672, 2, 448], 'label': '1344.8546.8.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.c1.a1', '16.e1.a1', '16.f1.a1', '56.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053233
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.h1.a1', '4.l1.a1', '4.p1.a1', '4.p1.b1', '4.q1.a1', '4.q1.b1'], 'contains': ['16.d1.a1', '16.h1.a1', '24.b1.a1', '56.w1.a1'], 'core': '8.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [4, 448, 672, 336, 192], 'label': '1344.8546.8.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.a1', 'normal_contained_in': ['4.b1.a1', '4.h1.a1', '4.l1.a1', '4.p1.a1', '4.p1.b1', '4.q1.a1', '4.q1.b1'], 'normal_contains': ['16.d1.a1', '24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053234
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.i1.a1', '4.m1.a1', '4.p1.a1', '4.r1.a1', '4.s1.a1', '4.t1.a1'], 'contains': ['16.d1.a1', '16.i1.a1', '24.c1.a1', '56.z1.a1'], 'core': '8.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [77, 448, 672, 336, 192], 'label': '1344.8546.8.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.a1', 'normal_contained_in': ['4.c1.a1', '4.i1.a1', '4.m1.a1', '4.p1.a1', '4.r1.a1', '4.s1.a1', '4.t1.a1'], 'normal_contains': ['16.d1.a1', '24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053235
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.i1.b1', '4.m1.b1', '4.p1.b1', '4.r1.b1', '4.s1.b1', '4.t1.b1'], 'contains': ['16.d1.a1', '16.i1.b1', '24.c1.b1', '56.z1.b1'], 'core': '8.i1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [76, 448, 672, 336, 192], 'label': '1344.8546.8.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.b1', 'normal_contained_in': ['4.c1.a1', '4.i1.b1', '4.m1.b1', '4.p1.b1', '4.r1.b1', '4.s1.b1', '4.t1.b1'], 'normal_contains': ['16.d1.a1', '24.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053236
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.j1.a1', '4.l1.a1', '4.r1.a1', '4.r1.b1', '4.u1.a1', '4.u1.b1'], 'contains': ['16.d1.a1', '16.j1.a1', '24.bd1.a1', '56.bd1.a1'], 'core': '8.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [6, 672, 448, 336, 192], 'label': '1344.8546.8.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': ['4.d1.a1', '4.j1.a1', '4.l1.a1', '4.r1.a1', '4.r1.b1', '4.u1.a1', '4.u1.b1'], 'normal_contains': ['16.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053237
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.j1.a1', '4.n1.a1', '4.s1.a1', '4.s1.b1', '4.v1.a1', '4.v1.b1'], 'contains': ['16.d1.a1', '16.k1.a1', '24.d1.a1', '56.be1.a1'], 'core': '8.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [5, 448, 672, 336, 192], 'label': '1344.8546.8.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': ['4.b1.a1', '4.j1.a1', '4.n1.a1', '4.s1.a1', '4.s1.b1', '4.v1.a1', '4.v1.b1'], 'normal_contains': ['16.d1.a1', '24.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053238
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.i1.a1', '4.m1.b1', '4.q1.a1', '4.u1.a1', '4.v1.a1', '4.w1.a1'], 'contains': ['16.d1.a1', '16.l1.a1', '24.be1.a1', '56.bf1.a1'], 'core': '8.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [974, 672, 448, 336, 192], 'label': '1344.8546.8.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.a1', 'normal_contained_in': ['4.e1.a1', '4.i1.a1', '4.m1.b1', '4.q1.a1', '4.u1.a1', '4.v1.a1', '4.w1.a1'], 'normal_contains': ['16.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053239
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '2.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['672.f1.b1', '672.d1.a1', '672.g1.a1', '672.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.h1.a1', '4.i1.a1', '4.k1.b1', '4.p1.a1', '4.q1.a1', '4.t1.a1', '4.w1.a1', '6.h1.a1', '14.h1.a1'], 'core': '2.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 448, 4, 336, 730, 192, 672], 'label': '1344.8546.2.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.h1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.h1.a1', '4.i1.a1', '4.k1.b1', '4.p1.a1', '4.q1.a1', '4.t1.a1', '4.w1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053240
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.i1.b1', '4.m1.a1', '4.q1.b1', '4.u1.b1', '4.v1.b1', '4.w1.b1'], 'contains': ['16.d1.a1', '16.l1.b1', '24.be1.b1', '56.bf1.b1'], 'core': '8.l1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [975, 672, 448, 336, 192], 'label': '1344.8546.8.l1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.b1', 'normal_contained_in': ['4.e1.a1', '4.i1.b1', '4.m1.a1', '4.q1.b1', '4.u1.b1', '4.v1.b1', '4.w1.b1'], 'normal_contains': ['16.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.l1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053241
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.h1.a1', '4.n1.a1', '4.t1.a1', '4.t1.b1', '4.w1.a1', '4.w1.b1'], 'contains': ['16.d1.a1', '16.m1.a1', '24.bf1.a1', '56.bg1.a1'], 'core': '8.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [7, 672, 448, 336, 192], 'label': '1344.8546.8.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.m1.a1', 'normal_contained_in': ['4.d1.a1', '4.h1.a1', '4.n1.a1', '4.t1.a1', '4.t1.b1', '4.w1.a1', '4.w1.b1'], 'normal_contains': ['16.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053242
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.n1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.k1.a1', '4.o1.a1', '4.p1.b1', '4.s1.a1', '4.u1.a1', '4.w1.b1'], 'contains': ['16.d1.a1', '24.e1.a1', '56.h1.a1'], 'core': '8.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [168, 192, 336, 448, 672], 'label': '1344.8546.8.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.n1.a1', 'normal_contained_in': ['4.f1.a1', '4.k1.a1', '4.o1.a1', '4.p1.b1', '4.s1.a1', '4.u1.a1', '4.w1.b1'], 'normal_contains': ['16.d1.a1', '24.e1.a1', '56.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053243
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.n1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.k1.b1', '4.o1.b1', '4.p1.a1', '4.s1.b1', '4.u1.b1', '4.w1.a1'], 'contains': ['16.d1.a1', '24.e1.b1', '56.h1.b1'], 'core': '8.n1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 192, 336, 448, 672], 'label': '1344.8546.8.n1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.n1.b1', 'normal_contained_in': ['4.f1.a1', '4.k1.b1', '4.o1.b1', '4.p1.a1', '4.s1.b1', '4.u1.b1', '4.w1.a1'], 'normal_contains': ['16.d1.a1', '24.e1.b1', '56.h1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.n1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053244
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.k1.b1', '4.o1.a1', '4.q1.a1', '4.r1.b1', '4.t1.a1', '4.v1.b1'], 'contains': ['16.d1.a1', '24.bg1.a1', '56.i1.a1'], 'core': '8.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [730, 336, 672, 192, 448], 'label': '1344.8546.8.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.o1.a1', 'normal_contained_in': ['4.g1.a1', '4.k1.b1', '4.o1.a1', '4.q1.a1', '4.r1.b1', '4.t1.a1', '4.v1.b1'], 'normal_contains': ['16.d1.a1', '56.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053245
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.k1.a1', '4.o1.b1', '4.q1.b1', '4.r1.a1', '4.t1.b1', '4.v1.a1'], 'contains': ['16.d1.a1', '24.bg1.b1', '56.i1.b1'], 'core': '8.o1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [731, 336, 672, 192, 448], 'label': '1344.8546.8.o1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.o1.b1', 'normal_contained_in': ['4.g1.a1', '4.k1.a1', '4.o1.b1', '4.q1.b1', '4.r1.a1', '4.t1.b1', '4.v1.a1'], 'normal_contains': ['16.d1.a1', '56.i1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.o1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.o1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053246
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.x1.a1', '4.z1.a1'], 'contains': ['16.a1.a1', '16.h1.a1', '16.k1.a1', '24.g1.a1', '56.j1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1009, 448, 672, 4, 192], 'label': '1344.8546.8.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053247
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.y1.a1', '4.ba1.a1'], 'contains': ['16.a1.a1', '16.i1.a1', '16.i1.b1', '16.o1.a1', '16.o1.a2', '24.h1.a1', '56.k1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1009, 672, 448, 76, 192], 'label': '1344.8546.8.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053248
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.x1.a1', '4.z1.a1'], 'contains': ['16.a1.a1', '16.j1.a1', '16.m1.a1', '24.i1.a1', '56.l1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1009, 672, 448, 6, 192], 'label': '1344.8546.8.r1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.r1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.r1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74053249
    {'ambient': '1344.8546', 'aut_centralizer_order': None, 'aut_label': '8.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.y1.a1', '4.ba1.a1'], 'contains': ['16.a1.a1', '16.l1.a1', '16.l1.b1', '24.k1.a1', '56.m1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1009, 672, 448, 974, 192], 'label': '1344.8546.8.s1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.s1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.s1.a1', 'subgroup_fusion': None, 'weyl_group': None}