Abstract group data - 128.1717

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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': '32.45', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [4, 4, 4, 4, 4, 4, 4, 4], 'aut_gens': [[1, 2, 4, 16], [73, 43, 4, 60], [73, 99, 68, 60], [73, 102, 4, 16], [1, 38, 68, 24], [65, 99, 76, 92], [65, 35, 68, 124], [73, 71, 68, 84], [65, 71, 68, 20]], 'aut_group': None, 'aut_hash': 6561509423110919394, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 2048, 'aut_permdeg': 32, 'aut_perms': [144269743097675971150054875320814745, 212102216686712230522211567927693286, 237355701091288425417959560851616224, 153252272604646558629810331995011928, 136046836513622598016305931321788797, 144196637566607498154494123335474036, 101143478443740490068486844148537116, 17048802623296319646981893359125486], 'aut_phi_ratio': 32.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 4, 1, 1], [4, 1, 4, 1], [4, 2, 2, 2], [4, 4, 1, 3], [4, 4, 4, 2], [8, 2, 8, 1], [8, 4, 4, 1], [8, 4, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^9.C_2^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': None, 'autcent_hash': 1718285292446712970, 'autcent_nilpotent': True, 'autcent_order': 512, 'autcent_solvable': True, 'autcent_split': None, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^9', 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': 4, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 4, 1], [4, 1, 4], [4, 2, 4], [4, 4, 11], [8, 2, 8], [8, 4, 12]], 'center_label': '8.2', 'center_order': 8, 'central_product': False, 'central_quotient': '16.14', 'commutator_count': 1, 'commutator_label': '4.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 1717, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 4, 1, 1], [4, 1, 2, 2], [4, 2, 1, 2], [4, 2, 2, 1], [4, 4, 1, 11], [8, 2, 4, 2], [8, 4, 2, 6]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 40320, 'exponent': 8, 'exponents_of_order': [7], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '16.14', 'hash': 1717, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 2, 2, 2], 'inner_gens': [[1, 66, 4, 88], [65, 2, 76, 16], [1, 74, 4, 16], [73, 2, 4, 16]], 'inner_hash': 14, 'inner_nilpotent': True, 'inner_order': 16, 'inner_split': None, 'inner_tex': 'C_2^4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 8], [4, 4]], 'label': '128.1717', 'linC_count': 32, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 6, 'linQ_dim': 16, 'linQ_dim_count': 8, 'linR_count': 12, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C4^2.C2^3', 'ngens': 4, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 16, 'number_characteristic_subgroups': 28, 'number_conjugacy_classes': 44, 'number_divisions': 29, 'number_normal_subgroups': 126, 'number_subgroup_autclasses': 82, 'number_subgroup_classes': 161, 'number_subgroups': 204, 'old_label': None, 'order': 128, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 7], [4, 56], [8, 64]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [4, 4, 4, 4, 2], 'outer_gen_pows': [0, 0, 0, 0, 4], 'outer_gens': [[65, 35, 4, 84], [65, 15, 68, 60], [1, 99, 4, 52], [1, 38, 4, 112], [65, 35, 4, 52]], 'outer_group': '128.2177', 'outer_hash': 2177, 'outer_nilpotent': True, 'outer_order': 128, 'outer_permdeg': 32, 'outer_perms': [227732416248362194766480527443156993, 158858142563222912435243846331173432, 183893309480178705202635741566159433, 219584079657772302757977603244270333, 41490044426195940842485257107371077], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4:D_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 32, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 4], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 8], [4, 2], [8, 3]], 'representations': {'PC': {'code': 5354203782202886460022, 'gens': [1, 2, 3, 5], 'pres': [7, 2, 2, 2, 2, 2, 2, 2, 925, 512, 807, 58, 3084, 102, 124]}, 'Perm': {'d': 32, 'gens': [9320481912519127633234485491777013, 17774109302822855883803370003626935, 26330857260118844511805485946184813, 34830447440542533069501355741135595, 5807915822933, 43274099818138533015058869723950933, 26330857260118844511801081655296000]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 4], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4^2.C_2^3', 'transitive_degree': 64, '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: 43228823
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 1717, 'group_order': 128, 'label': '1A', 'order': 1, 'powers': [1], 'representative': 0, 'size': 1}
  • id: 43228834
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 1717, 'group_order': 128, 'label': '2A', 'order': 2, 'powers': [1], 'representative': 72, 'size': 1}
  • id: 43228845
    {'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 1717, 'group_order': 128, 'label': '2B', 'order': 2, 'powers': [1], 'representative': 8, 'size': 1}
  • id: 43228856
    {'aut_label': '2C', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 1717, 'group_order': 128, 'label': '2C', 'order': 2, 'powers': [1], 'representative': 64, 'size': 1}
  • id: 43228862
    {'aut_label': '2D', 'centralizer': '4.a1.a1', 'counter': 5, 'group_counter': 1717, 'group_order': 128, 'label': '2D', 'order': 2, 'powers': [1], 'representative': 1, 'size': 4}
  • id: 43228863
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 6, 'group_counter': 1717, 'group_order': 128, 'label': '4A1', 'order': 4, 'powers': [4], 'representative': 32, 'size': 1}
  • id: 43228864
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 7, 'group_counter': 1717, 'group_order': 128, 'label': '4A-1', 'order': 4, 'powers': [4], 'representative': 96, 'size': 1}
  • id: 43228865
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 8, 'group_counter': 1717, 'group_order': 128, 'label': '4B1', 'order': 4, 'powers': [4], 'representative': 40, 'size': 1}
  • id: 43228866
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 9, 'group_counter': 1717, 'group_order': 128, 'label': '4B-1', 'order': 4, 'powers': [4], 'representative': 104, 'size': 1}
  • id: 43228824
    {'aut_label': '4C', 'centralizer': '2.b1.a1', 'counter': 10, 'group_counter': 1717, 'group_order': 128, 'label': '4C', 'order': 4, 'powers': [2], 'representative': 36, 'size': 2}
  • id: 43228825
    {'aut_label': '4C', 'centralizer': '2.b1.a1', 'counter': 11, 'group_counter': 1717, 'group_order': 128, 'label': '4D', 'order': 4, 'powers': [2], 'representative': 100, 'size': 2}
  • id: 43228826
    {'aut_label': '4E1', 'centralizer': '2.b1.a1', 'counter': 12, 'group_counter': 1717, 'group_order': 128, 'label': '4E1', 'order': 4, 'powers': [3], 'representative': 4, 'size': 2}
  • id: 43228827
    {'aut_label': '4E1', 'centralizer': '2.b1.a1', 'counter': 13, 'group_counter': 1717, 'group_order': 128, 'label': '4E-1', 'order': 4, 'powers': [3], 'representative': 68, 'size': 2}
  • id: 43228828
    {'aut_label': '4F', 'centralizer': '4.k2.a1', 'counter': 14, 'group_counter': 1717, 'group_order': 128, 'label': '4F', 'order': 4, 'powers': [2], 'representative': 2, 'size': 4}
  • id: 43228829
    {'aut_label': '4G', 'centralizer': '4.k2.a1', 'counter': 15, 'group_counter': 1717, 'group_order': 128, 'label': '4G', 'order': 4, 'powers': [3], 'representative': 34, 'size': 4}
  • id: 43228830
    {'aut_label': '4G', 'centralizer': '4.k2.b1', 'counter': 16, 'group_counter': 1717, 'group_order': 128, 'label': '4H', 'order': 4, 'powers': [3], 'representative': 6, 'size': 4}
  • id: 43228831
    {'aut_label': '4I', 'centralizer': '4.a1.a1', 'counter': 17, 'group_counter': 1717, 'group_order': 128, 'label': '4I', 'order': 4, 'powers': [4], 'representative': 33, 'size': 4}
  • id: 43228832
    {'aut_label': '4J', 'centralizer': '4.a1.a1', 'counter': 18, 'group_counter': 1717, 'group_order': 128, 'label': '4J', 'order': 4, 'powers': [3], 'representative': 5, 'size': 4}
  • id: 43228833
    {'aut_label': '4G', 'centralizer': '4.k2.c1', 'counter': 19, 'group_counter': 1717, 'group_order': 128, 'label': '4K', 'order': 4, 'powers': [3], 'representative': 3, 'size': 4}
  • id: 43228835
    {'aut_label': '4F', 'centralizer': '4.k2.b1', 'counter': 20, 'group_counter': 1717, 'group_order': 128, 'label': '4L', 'order': 4, 'powers': [2], 'representative': 38, 'size': 4}
  • id: 43228836
    {'aut_label': '4M', 'centralizer': '4.a1.a1', 'counter': 21, 'group_counter': 1717, 'group_order': 128, 'label': '4M', 'order': 4, 'powers': [2], 'representative': 37, 'size': 4}
  • id: 43228837
    {'aut_label': '4F', 'centralizer': '4.k2.c1', 'counter': 22, 'group_counter': 1717, 'group_order': 128, 'label': '4N', 'order': 4, 'powers': [2], 'representative': 35, 'size': 4}
  • id: 43228838
    {'aut_label': '4F', 'centralizer': '4.k2.d1', 'counter': 23, 'group_counter': 1717, 'group_order': 128, 'label': '4O', 'order': 4, 'powers': [2], 'representative': 7, 'size': 4}
  • id: 43228839
    {'aut_label': '4G', 'centralizer': '4.k2.d1', 'counter': 24, 'group_counter': 1717, 'group_order': 128, 'label': '4P', 'order': 4, 'powers': [3], 'representative': 39, 'size': 4}
  • id: 43228840
    {'aut_label': '8A1', 'centralizer': '2.e1.a1', 'counter': 25, 'group_counter': 1717, 'group_order': 128, 'label': '8A1', 'order': 8, 'powers': [6], 'representative': 16, 'size': 2}
  • id: 43228841
    {'aut_label': '8A1', 'centralizer': '2.e1.a1', 'counter': 26, 'group_counter': 1717, 'group_order': 128, 'label': '8A-1', 'order': 8, 'powers': [7], 'representative': 112, 'size': 2}
  • id: 43228842
    {'aut_label': '8A1', 'centralizer': '2.e1.a1', 'counter': 27, 'group_counter': 1717, 'group_order': 128, 'label': '8A3', 'order': 8, 'powers': [7], 'representative': 48, 'size': 2}
  • id: 43228843
    {'aut_label': '8A1', 'centralizer': '2.e1.a1', 'counter': 28, 'group_counter': 1717, 'group_order': 128, 'label': '8A-3', 'order': 8, 'powers': [6], 'representative': 80, 'size': 2}
  • id: 43228844
    {'aut_label': '8A1', 'centralizer': '2.e1.b1', 'counter': 29, 'group_counter': 1717, 'group_order': 128, 'label': '8B1', 'order': 8, 'powers': [8], 'representative': 20, 'size': 2}
  • id: 43228846
    {'aut_label': '8A1', 'centralizer': '2.e1.b1', 'counter': 30, 'group_counter': 1717, 'group_order': 128, 'label': '8B-1', 'order': 8, 'powers': [9], 'representative': 52, 'size': 2}
  • id: 43228847
    {'aut_label': '8A1', 'centralizer': '2.e1.b1', 'counter': 31, 'group_counter': 1717, 'group_order': 128, 'label': '8B3', 'order': 8, 'powers': [9], 'representative': 116, 'size': 2}
  • id: 43228848
    {'aut_label': '8A1', 'centralizer': '2.e1.b1', 'counter': 32, 'group_counter': 1717, 'group_order': 128, 'label': '8B-3', 'order': 8, 'powers': [8], 'representative': 84, 'size': 2}
  • id: 43228849
    {'aut_label': '8C1', 'centralizer': '4.k2.a1', 'counter': 33, 'group_counter': 1717, 'group_order': 128, 'label': '8C1', 'order': 8, 'powers': [9], 'representative': 18, 'size': 4}
  • id: 43228850
    {'aut_label': '8C1', 'centralizer': '4.k2.a1', 'counter': 34, 'group_counter': 1717, 'group_order': 128, 'label': '8C-1', 'order': 8, 'powers': [8], 'representative': 50, 'size': 4}
  • id: 43228851
    {'aut_label': '8D1', 'centralizer': '4.j1.a1', 'counter': 35, 'group_counter': 1717, 'group_order': 128, 'label': '8D1', 'order': 8, 'powers': [9], 'representative': 17, 'size': 4}
  • id: 43228852
    {'aut_label': '8D1', 'centralizer': '4.j1.a1', 'counter': 36, 'group_counter': 1717, 'group_order': 128, 'label': '8D-1', 'order': 8, 'powers': [8], 'representative': 49, 'size': 4}
  • id: 43228853
    {'aut_label': '8C1', 'centralizer': '4.k2.b1', 'counter': 37, 'group_counter': 1717, 'group_order': 128, 'label': '8E1', 'order': 8, 'powers': [8], 'representative': 22, 'size': 4}
  • id: 43228854
    {'aut_label': '8C1', 'centralizer': '4.k2.b1', 'counter': 38, 'group_counter': 1717, 'group_order': 128, 'label': '8E-1', 'order': 8, 'powers': [9], 'representative': 54, 'size': 4}
  • id: 43228855
    {'aut_label': '8D1', 'centralizer': '4.j1.a1', 'counter': 39, 'group_counter': 1717, 'group_order': 128, 'label': '8F1', 'order': 8, 'powers': [7], 'representative': 21, 'size': 4}
  • id: 43228857
    {'aut_label': '8D1', 'centralizer': '4.j1.a1', 'counter': 40, 'group_counter': 1717, 'group_order': 128, 'label': '8F-1', 'order': 8, 'powers': [6], 'representative': 53, 'size': 4}
  • id: 43228858
    {'aut_label': '8C1', 'centralizer': '4.k2.d1', 'counter': 41, 'group_counter': 1717, 'group_order': 128, 'label': '8G1', 'order': 8, 'powers': [7], 'representative': 19, 'size': 4}
  • id: 43228859
    {'aut_label': '8C1', 'centralizer': '4.k2.d1', 'counter': 42, 'group_counter': 1717, 'group_order': 128, 'label': '8G-1', 'order': 8, 'powers': [6], 'representative': 51, 'size': 4}
  • id: 43228860
    {'aut_label': '8C1', 'centralizer': '4.k2.c1', 'counter': 43, 'group_counter': 1717, 'group_order': 128, 'label': '8H1', 'order': 8, 'powers': [6], 'representative': 23, 'size': 4}
  • id: 43228861
    {'aut_label': '8C1', 'centralizer': '4.k2.c1', 'counter': 44, 'group_counter': 1717, 'group_order': 128, 'label': '8H-1', 'order': 8, 'powers': [7], 'representative': 55, 'size': 4}
• 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: 81082
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '128.1717', 'group_order': 128, 'image': None, 'label': '128.1717.1a', '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], 'schur_index': 1}
  • id: 81093
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '128.1717', 'group_order': 128, 'image': None, 'label': '128.1717.1b', '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], 'schur_index': 1}
  • id: 81104
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '128.1717', 'group_order': 128, 'image': None, 'label': '128.1717.1c', '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], 'schur_index': 1}
  • id: 81105
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '128.1717', 'group_order': 128, 'image': None, 'label': '128.1717.1d', '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], 'schur_index': 1}
  • id: 81106
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '128.1717', 'group_order': 128, 'image': None, 'label': '128.1717.1e', '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], 'schur_index': 1}
  • id: 81107
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '128.1717', 'group_order': 128, 'image': None, 'label': '128.1717.1f', '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], 'schur_index': 1}
  • id: 81108
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '128.1717', 'group_order': 128, 'image': None, 'label': '128.1717.1g', '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], 'schur_index': 1}
  • id: 81109
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '128.1717', 'group_order': 128, 'image': None, 'label': '128.1717.1h', '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], 'schur_index': 1}
  • id: 81110
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '128.1717', 'group_order': 128, 'image': None, 'label': '128.1717.1i', '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], 'schur_index': 1}
  • id: 81083
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '128.1717', 'group_order': 128, 'image': None, 'label': '128.1717.1j', '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], 'schur_index': 1}
  • id: 81084
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '128.1717', 'group_order': 128, 'image': None, 'label': '128.1717.1k', '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], 'schur_index': 1}
  • id: 81085
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '128.1717', 'group_order': 128, 'image': None, 'label': '128.1717.1l', '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], 'schur_index': 1}
  • id: 81086
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '128.1717', 'group_order': 128, 'image': None, 'label': '128.1717.1m', '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], 'schur_index': 1}
  • id: 81087
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '128.1717', 'group_order': 128, 'image': None, 'label': '128.1717.1n', '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], 'schur_index': 1}
  • id: 81088
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '128.1717', 'group_order': 128, 'image': None, 'label': '128.1717.1o', '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], 'schur_index': 1}
  • id: 81089
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '128.1717', 'group_order': 128, 'image': None, 'label': '128.1717.1p', '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], 'schur_index': 1}
  • id: 81090
    {'cdim': 1, 'counter': 17, 'faithful': False, 'group': '128.1717', 'group_order': 128, 'image': None, 'label': '128.1717.1q', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [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], 'schur_index': 1}
  • id: 81091
    {'cdim': 1, 'counter': 18, 'faithful': False, 'group': '128.1717', 'group_order': 128, 'image': None, 'label': '128.1717.1r', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [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], 'schur_index': 1}
  • id: 81092
    {'cdim': 1, 'counter': 19, 'faithful': False, 'group': '128.1717', 'group_order': 128, 'image': None, 'label': '128.1717.1s', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [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], 'schur_index': 1}
  • id: 81094
    {'cdim': 1, 'counter': 20, 'faithful': False, 'group': '128.1717', 'group_order': 128, 'image': None, 'label': '128.1717.1t', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [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], 'schur_index': 1}
  • id: 81095
    {'cdim': 1, 'counter': 21, 'faithful': False, 'group': '128.1717', 'group_order': 128, 'image': None, 'label': '128.1717.1u', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [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], 'schur_index': 1}
  • id: 81096
    {'cdim': 1, 'counter': 22, 'faithful': False, 'group': '128.1717', 'group_order': 128, 'image': None, 'label': '128.1717.1v', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [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], 'schur_index': 1}
  • id: 81097
    {'cdim': 1, 'counter': 23, 'faithful': False, 'group': '128.1717', 'group_order': 128, 'image': None, 'label': '128.1717.1w', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [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], 'schur_index': 1}
  • id: 81098
    {'cdim': 1, 'counter': 24, 'faithful': False, 'group': '128.1717', 'group_order': 128, 'image': None, 'label': '128.1717.1x', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [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], 'schur_index': 1}
  • id: 81101
    {'cdim': 4, 'counter': 27, 'faithful': False, 'group': '128.1717', 'group_order': 128, 'image': None, 'label': '128.1717.4a', 'multiplicity': 1, 'nt': [16, 20], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 81102
    {'cdim': 4, 'counter': 28, 'faithful': False, 'group': '128.1717', 'group_order': 128, 'image': None, 'label': '128.1717.4b', 'multiplicity': 1, 'nt': [16, 20], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 81099
    {'cdim': 2, 'counter': 25, 'faithful': False, 'group': '128.1717', 'group_order': 128, 'image': None, 'label': '128.1717.2a', 'multiplicity': 4, 'nt': [16, 16], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 0, 0, 0, 0, 0, -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], 'schur_index': 1}
  • id: 81100
    {'cdim': 2, 'counter': 26, 'faithful': False, 'group': '128.1717', 'group_order': 128, 'image': None, 'label': '128.1717.2b', 'multiplicity': 4, 'nt': [16, 16], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 0, 0, 0, 0, 0, 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], 'schur_index': 1}
  • id: 81103
    {'cdim': 4, 'counter': 29, 'faithful': False, 'group': '128.1717', 'group_order': 128, 'image': None, 'label': '128.1717.4c', 'multiplicity': 2, 'nt': [16, 70], 'qdim': 8, 'qvalues': [8, -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], 'schur_index': 1}
• gps_char •

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

  
  
  • id: 69866
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 128, 'label': '128.1717.1a', '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]]]}
  • id: 69877
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1.a1', 'kernel_order': 64, 'label': '128.1717.1b', '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]]]}
  • id: 69888
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1.b1', 'kernel_order': 64, 'label': '128.1717.1c', '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]]]}
  • id: 69899
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1.c1', 'kernel_order': 64, 'label': '128.1717.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 69905
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1.d1', 'kernel_order': 64, 'label': '128.1717.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 69906
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1.a1', 'kernel_order': 64, 'label': '128.1717.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 69907
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 64, 'label': '128.1717.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 69908
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1.b1', 'kernel_order': 64, 'label': '128.1717.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 69909
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 9, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.b1', 'kernel_order': 64, 'label': '128.1717.1i', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 69867
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 10, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.c1', 'kernel_order': 64, 'label': '128.1717.1j', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 69868
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 11, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.d1', 'kernel_order': 64, 'label': '128.1717.1k', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 69869
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 12, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 64, 'label': '128.1717.1l', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 69870
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 13, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.b1', 'kernel_order': 64, 'label': '128.1717.1m', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 69871
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 14, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 64, 'label': '128.1717.1n', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 69872
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 15, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 64, 'label': '128.1717.1o', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 69873
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 16, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 64, 'label': '128.1717.1p', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 69874
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 17, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.r1.b1', 'kernel_order': 32, 'label': '128.1717.1q1', 'nt': [4, 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, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 69875
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 18, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.r1.b1', 'kernel_order': 32, 'label': '128.1717.1q2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 69876
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 19, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.r1.a1', 'kernel_order': 32, 'label': '128.1717.1r1', 'nt': [4, 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, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 69878
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 20, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.r1.a1', 'kernel_order': 32, 'label': '128.1717.1r2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 69879
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 21, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.q1.a1', 'kernel_order': 32, 'label': '128.1717.1s1', 'nt': [4, 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, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]]]}
  • id: 69880
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 22, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.q1.a1', 'kernel_order': 32, 'label': '128.1717.1s2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]]]}
  • id: 69881
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 23, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.p1.a1', 'kernel_order': 32, 'label': '128.1717.1t1', 'nt': [4, 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, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]]]}
  • id: 69882
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 24, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.p1.a1', 'kernel_order': 32, 'label': '128.1717.1t2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]]]}
  • id: 69883
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 25, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.f1.a1', 'kernel_order': 32, 'label': '128.1717.1u1', 'nt': [4, 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, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 69884
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 26, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.f1.a1', 'kernel_order': 32, 'label': '128.1717.1u2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 69885
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 27, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.f1.b1', 'kernel_order': 32, 'label': '128.1717.1v1', 'nt': [4, 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, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 69886
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 28, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.f1.b1', 'kernel_order': 32, 'label': '128.1717.1v2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 69887
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 29, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.e1.a1', 'kernel_order': 32, 'label': '128.1717.1w1', 'nt': [4, 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, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]]]}
  • id: 69889
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 30, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.e1.a1', 'kernel_order': 32, 'label': '128.1717.1w2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]]]}
  • id: 69890
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 31, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.e1.b1', 'kernel_order': 32, 'label': '128.1717.1x1', 'nt': [4, 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, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]]]}
  • id: 69891
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 32, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.e1.b1', 'kernel_order': 32, 'label': '128.1717.1x2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]]]}
  • id: 69892
    {'center': '4.h1.a1', 'center_index': 4, 'center_order': 32, 'counter': 33, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '32.38', 'image_order': 32, 'indicator': 0, 'kernel': '32.b1.b1', 'kernel_order': 4, 'label': '128.1717.2a1', 'nt': [16, 16], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[2, 2]], [[-2, 2]], [[-2, 0]], [[2, 0]], [[-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]], [[-2, 1]], [[-2, 3]], [[-2, 1]], [[2, 3]], [[2, 1]], [[2, 3]], [[2, 1]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 69893
    {'center': '4.h1.a1', 'center_index': 4, 'center_order': 32, 'counter': 34, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '32.38', 'image_order': 32, 'indicator': 0, 'kernel': '32.b1.b1', 'kernel_order': 4, 'label': '128.1717.2a2', 'nt': [16, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[-2, 2]], [[2, 2]], [[-2, 0]], [[2, 0]], [[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]], [[2, 3]], [[2, 1]], [[2, 3]], [[-2, 1]], [[-2, 3]], [[-2, 1]], [[-2, 3]], [[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]]]}
  • id: 69894
    {'center': '4.h1.a1', 'center_index': 4, 'center_order': 32, 'counter': 35, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '32.38', 'image_order': 32, 'indicator': 0, 'kernel': '32.b1.b1', 'kernel_order': 4, 'label': '128.1717.2a3', 'nt': [16, 16], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[2, 2]], [[-2, 2]], [[-2, 0]], [[2, 0]], [[-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]], [[2, 1]], [[2, 3]], [[2, 1]], [[-2, 3]], [[-2, 1]], [[-2, 3]], [[-2, 1]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 69895
    {'center': '4.h1.a1', 'center_index': 4, 'center_order': 32, 'counter': 36, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '32.38', 'image_order': 32, 'indicator': 0, 'kernel': '32.b1.b1', 'kernel_order': 4, 'label': '128.1717.2a4', 'nt': [16, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[-2, 2]], [[2, 2]], [[-2, 0]], [[2, 0]], [[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]], [[-2, 3]], [[-2, 1]], [[-2, 3]], [[2, 1]], [[2, 3]], [[2, 1]], [[2, 3]], [[-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]]]}
  • id: 69896
    {'center': '4.h1.a1', 'center_index': 4, 'center_order': 32, 'counter': 37, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '32.38', 'image_order': 32, 'indicator': 0, 'kernel': '32.b1.a1', 'kernel_order': 4, 'label': '128.1717.2b1', 'nt': [16, 16], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[2, 2]], [[-2, 2]], [[2, 0]], [[-2, 0]], [[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]], [[-2, 1]], [[-2, 3]], [[2, 1]], [[-2, 3]], [[-2, 1]], [[2, 3]], [[2, 1]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 69897
    {'center': '4.h1.a1', 'center_index': 4, 'center_order': 32, 'counter': 38, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '32.38', 'image_order': 32, 'indicator': 0, 'kernel': '32.b1.a1', 'kernel_order': 4, 'label': '128.1717.2b2', 'nt': [16, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[-2, 2]], [[2, 2]], [[2, 0]], [[-2, 0]], [[-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]], [[2, 3]], [[2, 1]], [[-2, 3]], [[2, 1]], [[2, 3]], [[-2, 1]], [[-2, 3]], [[-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]]]}
  • id: 69898
    {'center': '4.h1.a1', 'center_index': 4, 'center_order': 32, 'counter': 39, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '32.38', 'image_order': 32, 'indicator': 0, 'kernel': '32.b1.a1', 'kernel_order': 4, 'label': '128.1717.2b3', 'nt': [16, 16], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[2, 2]], [[-2, 2]], [[2, 0]], [[-2, 0]], [[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]], [[2, 1]], [[2, 3]], [[-2, 1]], [[2, 3]], [[2, 1]], [[-2, 3]], [[-2, 1]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 69900
    {'center': '4.h1.a1', 'center_index': 4, 'center_order': 32, 'counter': 40, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '32.38', 'image_order': 32, 'indicator': 0, 'kernel': '32.b1.a1', 'kernel_order': 4, 'label': '128.1717.2b4', 'nt': [16, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[-2, 2]], [[2, 2]], [[2, 0]], [[-2, 0]], [[-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]], [[-2, 3]], [[-2, 1]], [[2, 3]], [[-2, 1]], [[-2, 3]], [[2, 1]], [[2, 3]], [[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]]]}
  • id: 69901
    {'center': '16.b1.a1', 'center_index': 16, 'center_order': 8, 'counter': 41, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '32.50', 'image_order': 32, 'indicator': -1, 'kernel': '32.c1.b1', 'kernel_order': 4, 'label': '128.1717.4a', 'nt': [16, 20], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 69902
    {'center': '16.b1.a1', 'center_index': 16, 'center_order': 8, 'counter': 42, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '32.50', 'image_order': 32, 'indicator': -1, 'kernel': '32.c1.a1', 'kernel_order': 4, 'label': '128.1717.4b', 'nt': [16, 20], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 69903
    {'center': '16.b1.a1', 'center_index': 16, 'center_order': 8, 'counter': 43, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '64.249', 'image_order': 64, 'indicator': 0, 'kernel': '64.b1.a1', 'kernel_order': 2, 'label': '128.1717.4c1', 'nt': [16, 70], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[-4, 1]], [[4, 1]], [[-4, 1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 69904
    {'center': '16.b1.a1', 'center_index': 16, 'center_order': 8, 'counter': 44, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '128.1717', 'group_counter': 1717, 'group_order': 128, 'image': None, 'image_isoclass': '64.249', 'image_order': 64, 'indicator': 0, 'kernel': '64.b1.a1', 'kernel_order': 2, 'label': '128.1717.4c2', 'nt': [16, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[4, 1]], [[-4, 1]], [[4, 1]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 7995106
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '128.1717.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': ['F', 'R', 'U0', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1717', 'subgroup_hash': 1717, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 2}
  • id: 7995179
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.214', 'subgroup_hash': 214, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 7995190
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.112', 'subgroup_hash': 112, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995201
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.113', 'subgroup_hash': 113, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995212
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.114', 'subgroup_hash': 114, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 7995223
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.2.d1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.d1.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': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.114', 'subgroup_hash': 114, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 7995234
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.2.d1.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.d1.c1', '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.114', 'subgroup_hash': 114, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 7995245
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.2.d1.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.d1.d1', '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.114', 'subgroup_hash': 114, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 7995256
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.126', 'subgroup_hash': 126, 'subgroup_order': 64, 'subgroup_tex': 'C_8\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995107
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.2.e1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.e1.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': '64.126', 'subgroup_hash': 126, 'subgroup_order': 64, 'subgroup_tex': 'C_8\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995118
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.2.f1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '64.127', 'subgroup_hash': 127, 'subgroup_order': 64, 'subgroup_tex': 'C_8:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995129
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.2.f1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.f1.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': '64.127', 'subgroup_hash': 127, 'subgroup_order': 64, 'subgroup_tex': 'C_8:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995140
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.2.g1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '64.127', 'subgroup_hash': 127, 'subgroup_order': 64, 'subgroup_tex': 'C_8:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995151
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.2.g1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.g1.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': '64.127', 'subgroup_hash': 127, 'subgroup_order': 64, 'subgroup_tex': 'C_8:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995162
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.2.g1.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.g1.c1', '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': '64.127', 'subgroup_hash': 127, 'subgroup_order': 64, 'subgroup_tex': 'C_8:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995173
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.2.g1.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.g1.d1', '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': '64.127', 'subgroup_hash': 127, 'subgroup_order': 64, 'subgroup_tex': 'C_8:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995176
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 7995177
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 7995178
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 7995180
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995181
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1.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': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995182
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995183
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1.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': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995184
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995185
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995186
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995187
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995188
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995189
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.g1.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': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995191
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995192
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995193
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995194
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995195
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995196
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995197
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.k1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.k1.c1', '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': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995198
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.k1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.k1.d1', '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': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995199
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 32, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.k2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.k2.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': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995200
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 32, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.k2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.k2.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': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995202
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 32, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.k2.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.k2.c1', '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': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995203
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 32, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.k2.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.k2.d1', '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': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995204
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995205
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995206
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.l1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.l1.c1', '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': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995207
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.l1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.l1.d1', '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': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995208
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.l2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.l2.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': '32.4', 'subgroup_hash': 4, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995209
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.l2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.l2.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': '32.4', 'subgroup_hash': 4, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995210
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.l2.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.l2.c1', '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': '32.4', 'subgroup_hash': 4, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995211
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.l2.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.l2.d1', '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': '32.4', 'subgroup_hash': 4, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995213
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995214
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995215
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995216
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 53, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995217
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 54, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.4', 'subgroup_hash': 4, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995218
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 55, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.4', 'subgroup_hash': 4, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995219
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 56, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995220
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 57, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995221
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 58, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.32', 'subgroup_hash': 32, 'subgroup_order': 32, 'subgroup_tex': 'C_4.Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995222
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 59, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.4.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.32', 'subgroup_hash': 32, 'subgroup_order': 32, 'subgroup_tex': 'C_4.Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995224
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 60, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995225
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 61, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 7995226
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 62, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 7995227
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 63, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995228
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 64, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995229
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 65, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995230
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 66, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995231
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 67, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 7995232
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 68, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 7995233
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 69, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1.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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 7995235
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 70, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1.c1', '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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 7995236
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 71, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.f1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1.d1', '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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 7995237
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 72, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 7995238
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 73, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': ['C3'], 'split': False, '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: 7995239
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 74, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.h1.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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995240
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 75, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995241
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 76, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995242
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 77, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.i1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.i1.c1', '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995243
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 78, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.i1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.i1.d1', '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995244
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 79, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995246
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 80, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995247
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 81, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 7995248
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 82, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 7995249
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 83, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995250
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 84, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995251
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 85, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 7995252
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 86, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.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': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995253
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 87, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.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': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995254
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 88, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.n1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.n1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995255
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 89, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.n1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.n1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995257
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 90, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 7995258
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 91, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995259
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 92, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995260
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 93, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.p1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.p1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995261
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 94, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.p1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.p1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995262
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 95, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995263
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 96, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995264
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 97, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995265
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 98, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995266
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 99, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995108
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 100, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995109
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 101, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 7995110
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 102, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.8.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 7995111
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 103, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 7995112
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 8, 'counter': 104, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1.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': ['Z', 'Phi', 'U1', 'C4'], '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: 7995113
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 105, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995114
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 106, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.16.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': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995115
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 107, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.16.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': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995116
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 108, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.16.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995117
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 109, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.16.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.e1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995119
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 110, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.16.e1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.e1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995120
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 111, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995121
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 112, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.16.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995122
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 113, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.16.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.f1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995123
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 114, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.16.f1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.f1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995124
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 115, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995125
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 116, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.16.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995126
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 117, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.16.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995127
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1717.16.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995128
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1717.16.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995130
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1717.16.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995131
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1717.16.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995132
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1717.16.k1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.k1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995133
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1717.16.k1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.k1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995134
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1717.16.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995135
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1717.16.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995136
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1717.16.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995137
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1717.16.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995138
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1717.16.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995139
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 129, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.1717.16.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995141
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 130, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.1717.16.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995142
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 131, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.1717.16.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995143
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 132, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.1717.16.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995144
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 133, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.1717.16.p1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.p1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995145
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 134, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.1717.16.p1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.p1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995146
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 135, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.1717.16.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995147
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 136, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.1717.16.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 7995148
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 137, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1717.32.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': '32.45', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'S', 'L1', 'D1'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 7995149
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 138, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.1717.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.38', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\OD_{16}:C_2', '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: 7995150
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 139, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.1717.32.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.38', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\OD_{16}:C_2', '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: 7995152
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 140, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.1717.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.50', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 50, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4.C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C5'], '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: 7995153
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 141, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.1717.32.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.50', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 50, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4.C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], '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: 7995154
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1717.32.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 7995155
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 143, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.1717.32.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995156
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 144, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.1717.32.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995157
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 145, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.1717.32.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.e1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995158
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 146, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.1717.32.e1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.e1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995159
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 147, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.1717.32.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995160
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1717.32.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 7995161
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 149, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.1717.32.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995163
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 150, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.1717.32.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995164
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 151, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.1717.32.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995165
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 152, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.1717.32.i1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.i1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995166
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 153, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.1717.32.i1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.i1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995167
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 154, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.1717.32.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995168
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1717.32.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 7995169
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 156, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.1717.32.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 7995170
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 2, 'counter': 157, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.1717.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '64.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.248', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 248, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8.C_2^3', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 7995171
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 2, 'counter': 158, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.1717.64.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '64.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.249', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 249, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8.C_2^3', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 7995172
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 2, 'counter': 159, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.1717.64.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '64.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.200', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 200, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2.C_2^2', 'simple': True, 'solvable': True, 'special_labels': ['C6'], '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: 7995174
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 160, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.1717.64.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 64, '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: 7995175
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1717', 'ambient_counter': 1717, 'ambient_order': 128, 'ambient_tex': 'C_4^2.C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 1, 'counter': 161, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '128.1717.128.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '128.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '128.1717', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1717, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2.C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'L2', 'D2', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 7995106
    {'ambient': '128.1717', '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': '16.b1.a1', 'complements': ['128.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.d1.b1', '2.d1.c1', '2.d1.d1', '2.e1.a1', '2.e1.b1', '2.f1.a1', '2.f1.b1', '2.g1.a1', '2.g1.b1', '2.g1.c1', '2.g1.d1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6697, 3059, 3370, 6638, 6731, 3084, 3370, 6638], 'generators': [1, 2, 4, 16], 'label': '128.1717.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.d1.b1', '2.d1.c1', '2.d1.d1', '2.e1.b1', '2.e1.a1', '2.f1.b1', '2.f1.a1', '2.g1.c1', '2.g1.d1', '2.g1.a1', '2.g1.b1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '16.14', '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': '16.14'}
  • id: 7995107
    {'ambient': '128.1717', 'aut_centralizer_order': 4, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '256.55643', 'aut_weyl_index': 8, 'centralizer': '8.h1.b1', 'complements': ['64.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.g1.b1', '4.h1.a1', '4.i1.b1', '4.k1.c1', '4.k1.d1', '4.k2.c1', '4.k2.d1'], 'core': '2.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7275, 1728, 1788, 9030, 7311, 1742, 1788, 9029], 'generators': [3, 4, 16], 'label': '128.1717.2.e1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.g1.b1', '4.h1.a1', '4.i1.b1', '4.k1.c1', '4.k1.d1', '4.k2.c1', '4.k2.d1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.b1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 7995108
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '8.s1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '4.q1.a1', '4.r1.a1'], 'contains': ['16.f1.b1', '16.f1.d1', '16.g1.a1'], 'core': '8.s1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3777, 8268, 5897, 2865, 3794, 8337, 5897, 2866], 'generators': [33, 6], 'label': '128.1717.8.s1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.s1.b1', 'normal_contained_in': ['4.b1.b1', '4.r1.a1', '4.q1.a1'], 'normal_contains': ['16.f1.d1', '16.f1.b1', '16.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.s1.b1', 'projective_image': '32.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.s1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 7995109
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '8.t1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '4.m1.a1', '4.q1.a1'], 'contains': ['16.f1.a1', '16.f1.d1', '16.h1.a1', '16.m1.a1'], 'core': '8.t1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [217, 9349, 5271, 1072, 218, 9427, 5271, 1071], 'generators': [5, 34, 64], 'label': '128.1717.8.t1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.t1.a1', 'normal_contained_in': ['4.f1.b1', '4.m1.a1', '4.q1.a1'], 'normal_contains': ['16.f1.d1', '16.f1.a1', '16.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.t1.a1', 'projective_image': '32.45', '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': '16.14'}
  • id: 7995110
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '8.t1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.m1.b1', '4.q1.a1'], 'contains': ['16.f1.b1', '16.f1.c1', '16.h1.a1', '16.m1.b1'], 'core': '8.t1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [217, 9349, 6783, 3830, 218, 9427, 6782, 3830], 'generators': [5, 6, 64], 'label': '128.1717.8.t1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.t1.b1', 'normal_contained_in': ['4.f1.a1', '4.m1.b1', '4.q1.a1'], 'normal_contains': ['16.f1.b1', '16.f1.c1', '16.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.t1.b1', 'projective_image': '32.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.t1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 7995111
    {'ambient': '128.1717', 'aut_centralizer_order': 512, 'aut_label': '16.a1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.d1.a1', '8.d1.b1', '8.d1.c1', '8.d1.d1'], 'contains': ['32.a1.a1', '32.d1.a1', '32.g1.a1', '32.k1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3559, 6114, 7473, 2757, 3574, 6165, 7472, 2757], 'generators': [1, 72, 64], 'label': '128.1717.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.c1.a1', '8.b1.a1', '8.d1.b1', '8.d1.d1', '8.d1.c1', '8.d1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '32.45', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995112
    {'ambient': '128.1717', 'aut_centralizer_order': 512, 'aut_label': '16.b1', 'aut_quo_index': 5040, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.e1.a1', '8.f1.a1', '8.f1.b1', '8.f1.c1', '8.f1.d1', '8.g1.a1', '8.h1.a1', '8.h1.b1', '8.i1.a1', '8.i1.b1', '8.i1.c1', '8.i1.d1', '8.j1.a1', '8.j1.b1'], 'contains': ['32.a1.a1', '32.c1.a1', '32.c1.b1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5944, 3587, 3924, 5744, 5971, 3616, 3922, 5744], 'generators': [72, 32], 'label': '128.1717.16.b1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1', '8.e1.a1', '8.f1.c1', '8.f1.d1', '8.f1.b1', '8.f1.a1', '8.g1.a1', '8.h1.a1', '8.h1.b1', '8.i1.a1', '8.i1.b1', '8.i1.c1', '8.i1.d1', '8.j1.a1', '8.j1.b1'], 'normal_contains': ['32.a1.a1', '32.c1.b1', '32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '16.14', 'quotient_action_image': '1.1', 'quotient_action_kernel': '16.14', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 7995113
    {'ambient': '128.1717', 'aut_centralizer_order': 512, 'aut_label': '16.c1', 'aut_quo_index': 48, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.e1.a1', '8.k1.a1', '8.k1.b1', '8.l1.a1', '8.l1.b1', '8.m1.a1'], 'contains': ['32.a1.a1', '32.b1.a1', '32.b1.b1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3957, 5706, 8099, 1460, 3974, 5754, 8098, 1461], 'generators': [36, 64], 'label': '128.1717.16.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.b1.a1', '8.e1.a1', '8.k1.b1', '8.k1.a1', '8.l1.b1', '8.l1.a1', '8.m1.a1'], 'normal_contains': ['32.a1.a1', '32.b1.b1', '32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.a1', 'projective_image': '32.45', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 7995114
    {'ambient': '128.1717', 'aut_centralizer_order': 512, 'aut_label': '16.d1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.e1.a1', '8.n1.a1', '8.n1.b1', '8.n1.c1', '8.n1.d1', '8.o1.a1'], 'contains': ['32.a1.a1', '32.h1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2896, 6522, 6281, 4053, 2909, 6576, 6281, 4054], 'generators': [4, 64], 'label': '128.1717.16.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': ['8.c1.a1', '8.e1.a1', '8.n1.d1', '8.n1.a1', '8.n1.c1', '8.n1.b1', '8.o1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.d1.a1', 'projective_image': '32.45', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 7995115
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '16.e1', 'aut_quo_index': 96, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.k2.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.f1.a1', '8.k1.a1', '8.n1.a1', '8.p1.a1', '8.q1.a1', '8.r1.a1'], 'contains': ['32.a1.a1', '32.e1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2399, 7539, 8322, 3383, 2410, 7602, 8322, 3383], 'generators': [2, 64], 'label': '128.1717.16.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': ['8.d1.a1', '8.f1.a1', '8.n1.a1', '8.k1.a1', '8.p1.a1', '8.r1.a1', '8.q1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.e1.a1', 'projective_image': '32.45', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995116
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '16.e1', 'aut_quo_index': 96, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.k2.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.d1', '8.f1.b1', '8.k1.a1', '8.n1.b1', '8.p1.d1', '8.q1.b1', '8.r1.b1'], 'contains': ['32.a1.a1', '32.e1.b1'], 'core': '16.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2399, 7539, 8769, 2131, 2410, 7602, 8769, 2131], 'generators': [38, 64], 'label': '128.1717.16.e1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.e1.b1', 'normal_contained_in': ['8.d1.d1', '8.f1.b1', '8.n1.b1', '8.k1.a1', '8.p1.d1', '8.r1.b1', '8.q1.b1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.e1.b1', 'projective_image': '32.45', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.e1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995117
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '16.e1', 'aut_quo_index': 96, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.k2.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '8.f1.c1', '8.k1.b1', '8.n1.d1', '8.p1.c1', '8.q1.a1', '8.r1.b1'], 'contains': ['32.a1.a1', '32.e1.c1'], 'core': '16.e1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [2399, 7539, 7876, 2578, 2410, 7602, 7875, 2578], 'generators': [35, 64], 'label': '128.1717.16.e1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.e1.c1', 'normal_contained_in': ['8.d1.b1', '8.f1.c1', '8.n1.d1', '8.k1.b1', '8.p1.c1', '8.r1.b1', '8.q1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.e1.c1', 'projective_image': '32.45', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.e1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995118
    {'ambient': '128.1717', 'aut_centralizer_order': 4, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '256.55643', 'aut_weyl_index': 8, 'centralizer': '16.b1.a1', 'complements': ['64.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.g1.a1', '4.i1.b1', '4.j1.a1', '4.l1.a1', '4.l1.b1', '4.l2.a1', '4.l2.b1'], 'core': '2.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6047, 3724, 1022, 4817, 6077, 3756, 810, 4818], 'generators': [17, 2, 4], 'label': '128.1717.2.f1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.g1.a1', '4.i1.b1', '4.j1.a1', '4.l1.b1', '4.l1.a1', '4.l2.b1', '4.l2.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.f1.a1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.f1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 7995119
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '16.e1', 'aut_quo_index': 96, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.k2.d1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.c1', '8.f1.d1', '8.k1.b1', '8.n1.c1', '8.p1.b1', '8.q1.b1', '8.r1.a1'], 'contains': ['32.a1.a1', '32.e1.d1'], 'core': '16.e1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [2399, 7539, 8546, 4277, 2410, 7602, 8545, 4277], 'generators': [7, 64], 'label': '128.1717.16.e1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.e1.d1', 'normal_contained_in': ['8.d1.c1', '8.f1.d1', '8.n1.c1', '8.k1.b1', '8.p1.b1', '8.r1.a1', '8.q1.b1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.e1.d1', 'projective_image': '32.45', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.e1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995120
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '16.f1', 'aut_quo_index': 96, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.k2.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '8.f1.a1', '8.l1.a1', '8.n1.b1', '8.p1.b1', '8.s1.a1', '8.t1.a1'], 'contains': ['32.a1.a1', '32.i1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1902, 7030, 5611, 1685, 1911, 7089, 5611, 1684], 'generators': [34, 64], 'label': '128.1717.16.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': ['8.d1.b1', '8.f1.a1', '8.n1.b1', '8.l1.a1', '8.p1.b1', '8.t1.a1', '8.s1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.f1.a1', 'projective_image': '32.45', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995121
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '16.f1', 'aut_quo_index': 96, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.k2.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.c1', '8.f1.b1', '8.l1.a1', '8.n1.a1', '8.p1.c1', '8.s1.b1', '8.t1.b1'], 'contains': ['32.a1.a1', '32.i1.b1'], 'core': '16.f1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1902, 7030, 7071, 3607, 1911, 7089, 7070, 3607], 'generators': [6, 64], 'label': '128.1717.16.f1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.f1.b1', 'normal_contained_in': ['8.d1.c1', '8.f1.b1', '8.n1.a1', '8.l1.a1', '8.p1.c1', '8.t1.b1', '8.s1.b1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.f1.b1', 'projective_image': '32.45', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.f1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995122
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '16.f1', 'aut_quo_index': 96, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.k2.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.f1.c1', '8.l1.b1', '8.n1.c1', '8.p1.d1', '8.s1.a1', '8.t1.b1'], 'contains': ['32.a1.a1', '32.i1.c1'], 'core': '16.f1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [1902, 7030, 7294, 2936, 1911, 7089, 7293, 2936], 'generators': [3, 64], 'label': '128.1717.16.f1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.f1.c1', 'normal_contained_in': ['8.d1.a1', '8.f1.c1', '8.n1.c1', '8.l1.b1', '8.p1.d1', '8.t1.b1', '8.s1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.f1.c1', 'projective_image': '32.45', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.f1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995123
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '16.f1', 'aut_quo_index': 96, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.k2.d1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.d1', '8.f1.d1', '8.l1.b1', '8.n1.d1', '8.p1.a1', '8.s1.b1', '8.t1.a1'], 'contains': ['32.a1.a1', '32.i1.d1'], 'core': '16.f1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [1902, 7030, 6505, 1908, 1911, 7089, 6505, 1908], 'generators': [39, 64], 'label': '128.1717.16.f1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.f1.d1', 'normal_contained_in': ['8.d1.d1', '8.f1.d1', '8.n1.d1', '8.l1.b1', '8.p1.a1', '8.t1.a1', '8.s1.b1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.f1.d1', 'projective_image': '32.45', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.f1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995124
    {'ambient': '128.1717', 'aut_centralizer_order': 512, 'aut_label': '16.g1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.m1.a1', '8.o1.a1', '8.q1.a1', '8.q1.b1', '8.s1.a1', '8.s1.b1'], 'contains': ['32.a1.a1', '32.l1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4454, 8160, 5835, 3160, 4473, 8224, 5834, 3160], 'generators': [33, 72], 'label': '128.1717.16.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': ['8.a1.a1', '8.o1.a1', '8.m1.a1', '8.q1.a1', '8.q1.b1', '8.s1.b1', '8.s1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.g1.a1', 'projective_image': '32.45', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995125
    {'ambient': '128.1717', 'aut_centralizer_order': 512, 'aut_label': '16.h1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.g1.a1', '8.m1.a1', '8.r1.a1', '8.r1.b1', '8.t1.a1', '8.t1.b1'], 'contains': ['32.a1.a1', '32.j1.a1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1406, 8803, 6728, 3830, 1412, 8873, 6728, 3830], 'generators': [5, 64], 'label': '128.1717.16.h1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.h1.a1', 'normal_contained_in': ['8.c1.a1', '8.g1.a1', '8.m1.a1', '8.r1.b1', '8.r1.a1', '8.t1.a1', '8.t1.b1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.h1.a1', 'projective_image': '32.45', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995167
    {'ambient': '128.1717', 'aut_centralizer_order': 512, 'aut_label': '32.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.l1.a1', '16.m1.a1', '16.m1.b1'], 'contains': ['64.b1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1157, -1, 6696, -1, 1162, -1, 6695, -1], 'generators': [5], 'label': '128.1717.32.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.j1.a1', 'projective_image': '64.249', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 7995126
    {'ambient': '128.1717', 'aut_centralizer_order': 512, 'aut_label': '16.i1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.g1.a1', '8.o1.a1', '8.p1.a1', '8.p1.b1', '8.p1.c1', '8.p1.d1'], 'contains': ['32.a1.a1', '32.f1.a1'], 'core': '16.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4951, 5199, 7652, 2354, 4972, 5241, 7651, 2355], 'generators': [37, 64], 'label': '128.1717.16.i1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.i1.a1', 'normal_contained_in': ['8.b1.a1', '8.g1.a1', '8.o1.a1', '8.p1.c1', '8.p1.a1', '8.p1.d1', '8.p1.b1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.i1.a1', 'projective_image': '32.45', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995127
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1'], 'contains': ['32.b1.a1', '32.d1.a1', '32.f1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5448, -1, 9217, -1, 5472, -1, 9215, -1], 'generators': [1, 36], 'label': '128.1717.16.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.j1.a1', 'projective_image': '64.248', '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': '2.1'}
  • id: 7995128
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1'], 'contains': ['32.b1.b1', '32.d1.a1', '32.f1.a1'], 'core': '32.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5448, -1, 8993, -1, 5472, -1, 8992, -1], 'generators': [1, 100], 'label': '128.1717.16.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.j1.b1', 'projective_image': '64.248', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 7995129
    {'ambient': '128.1717', 'aut_centralizer_order': 4, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '256.55643', 'aut_weyl_index': 8, 'centralizer': '16.b1.a1', 'complements': ['64.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.g1.b1', '4.i1.a1', '4.j1.a1', '4.l1.c1', '4.l1.d1', '4.l2.c1', '4.l2.d1'], 'core': '2.f1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6047, 3724, 5002, 5402, 6077, 3756, 5001, 5403], 'generators': [17, 18, 4], 'label': '128.1717.2.f1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.f1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.g1.b1', '4.i1.a1', '4.j1.a1', '4.l1.c1', '4.l1.d1', '4.l2.c1', '4.l2.d1'], 'normalizer': '1.a1.a1', 'old_label': '2.f1.b1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.f1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 7995130
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '8.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1'], 'contains': ['32.b1.a1', '32.e1.a1', '32.e1.b1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3277, -1, 9742, -1, 3291, -1, 9741, -1], 'generators': [2, 36], 'label': '128.1717.16.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.k1.a1', 'projective_image': '64.248', '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': '4.2'}
  • id: 7995131
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '8.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.b1'], 'contains': ['32.b1.a1', '32.e1.c1', '32.e1.d1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3277, -1, 9505, -1, 3291, -1, 9505, -1], 'generators': [35, 36], 'label': '128.1717.16.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.k1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.b1', 'old_label': '16.k1.b1', 'projective_image': '64.248', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995132
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '8.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1'], 'contains': ['32.b1.b1', '32.e1.a1', '32.e1.b1'], 'core': '32.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3277, -1, 9624, -1, 3291, -1, 9623, -1], 'generators': [2, 100], 'label': '128.1717.16.k1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.k1.c1', 'projective_image': '64.248', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995133
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '8.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.b1'], 'contains': ['32.b1.b1', '32.e1.c1', '32.e1.d1'], 'core': '32.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3277, -1, 9387, -1, 3291, -1, 9386, -1], 'generators': [35, 100], 'label': '128.1717.16.k1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.k1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.b1', 'old_label': '16.k1.d1', 'projective_image': '64.248', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995134
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1'], 'contains': ['32.g1.a1', '32.h1.a1', '32.j1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [909, -1, 6058, -1, 912, -1, 6058, -1], 'generators': [1, 4], 'label': '128.1717.16.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.l1.a1', 'projective_image': '64.249', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 7995135
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.t1.a1'], 'contains': ['32.i1.a1', '32.i1.d1', '32.j1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [528, -1, 5440, -1, 530, -1, 5440, -1], 'generators': [5, 34], 'label': '128.1717.16.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.m1.a1', 'old_label': '16.m1.a1', 'projective_image': '64.249', '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': '4.2'}
  • id: 7995136
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.t1.b1'], 'contains': ['32.i1.b1', '32.i1.c1', '32.j1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [528, -1, 6900, -1, 530, -1, 6899, -1], 'generators': [5, 6], 'label': '128.1717.16.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.t1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.m1.b1', 'old_label': '16.m1.b1', 'projective_image': '64.249', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995137
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '16.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1'], 'contains': ['32.c1.a1', '32.k1.a1', '32.l1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6441, -1, 4354, -1, 6470, -1, 4354, -1], 'generators': [1, 32], 'label': '128.1717.16.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.n1.a1', 'projective_image': '32.50', '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': '2.1'}
  • id: 7995138
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '16.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1'], 'contains': ['32.c1.b1', '32.k1.a1', '32.l1.a1'], 'core': '32.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6441, -1, 4577, -1, 6470, -1, 4577, -1], 'generators': [1, 104], 'label': '128.1717.16.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.n1.b1', 'projective_image': '32.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.n1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 7995139
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '16.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '2.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1'], 'contains': ['32.c1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7761, -1, 1965, -1, 7803, -1, 2221, -1], 'generators': [16], 'label': '128.1717.16.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.o1.a1', 'projective_image': '32.50', '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': '1.1'}
  • id: 7995140
    {'ambient': '128.1717', 'aut_centralizer_order': 4, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 16, 'centralizer': '16.b1.a1', 'complements': ['64.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.k1.d1', '4.k2.a1', '4.l1.a1', '4.l2.d1', '4.m1.a1', '4.n1.a1', '4.o1.a1'], 'core': '2.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6697, 3059, 3061, 7789, 6731, 3084, 3061, 7790], 'generators': [5, 2, 16], 'label': '128.1717.2.g1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.k1.d1', '4.k2.a1', '4.l1.a1', '4.l2.d1', '4.m1.a1', '4.n1.a1', '4.o1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.g1.a1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.g1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 7995141
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '16.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '2.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.b1'], 'contains': ['32.c1.b1'], 'core': '32.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7761, -1, 3581, -1, 7803, -1, 3578, -1], 'generators': [20], 'label': '128.1717.16.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.b1', 'old_label': '16.o1.b1', 'projective_image': '32.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.o1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 7995142
    {'ambient': '128.1717', 'aut_centralizer_order': 64, 'aut_label': '16.p1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.k2.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.c1'], 'contains': ['32.c1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6866, -1, 2821, -1, 6892, -1, 2821, -1], 'generators': [19], 'label': '128.1717.16.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.b1', 'old_label': '16.p1.a1', 'projective_image': '32.50', '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': '2.1'}
  • id: 7995143
    {'ambient': '128.1717', 'aut_centralizer_order': 64, 'aut_label': '16.p1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.k2.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.d1'], 'contains': ['32.c1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6866, -1, 2651, -1, 6892, -1, 2650, -1], 'generators': [23], 'label': '128.1717.16.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.d1', 'old_label': '16.p1.b1', 'projective_image': '32.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.p1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 7995144
    {'ambient': '128.1717', 'aut_centralizer_order': 64, 'aut_label': '16.p1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.k2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1'], 'contains': ['32.c1.b1'], 'core': '32.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6866, -1, 4095, -1, 6892, -1, 4093, -1], 'generators': [18], 'label': '128.1717.16.p1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '16.p1.c1', 'projective_image': '32.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.p1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 7995145
    {'ambient': '128.1717', 'aut_centralizer_order': 64, 'aut_label': '16.p1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.k2.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.b1'], 'contains': ['32.c1.b1'], 'core': '32.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6866, -1, 3753, -1, 6892, -1, 3751, -1], 'generators': [22], 'label': '128.1717.16.p1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.c1', 'old_label': '16.p1.d1', 'projective_image': '32.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.p1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 7995146
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '16.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.b1'], 'contains': ['32.c1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7256, -1, 1613, -1, 7296, -1, 1536, -1], 'generators': [21], 'label': '128.1717.16.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.b1', 'old_label': '16.q1.a1', 'projective_image': '32.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.q1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 7995147
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '16.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1'], 'contains': ['32.c1.b1'], 'core': '32.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7256, -1, 3409, -1, 7296, -1, 3381, -1], 'generators': [17], 'label': '128.1717.16.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.q1.b1', 'projective_image': '32.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.q1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 7995148
    {'ambient': '128.1717', 'aut_centralizer_order': 2048, 'aut_label': '32.a1', 'aut_quo_index': 2688, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.d1.a1', '16.e1.a1', '16.e1.b1', '16.e1.c1', '16.e1.d1', '16.f1.a1', '16.f1.b1', '16.f1.c1', '16.f1.d1', '16.g1.a1', '16.h1.a1', '16.i1.a1'], 'contains': ['64.a1.a1', '64.b1.a1', '64.c1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3675, 6114, 7228, 2936, 3691, 6165, 7227, 2936], 'generators': [72, 64], 'label': '128.1717.32.a1.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1', '16.b1.a1', '16.d1.a1', '16.c1.a1', '16.e1.c1', '16.e1.a1', '16.e1.d1', '16.e1.b1', '16.f1.d1', '16.f1.b1', '16.f1.c1', '16.f1.a1', '16.h1.a1', '16.g1.a1', '16.i1.a1'], 'normal_contains': ['64.b1.a1', '64.c1.a1', '64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '32.45', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.45', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 7995149
    {'ambient': '128.1717', 'aut_centralizer_order': 512, 'aut_label': '32.b1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.j1.a1', '16.k1.a1', '16.k1.b1'], 'contains': ['64.a1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3957, 5767, 9467, 1769, 3974, 5815, 9465, 1770], 'generators': [36], 'label': '128.1717.32.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': ['16.c1.a1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.b1.a1', 'projective_image': '64.248', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.5', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 7995150
    {'ambient': '128.1717', 'aut_centralizer_order': 512, 'aut_label': '32.b1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.j1.b1', '16.k1.c1', '16.k1.d1'], 'contains': ['64.a1.a1'], 'core': '32.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3957, 5767, 9230, 2502, 3974, 5815, 9229, 2502], 'generators': [100], 'label': '128.1717.32.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.b1.b1', 'normal_contained_in': ['16.c1.a1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.b1.b1', 'projective_image': '64.248', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.5', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 7995151
    {'ambient': '128.1717', 'aut_centralizer_order': 4, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 16, 'centralizer': '16.b1.a1', 'complements': ['64.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.k1.a1', '4.k2.d1', '4.l1.d1', '4.l2.a1', '4.m1.a1', '4.n1.b1', '4.o1.b1'], 'core': '2.g1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6697, 3059, 3679, 6020, 6731, 3084, 3679, 6020], 'generators': [17, 2, 20], 'label': '128.1717.2.g1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.k1.a1', '4.k2.d1', '4.l1.d1', '4.l2.a1', '4.m1.a1', '4.n1.b1', '4.o1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.g1.b1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.g1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 7995152
    {'ambient': '128.1717', 'aut_centralizer_order': 512, 'aut_label': '32.c1', 'aut_quo_index': 60, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.n1.a1', '16.o1.a1', '16.p1.a1', '16.p1.b1', '16.q1.a1'], 'contains': ['64.c1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6643, 4513, 2821, 5077, 6680, 4612, 2821, 5030], 'generators': [32], 'label': '128.1717.32.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': ['16.b1.a1'], 'normal_contains': ['64.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.c1.a1', 'projective_image': '32.50', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.50', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 7995153
    {'ambient': '128.1717', 'aut_centralizer_order': 512, 'aut_label': '32.c1', 'aut_quo_index': 60, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.n1.b1', '16.o1.b1', '16.p1.c1', '16.p1.d1', '16.q1.b1'], 'contains': ['64.c1.a1'], 'core': '32.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6643, 4513, 3924, 4625, 6680, 4612, 3922, 4295], 'generators': [104], 'label': '128.1717.32.c1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.c1.b1', 'normal_contained_in': ['16.b1.a1'], 'normal_contains': ['64.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.c1.b1', 'projective_image': '32.50', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.50', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 7995154
    {'ambient': '128.1717', 'aut_centralizer_order': 512, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.j1.a1', '16.j1.b1'], 'contains': ['64.a1.a1', '64.d1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4500, -1, 8866, -1, 4521, -1, 8865, -1], 'generators': [1, 72], 'label': '128.1717.32.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.d1.a1', 'projective_image': '64.248', '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': '2.1'}
  • id: 7995155
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '4.k2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '16.k1.a1', '16.k1.c1'], 'contains': ['64.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3094, -1, 9585, -1, 3108, -1, 9583, -1], 'generators': [2], 'label': '128.1717.32.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '32.e1.a1', 'projective_image': '64.248', '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': '2.1'}
  • id: 7995156
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '4.k2.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.b1', '16.k1.a1', '16.k1.c1'], 'contains': ['64.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3094, -1, 9703, -1, 3108, -1, 9702, -1], 'generators': [38], 'label': '128.1717.32.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '32.e1.b1', 'projective_image': '64.248', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 7995157
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '4.k2.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.c1', '16.k1.b1', '16.k1.d1'], 'contains': ['64.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3094, -1, 9112, -1, 3108, -1, 9110, -1], 'generators': [35], 'label': '128.1717.32.e1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.b1', 'old_label': '32.e1.c1', 'projective_image': '64.248', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 7995158
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '4.k2.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.d1', '16.k1.b1', '16.k1.d1'], 'contains': ['64.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3094, -1, 9348, -1, 3108, -1, 9347, -1], 'generators': [7], 'label': '128.1717.32.e1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.b1', 'old_label': '32.e1.d1', 'projective_image': '64.248', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 7995159
    {'ambient': '128.1717', 'aut_centralizer_order': 512, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.j1.a1', '16.j1.b1'], 'contains': ['64.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4220, -1, 8993, -1, 4238, -1, 8992, -1], 'generators': [37], 'label': '128.1717.32.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.f1.a1', 'projective_image': '64.248', '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': '2.1'}
  • id: 7995160
    {'ambient': '128.1717', 'aut_centralizer_order': 512, 'aut_label': '32.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.l1.a1'], 'contains': ['64.b1.a1', '64.d1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3376, -1, 7059, -1, 3390, -1, 7058, -1], 'generators': [1, 8], 'label': '128.1717.32.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.g1.a1', 'projective_image': '64.249', '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': '2.1'}
  • id: 7995161
    {'ambient': '128.1717', 'aut_centralizer_order': 512, 'aut_label': '32.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.l1.a1'], 'contains': ['64.b1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2831, -1, 6281, -1, 2843, -1, 6281, -1], 'generators': [4], 'label': '128.1717.32.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.h1.a1', 'projective_image': '64.249', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 7995162
    {'ambient': '128.1717', 'aut_centralizer_order': 4, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 16, 'centralizer': '16.b1.a1', 'complements': ['64.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.k1.c1', '4.k2.b1', '4.l1.b1', '4.l2.c1', '4.m1.b1', '4.n1.a1', '4.o1.b1'], 'core': '2.g1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [6697, 3059, 2118, 7498, 6731, 3084, 2118, 7498], 'generators': [5, 6, 16], 'label': '128.1717.2.g1.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1.c1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.k1.c1', '4.k2.b1', '4.l1.b1', '4.l2.c1', '4.m1.b1', '4.n1.a1', '4.o1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.g1.c1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.g1.c1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 7995163
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '4.k2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '16.m1.a1'], 'contains': ['64.b1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1902, -1, 5611, -1, 1911, -1, 5611, -1], 'generators': [34], 'label': '128.1717.32.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '32.i1.a1', 'projective_image': '64.249', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 7995164
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '4.k2.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.b1', '16.m1.b1'], 'contains': ['64.b1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1902, -1, 6814, -1, 1911, -1, 6813, -1], 'generators': [6], 'label': '128.1717.32.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.c1', 'old_label': '32.i1.b1', 'projective_image': '64.249', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.i1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 7995165
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '4.k2.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.c1', '16.m1.b1'], 'contains': ['64.b1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1902, -1, 6932, -1, 1911, -1, 6932, -1], 'generators': [3], 'label': '128.1717.32.i1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.d1', 'old_label': '32.i1.c1', 'projective_image': '64.249', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.i1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 7995166
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '4.k2.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.d1', '16.m1.a1'], 'contains': ['64.b1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1902, -1, 6505, -1, 1911, -1, 6505, -1], 'generators': [39], 'label': '128.1717.32.i1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.b1', 'old_label': '32.i1.d1', 'projective_image': '64.249', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.i1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 7995168
    {'ambient': '128.1717', 'aut_centralizer_order': 512, 'aut_label': '32.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.n1.a1', '16.n1.b1'], 'contains': ['64.c1.a1', '64.d1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4801, -1, 4705, -1, 4822, -1, 4704, -1], 'generators': [1, 64], 'label': '128.1717.32.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.k1.a1', 'projective_image': '64.200', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 7995169
    {'ambient': '128.1717', 'aut_centralizer_order': 512, 'aut_label': '32.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '16.n1.a1', '16.n1.b1'], 'contains': ['64.c1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5082, -1, 4577, -1, 5105, -1, 4577, -1], 'generators': [33], 'label': '128.1717.32.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.l1.a1', 'projective_image': '64.200', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 7995170
    {'ambient': '128.1717', 'aut_centralizer_order': 2048, 'aut_label': '64.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.b1.a1', '32.b1.b1', '32.d1.a1', '32.e1.a1', '32.e1.b1', '32.e1.c1', '32.e1.d1', '32.f1.a1'], 'contains': ['128.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4088, 5845, 9171, 2814, 4044, 5894, 9169, 2815], 'generators': [72], 'label': '128.1717.64.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': ['32.a1.a1', '32.b1.b1', '32.b1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.a1.a1', 'projective_image': '64.248', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.248', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 7995171
    {'ambient': '128.1717', 'aut_centralizer_order': 2048, 'aut_label': '64.b1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.g1.a1', '32.h1.a1', '32.i1.a1', '32.i1.b1', '32.i1.c1', '32.i1.d1', '32.j1.a1'], 'contains': ['128.a1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3105, 6114, 6814, 2936, 3119, 6165, 6813, 2936], 'generators': [8], 'label': '128.1717.64.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '64.b1.a1', 'normal_contained_in': ['32.a1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.b1.a1', 'projective_image': '64.249', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.249', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 7995172
    {'ambient': '128.1717', 'aut_centralizer_order': 2048, 'aut_label': '64.c1', 'aut_quo_index': 96, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.c1.a1', '32.c1.b1', '32.k1.a1', '32.l1.a1'], 'contains': ['128.a1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4801, 5576, 4642, 3291, 4822, 5622, 4641, 3058], 'generators': [64], 'label': '128.1717.64.c1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '64.c1.a1', 'normal_contained_in': ['32.a1.a1', '32.c1.b1', '32.c1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.c1.a1', 'projective_image': '64.200', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.200', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 7995173
    {'ambient': '128.1717', 'aut_centralizer_order': 4, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 16, 'centralizer': '16.b1.a1', 'complements': ['64.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.k1.b1', '4.k2.c1', '4.l1.c1', '4.l2.b1', '4.m1.b1', '4.n1.b1', '4.o1.a1'], 'core': '2.g1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [6697, 3059, 4709, 5110, 6731, 3084, 4709, 5110], 'generators': [17, 18, 20], 'label': '128.1717.2.g1.d1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1.d1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.k1.b1', '4.k2.c1', '4.l1.c1', '4.l2.b1', '4.m1.b1', '4.n1.b1', '4.o1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.g1.d1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.g1.d1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 7995174
    {'ambient': '128.1717', 'aut_centralizer_order': 512, 'aut_label': '64.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '32.g1.a1', '32.k1.a1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4493, -1, 6998, -1, 4385, -1, 6997, -1], 'generators': [1], 'label': '128.1717.64.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.d1.a1', 'projective_image': '128.1717', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 7995175
    {'ambient': '128.1717', 'aut_centralizer_order': None, 'aut_label': '128.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': ['64.a1.a1', '64.b1.a1', '64.c1.a1', '64.d1.a1'], 'contains': [], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4355, 5845, 6935, 2936, 4315, 5894, 6935, 2936], 'generators': [], 'label': '128.1717.128.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '128.a1.a1', 'normal_contained_in': ['64.b1.a1', '64.c1.a1', '64.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '128.a1.a1', 'projective_image': '128.1717', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 7995176
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 32, 'centralizer': '4.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.e1.a1', '8.g1.a1', '8.m1.a1', '8.o1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4731, 5860, 5774, 3935, 4752, 5909, 5773, 3935], 'generators': [1, 4, 32], 'label': '128.1717.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '8.c1.a1', '8.b1.a1', '8.e1.a1', '8.g1.a1', '8.o1.a1', '8.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995177
    {'ambient': '128.1717', 'aut_centralizer_order': 16, 'aut_label': '4.b1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '64.202', 'aut_weyl_index': 32, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.d1.b1'], 'contains': ['8.a1.a1', '8.d1.a1', '8.d1.b1', '8.f1.a1', '8.f1.c1', '8.q1.a1', '8.s1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4121, 6907, 6273, 2800, 4139, 6965, 6273, 2800], 'generators': [1, 2, 32], 'label': '128.1717.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.d1.a1', '2.d1.b1'], 'normal_contains': ['8.a1.a1', '8.d1.b1', '8.d1.a1', '8.f1.c1', '8.f1.a1', '8.q1.a1', '8.s1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '16.14', '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': '16.14'}
  • id: 7995178
    {'ambient': '128.1717', 'aut_centralizer_order': 16, 'aut_label': '4.b1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '64.202', 'aut_weyl_index': 32, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.c1', '2.d1.d1'], 'contains': ['8.a1.a1', '8.d1.c1', '8.d1.d1', '8.f1.b1', '8.f1.d1', '8.q1.b1', '8.s1.b1'], 'core': '4.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4121, 6907, 6789, 4209, 4139, 6965, 6789, 4210], 'generators': [1, 6, 32], 'label': '128.1717.4.b1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.b1', 'normal_contained_in': ['2.a1.a1', '2.d1.c1', '2.d1.d1'], 'normal_contains': ['8.a1.a1', '8.d1.d1', '8.d1.c1', '8.f1.d1', '8.f1.b1', '8.q1.b1', '8.s1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.b1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 7995179
    {'ambient': '128.1717', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '512.10493360', 'aut_weyl_index': 4, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '4.e1.a1', '4.e1.b1', '4.f1.a1', '4.f1.b1', '4.g1.a1', '4.g1.b1', '4.m1.a1', '4.m1.b1', '4.p1.a1', '4.q1.a1', '4.r1.a1', '4.r1.b1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2959, 7202, 7332, 2672, 2972, 7259, 7329, 2672], 'generators': [1, 2, 4, 32], 'label': '128.1717.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '4.f1.b1', '4.f1.a1', '4.e1.b1', '4.e1.a1', '4.g1.b1', '4.g1.a1', '4.m1.b1', '4.m1.a1', '4.r1.a1', '4.r1.b1', '4.p1.a1', '4.q1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '16.14', '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': '16.14'}
  • id: 7995180
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 64, 'centralizer': '8.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.d1.c1'], 'contains': ['8.a1.a1', '8.h1.a1', '8.j1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9783, 688, 1130, 6566, 9826, 694, 1130, 6566], 'generators': [1, 16], 'label': '128.1717.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.d1.c1'], 'normal_contains': ['8.a1.a1', '8.h1.a1', '8.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '16.14', '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': '8.5'}
  • id: 7995181
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 64, 'centralizer': '8.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.b1', '2.d1.d1'], 'contains': ['8.a1.a1', '8.h1.b1', '8.j1.b1'], 'core': '4.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9783, 688, 1912, 8166, 9826, 694, 1912, 8166], 'generators': [1, 20], 'label': '128.1717.4.c1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.b1', 'normal_contained_in': ['2.b1.a1', '2.d1.b1', '2.d1.d1'], 'normal_contains': ['8.a1.a1', '8.h1.b1', '8.j1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.b1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 7995182
    {'ambient': '128.1717', 'aut_centralizer_order': 16, 'aut_label': '4.d1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '64.202', 'aut_weyl_index': 32, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.d1.d1'], 'contains': ['8.a1.a1', '8.i1.a1', '8.i1.c1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6215, 4173, 4512, 9172, 6243, 4208, 4512, 9172], 'generators': [1, 18], 'label': '128.1717.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.d1.d1'], 'normal_contains': ['8.a1.a1', '8.i1.a1', '8.i1.c1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '16.14', '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': '16.14'}
  • id: 7995183
    {'ambient': '128.1717', 'aut_centralizer_order': 16, 'aut_label': '4.d1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '64.202', 'aut_weyl_index': 32, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.b1', '2.d1.c1'], 'contains': ['8.a1.a1', '8.i1.b1', '8.i1.d1'], 'core': '4.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6215, 4173, 2616, 5711, 6243, 4208, 2616, 5711], 'generators': [1, 22], 'label': '128.1717.4.d1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.b1', 'normal_contained_in': ['2.c1.a1', '2.d1.b1', '2.d1.c1'], 'normal_contains': ['8.a1.a1', '8.i1.b1', '8.i1.d1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.b1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 7995184
    {'ambient': '128.1717', 'aut_centralizer_order': 8, 'aut_label': '4.e1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 16, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.a1', '8.d1.a1', '8.d1.d1', '8.k1.a1', '8.l1.b1', '8.p1.a1', '8.p1.d1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1913, 6365, 8492, 1316, 1922, 6418, 8491, 1316], 'generators': [1, 2, 36], 'label': '128.1717.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.b1.a1', '8.d1.d1', '8.d1.a1', '8.k1.a1', '8.l1.b1', '8.p1.a1', '8.p1.d1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '32.45', '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': '16.14'}
  • id: 7995185
    {'ambient': '128.1717', 'aut_centralizer_order': 8, 'aut_label': '4.e1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 16, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.a1', '8.d1.b1', '8.d1.c1', '8.k1.b1', '8.l1.a1', '8.p1.b1', '8.p1.c1'], 'core': '4.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1913, 6365, 8306, 1543, 1922, 6418, 8305, 1543], 'generators': [1, 34, 36], 'label': '128.1717.4.e1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.e1.b1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.b1.a1', '8.d1.b1', '8.d1.c1', '8.k1.b1', '8.l1.a1', '8.p1.c1', '8.p1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.b1', 'projective_image': '32.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 7995186
    {'ambient': '128.1717', 'aut_centralizer_order': 8, 'aut_label': '4.f1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 16, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.c1.a1', '8.d1.a1', '8.d1.c1', '8.n1.a1', '8.n1.c1', '8.r1.a1', '8.t1.b1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1073, 8653, 8120, 3263, 1077, 8726, 8120, 3263], 'generators': [1, 2, 4], 'label': '128.1717.4.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.c1.a1', '8.d1.c1', '8.d1.a1', '8.n1.a1', '8.n1.c1', '8.r1.a1', '8.t1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '32.45', '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': '16.14'}
  • id: 7995187
    {'ambient': '128.1717', 'aut_centralizer_order': 8, 'aut_label': '4.f1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 16, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.c1.a1', '8.d1.b1', '8.d1.d1', '8.n1.b1', '8.n1.d1', '8.r1.b1', '8.t1.a1'], 'core': '4.f1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1073, 8653, 7631, 1881, 1077, 8726, 7630, 1881], 'generators': [1, 34, 4], 'label': '128.1717.4.f1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.f1.b1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.c1.a1', '8.d1.b1', '8.d1.d1', '8.n1.d1', '8.n1.b1', '8.r1.b1', '8.t1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.b1', 'projective_image': '32.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 7995188
    {'ambient': '128.1717', 'aut_centralizer_order': 16, 'aut_label': '4.g1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '64.202', 'aut_weyl_index': 32, 'centralizer': '8.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.e1.a1', '2.f1.a1'], 'contains': ['8.e1.a1', '8.f1.a1', '8.f1.b1', '8.k1.a1', '8.l1.a1', '8.n1.a1', '8.n1.b1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3547, 5310, 6015, 2542, 3563, 5354, 6015, 2542], 'generators': [2, 4, 32], 'label': '128.1717.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.a1.a1', '2.e1.a1', '2.f1.a1'], 'normal_contains': ['8.e1.a1', '8.f1.b1', '8.f1.a1', '8.n1.a1', '8.n1.b1', '8.k1.a1', '8.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '16.14', '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': '8.5'}
  • id: 7995189
    {'ambient': '128.1717', 'aut_centralizer_order': 16, 'aut_label': '4.g1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '64.202', 'aut_weyl_index': 32, 'centralizer': '8.h1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.e1.b1', '2.f1.b1'], 'contains': ['8.e1.a1', '8.f1.c1', '8.f1.d1', '8.k1.b1', '8.l1.b1', '8.n1.c1', '8.n1.d1'], 'core': '4.g1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3547, 5310, 7047, 3693, 3563, 5354, 7047, 3694], 'generators': [3, 4, 32], 'label': '128.1717.4.g1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1.b1', 'normal_contained_in': ['2.a1.a1', '2.e1.b1', '2.f1.b1'], 'normal_contains': ['8.e1.a1', '8.f1.c1', '8.f1.d1', '8.n1.d1', '8.n1.c1', '8.k1.b1', '8.l1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.b1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 7995190
    {'ambient': '128.1717', 'aut_centralizer_order': 8, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.55643', 'aut_weyl_index': 8, 'centralizer': '8.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '4.c1.b1', '4.h1.a1', '4.j1.a1', '4.n1.a1', '4.n1.b1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8795, 1107, 1387, 6638, 8629, 1116, 1387, 6638], 'generators': [1, 4, 16], 'label': '128.1717.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.c1.a1', '4.c1.b1', '4.h1.a1', '4.j1.a1', '4.n1.a1', '4.n1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '16.14', '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': '8.5'}
  • id: 7995191
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '4.h1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '64.202', 'aut_weyl_index': 32, 'centralizer': '4.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.e1.a1', '2.e1.b1'], 'contains': ['8.e1.a1', '8.h1.a1', '8.h1.b1'], 'core': '4.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9325, 221, 925, 9528, 9367, 222, 925, 9528], 'generators': [4, 16], 'label': '128.1717.4.h1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.h1.a1', 'normal_contained_in': ['2.b1.a1', '2.e1.b1', '2.e1.a1'], 'normal_contains': ['8.e1.a1', '8.h1.a1', '8.h1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.h1.a1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995192
    {'ambient': '128.1717', 'aut_centralizer_order': 16, 'aut_label': '4.i1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '64.202', 'aut_weyl_index': 32, 'centralizer': '8.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.b1'], 'contains': ['8.e1.a1', '8.i1.a1', '8.i1.b1'], 'core': '4.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5838, 3788, 5418, 7179, 5865, 3820, 5417, 7179], 'generators': [18, 4], 'label': '128.1717.4.i1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.i1.a1', 'normal_contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.b1'], 'normal_contains': ['8.e1.a1', '8.i1.a1', '8.i1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.i1.a1', 'projective_image': '16.14', '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': '8.5'}
  • id: 7995193
    {'ambient': '128.1717', 'aut_centralizer_order': 16, 'aut_label': '4.i1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '64.202', 'aut_weyl_index': 32, 'centralizer': '8.h1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.e1.b1', '2.f1.a1'], 'contains': ['8.e1.a1', '8.i1.c1', '8.i1.d1'], 'core': '4.i1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5838, 3788, 586, 7329, 5865, 3820, 587, 7330], 'generators': [19, 4], 'label': '128.1717.4.i1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.i1.b1', 'normal_contained_in': ['2.c1.a1', '2.e1.b1', '2.f1.a1'], 'normal_contains': ['8.e1.a1', '8.i1.c1', '8.i1.d1'], 'normalizer': '1.a1.a1', 'old_label': '4.i1.b1', 'projective_image': '16.14', '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': '8.5'}
  • id: 7995194
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '4.j1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '64.202', 'aut_weyl_index': 32, 'centralizer': '4.j1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.f1.a1', '2.f1.b1'], 'contains': ['8.e1.a1', '8.j1.a1', '8.j1.b1'], 'core': '4.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8493, 2352, 97, 4760, 8530, 2372, 97, 4760], 'generators': [17, 4], 'label': '128.1717.4.j1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.j1.a1', 'normal_contained_in': ['2.b1.a1', '2.f1.b1', '2.f1.a1'], 'normal_contains': ['8.e1.a1', '8.j1.a1', '8.j1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.j1.a1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995195
    {'ambient': '128.1717', 'aut_centralizer_order': 16, 'aut_label': '4.k1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '32.51', 'aut_weyl_index': 64, 'centralizer': '8.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.b1', '2.e1.a1', '2.g1.b1'], 'contains': ['8.f1.a1', '8.h1.b1', '8.i1.b1'], 'core': '4.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7579, 1417, 3968, 7028, 7612, 1429, 3968, 7028], 'generators': [2, 20], 'label': '128.1717.4.k1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.k1.a1', 'normal_contained_in': ['2.d1.b1', '2.e1.a1', '2.g1.b1'], 'normal_contains': ['8.f1.a1', '8.h1.b1', '8.i1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.k1.a1', 'projective_image': '16.14', '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': '8.5'}
  • id: 7995196
    {'ambient': '128.1717', 'aut_centralizer_order': 16, 'aut_label': '4.k1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '32.51', 'aut_weyl_index': 64, 'centralizer': '8.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.d1', '2.e1.a1', '2.g1.d1'], 'contains': ['8.f1.b1', '8.h1.b1', '8.i1.a1'], 'core': '4.k1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7579, 1417, 5267, 9003, 7612, 1429, 5266, 9003], 'generators': [18, 20], 'label': '128.1717.4.k1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.k1.b1', 'normal_contained_in': ['2.d1.d1', '2.e1.a1', '2.g1.d1'], 'normal_contains': ['8.f1.b1', '8.h1.b1', '8.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.k1.b1', 'projective_image': '16.14', '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': '8.5'}
  • id: 7995197
    {'ambient': '128.1717', 'aut_centralizer_order': 16, 'aut_label': '4.k1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '32.51', 'aut_weyl_index': 64, 'centralizer': '8.h1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.e1.b1', '2.g1.c1'], 'contains': ['8.f1.c1', '8.h1.a1', '8.i1.c1'], 'core': '4.k1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [7579, 1417, 1451, 9939, 7612, 1429, 1451, 9939], 'generators': [3, 16], 'label': '128.1717.4.k1.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.k1.c1', 'normal_contained_in': ['2.d1.a1', '2.e1.b1', '2.g1.c1'], 'normal_contains': ['8.f1.c1', '8.h1.a1', '8.i1.c1'], 'normalizer': '1.a1.a1', 'old_label': '4.k1.c1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.k1.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 7995198
    {'ambient': '128.1717', 'aut_centralizer_order': 16, 'aut_label': '4.k1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '32.51', 'aut_weyl_index': 64, 'centralizer': '8.h1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.c1', '2.e1.b1', '2.g1.a1'], 'contains': ['8.f1.d1', '8.h1.a1', '8.i1.d1'], 'core': '4.k1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [7579, 1417, 1299, 9340, 7612, 1429, 1300, 9341], 'generators': [7, 16], 'label': '128.1717.4.k1.d1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.k1.d1', 'normal_contained_in': ['2.d1.c1', '2.e1.b1', '2.g1.a1'], 'normal_contains': ['8.f1.d1', '8.h1.a1', '8.i1.d1'], 'normalizer': '1.a1.a1', 'old_label': '4.k1.d1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.k1.d1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 7995199
    {'ambient': '128.1717', 'aut_centralizer_order': 16, 'aut_label': '4.k2', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '32.51', 'aut_weyl_index': 64, 'centralizer': '4.k2.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.e1.a1', '2.g1.a1'], 'contains': ['8.f1.a1', '8.h1.a1', '8.i1.a1'], 'core': '4.k2.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7995, 1844, 4155, 8815, 8031, 1859, 4155, 8815], 'generators': [2, 16], 'label': '128.1717.4.k2.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.k2.a1', 'normal_contained_in': ['2.d1.a1', '2.e1.a1', '2.g1.a1'], 'normal_contains': ['8.f1.a1', '8.h1.a1', '8.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.k2.a1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.k2.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995200
    {'ambient': '128.1717', 'aut_centralizer_order': 16, 'aut_label': '4.k2', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '32.51', 'aut_weyl_index': 64, 'centralizer': '4.k2.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.c1', '2.e1.a1', '2.g1.c1'], 'contains': ['8.f1.b1', '8.h1.a1', '8.i1.b1'], 'core': '4.k2.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7995, 1844, 2118, 7961, 8031, 1859, 2118, 7961], 'generators': [6, 16], 'label': '128.1717.4.k2.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.k2.b1', 'normal_contained_in': ['2.d1.c1', '2.e1.a1', '2.g1.c1'], 'normal_contains': ['8.f1.b1', '8.h1.a1', '8.i1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.k2.b1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.k2.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995201
    {'ambient': '128.1717', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '512.10493360', 'aut_weyl_index': 4, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.d1.a1', '4.d1.b1', '4.i1.a1', '4.i1.b1', '4.o1.a1', '4.o1.b1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5513, 4271, 4244, 7203, 5541, 4306, 4244, 7203], 'generators': [1, 18, 4], 'label': '128.1717.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.d1.a1', '4.d1.b1', '4.i1.a1', '4.i1.b1', '4.o1.a1', '4.o1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '16.14', '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': '16.14'}
  • id: 7995202
    {'ambient': '128.1717', 'aut_centralizer_order': 16, 'aut_label': '4.k2', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '32.51', 'aut_weyl_index': 64, 'centralizer': '4.k2.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.b1', '2.e1.b1', '2.g1.d1'], 'contains': ['8.f1.c1', '8.h1.b1', '8.i1.d1'], 'core': '4.k2.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [7995, 1844, 3044, 6361, 8031, 1859, 3044, 6360], 'generators': [3, 20], 'label': '128.1717.4.k2.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.k2.c1', 'normal_contained_in': ['2.d1.b1', '2.e1.b1', '2.g1.d1'], 'normal_contains': ['8.f1.c1', '8.h1.b1', '8.i1.d1'], 'normalizer': '1.a1.a1', 'old_label': '4.k2.c1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.k2.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995203
    {'ambient': '128.1717', 'aut_centralizer_order': 16, 'aut_label': '4.k2', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '32.51', 'aut_weyl_index': 64, 'centralizer': '4.k2.d1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.d1', '2.e1.b1', '2.g1.b1'], 'contains': ['8.f1.d1', '8.h1.b1', '8.i1.c1'], 'core': '4.k2.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [7995, 1844, 2821, 9751, 8031, 1859, 2821, 9752], 'generators': [19, 20], 'label': '128.1717.4.k2.d1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.k2.d1', 'normal_contained_in': ['2.d1.d1', '2.e1.b1', '2.g1.b1'], 'normal_contains': ['8.f1.d1', '8.h1.b1', '8.i1.c1'], 'normalizer': '1.a1.a1', 'old_label': '4.k2.d1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.k2.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995204
    {'ambient': '128.1717', 'aut_centralizer_order': 16, 'aut_label': '4.l1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '32.51', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.b1', '2.f1.a1', '2.g1.a1'], 'contains': ['8.f1.a1', '8.i1.d1', '8.j1.b1'], 'core': '4.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6592, 2778, 435, 5880, 6621, 2802, 435, 5881], 'generators': [21, 2], 'label': '128.1717.4.l1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.l1.a1', 'normal_contained_in': ['2.d1.b1', '2.f1.a1', '2.g1.a1'], 'normal_contains': ['8.f1.a1', '8.i1.d1', '8.j1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.l1.a1', 'projective_image': '16.14', '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': '16.14'}
  • id: 7995205
    {'ambient': '128.1717', 'aut_centralizer_order': 16, 'aut_label': '4.l1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '32.51', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.d1', '2.f1.a1', '2.g1.c1'], 'contains': ['8.f1.b1', '8.i1.c1', '8.j1.b1'], 'core': '4.l1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6592, 2778, 737, 7773, 6621, 2802, 738, 7774], 'generators': [21, 6], 'label': '128.1717.4.l1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.l1.b1', 'normal_contained_in': ['2.d1.d1', '2.f1.a1', '2.g1.c1'], 'normal_contains': ['8.f1.b1', '8.i1.c1', '8.j1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.l1.b1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.l1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 7995206
    {'ambient': '128.1717', 'aut_centralizer_order': 16, 'aut_label': '4.l1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '32.51', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.f1.b1', '2.g1.d1'], 'contains': ['8.f1.c1', '8.i1.a1', '8.j1.a1'], 'core': '4.l1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [6592, 2778, 5569, 4947, 6621, 2802, 5568, 4947], 'generators': [17, 18], 'label': '128.1717.4.l1.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.l1.c1', 'normal_contained_in': ['2.d1.a1', '2.f1.b1', '2.g1.d1'], 'normal_contains': ['8.f1.c1', '8.i1.a1', '8.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.l1.c1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.l1.c1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 7995207
    {'ambient': '128.1717', 'aut_centralizer_order': 16, 'aut_label': '4.l1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '32.51', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.c1', '2.f1.b1', '2.g1.b1'], 'contains': ['8.f1.d1', '8.i1.b1', '8.j1.a1'], 'core': '4.l1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [6592, 2778, 4343, 5098, 6621, 2802, 4342, 5099], 'generators': [17, 22], 'label': '128.1717.4.l1.d1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.l1.d1', 'normal_contained_in': ['2.d1.c1', '2.f1.b1', '2.g1.b1'], 'normal_contains': ['8.f1.d1', '8.i1.b1', '8.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.l1.d1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.l1.d1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 7995208
    {'ambient': '128.1717', 'aut_centralizer_order': 16, 'aut_label': '4.l2', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '32.51', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.f1.a1', '2.g1.b1'], 'contains': ['8.f1.a1', '8.i1.c1', '8.j1.a1'], 'core': '4.l2.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7085, 3283, 1673, 5321, 7117, 3311, 1673, 5320], 'generators': [17, 2], 'label': '128.1717.4.l2.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.l2.a1', 'normal_contained_in': ['2.d1.a1', '2.f1.a1', '2.g1.b1'], 'normal_contains': ['8.f1.a1', '8.i1.c1', '8.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.l2.a1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.l2.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 7995209
    {'ambient': '128.1717', 'aut_centralizer_order': 16, 'aut_label': '4.l2', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '32.51', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.c1', '2.f1.a1', '2.g1.d1'], 'contains': ['8.f1.b1', '8.i1.d1', '8.j1.a1'], 'core': '4.l2.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7085, 3283, 2376, 4502, 7117, 3311, 2376, 4502], 'generators': [17, 6], 'label': '128.1717.4.l2.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.l2.b1', 'normal_contained_in': ['2.d1.c1', '2.f1.a1', '2.g1.d1'], 'normal_contains': ['8.f1.b1', '8.i1.d1', '8.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.l2.b1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.l2.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 7995210
    {'ambient': '128.1717', 'aut_centralizer_order': 16, 'aut_label': '4.l2', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '32.51', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.b1', '2.f1.b1', '2.g1.c1'], 'contains': ['8.f1.c1', '8.i1.b1', '8.j1.b1'], 'core': '4.l2.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [7085, 3283, 3746, 6103, 7117, 3311, 3746, 6102], 'generators': [21, 22], 'label': '128.1717.4.l2.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.l2.c1', 'normal_contained_in': ['2.d1.b1', '2.f1.b1', '2.g1.c1'], 'normal_contains': ['8.f1.c1', '8.i1.b1', '8.j1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.l2.c1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.l2.c1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 7995211
    {'ambient': '128.1717', 'aut_centralizer_order': 16, 'aut_label': '4.l2', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '32.51', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.d1', '2.f1.b1', '2.g1.a1'], 'contains': ['8.f1.d1', '8.i1.a1', '8.j1.b1'], 'core': '4.l2.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [7085, 3283, 4752, 8557, 7117, 3311, 4752, 8557], 'generators': [21, 18], 'label': '128.1717.4.l2.d1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.l2.d1', 'normal_contained_in': ['2.d1.d1', '2.f1.b1', '2.g1.a1'], 'normal_contains': ['8.f1.d1', '8.i1.a1', '8.j1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.l2.d1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.l2.d1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 7995212
    {'ambient': '128.1717', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 16, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.a1', '4.d1.a1', '4.k1.c1', '4.k2.a1', '4.l1.c1', '4.l2.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7889, 2356, 3370, 6947, 7928, 2376, 3370, 6947], 'generators': [1, 2, 16], 'label': '128.1717.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.c1.a1', '4.d1.a1', '4.k1.c1', '4.k2.a1', '4.l1.c1', '4.l2.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '16.14', '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': '16.14'}
  • id: 7995213
    {'ambient': '128.1717', 'aut_centralizer_order': 16, 'aut_label': '4.m1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '64.202', 'aut_weyl_index': 32, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.g1.a1', '2.g1.b1'], 'contains': ['8.f1.a1', '8.f1.d1', '8.g1.a1', '8.p1.a1', '8.p1.b1', '8.r1.a1', '8.t1.a1'], 'core': '4.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2370, 7495, 6531, 3469, 2381, 7557, 6531, 3469], 'generators': [5, 2, 32], 'label': '128.1717.4.m1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.m1.a1', 'normal_contained_in': ['2.a1.a1', '2.g1.a1', '2.g1.b1'], 'normal_contains': ['8.f1.d1', '8.f1.a1', '8.g1.a1', '8.p1.a1', '8.p1.b1', '8.r1.a1', '8.t1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.m1.a1', 'projective_image': '16.14', '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': '16.14'}
  • id: 7995214
    {'ambient': '128.1717', 'aut_centralizer_order': 16, 'aut_label': '4.m1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '64.202', 'aut_weyl_index': 32, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.g1.c1', '2.g1.d1'], 'contains': ['8.f1.b1', '8.f1.c1', '8.g1.a1', '8.p1.c1', '8.p1.d1', '8.r1.b1', '8.t1.b1'], 'core': '4.m1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2370, 7495, 7426, 3058, 2381, 7557, 7425, 3058], 'generators': [5, 6, 32], 'label': '128.1717.4.m1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.m1.b1', 'normal_contained_in': ['2.a1.a1', '2.g1.c1', '2.g1.d1'], 'normal_contains': ['8.f1.c1', '8.f1.b1', '8.g1.a1', '8.p1.c1', '8.p1.d1', '8.r1.b1', '8.t1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.m1.b1', 'projective_image': '16.14', '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': '16.14'}
  • id: 7995215
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '4.n1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 64, 'centralizer': '8.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.g1.a1', '2.g1.c1'], 'contains': ['8.g1.a1', '8.h1.a1', '8.j1.b1'], 'core': '4.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8908, 1073, 285, 8335, 8948, 1082, 284, 8335], 'generators': [5, 16], 'label': '128.1717.4.n1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.n1.a1', 'normal_contained_in': ['2.b1.a1', '2.g1.c1', '2.g1.a1'], 'normal_contains': ['8.g1.a1', '8.h1.a1', '8.j1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.n1.a1', 'projective_image': '16.14', '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': '8.5'}
  • id: 7995216
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '4.n1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 64, 'centralizer': '8.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.g1.b1', '2.g1.d1'], 'contains': ['8.g1.a1', '8.h1.b1', '8.j1.a1'], 'core': '4.n1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8908, 1073, 3525, 5542, 8948, 1082, 3524, 5542], 'generators': [17, 20], 'label': '128.1717.4.n1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.n1.b1', 'normal_contained_in': ['2.b1.a1', '2.g1.d1', '2.g1.b1'], 'normal_contains': ['8.g1.a1', '8.h1.b1', '8.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.n1.b1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.n1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 7995217
    {'ambient': '128.1717', 'aut_centralizer_order': 16, 'aut_label': '4.o1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '64.202', 'aut_weyl_index': 32, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.g1.a1', '2.g1.d1'], 'contains': ['8.g1.a1', '8.i1.a1', '8.i1.d1'], 'core': '4.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5345, 4720, 5044, 6805, 5369, 4759, 5044, 6806], 'generators': [5, 18], 'label': '128.1717.4.o1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.o1.a1', 'normal_contained_in': ['2.c1.a1', '2.g1.d1', '2.g1.a1'], 'normal_contains': ['8.g1.a1', '8.i1.a1', '8.i1.d1'], 'normalizer': '1.a1.a1', 'old_label': '4.o1.a1', 'projective_image': '16.14', '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': '16.14'}
  • id: 7995218
    {'ambient': '128.1717', 'aut_centralizer_order': 16, 'aut_label': '4.o1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '64.202', 'aut_weyl_index': 32, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.g1.b1', '2.g1.c1'], 'contains': ['8.g1.a1', '8.i1.b1', '8.i1.c1'], 'core': '4.o1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5345, 4720, 3302, 7552, 5369, 4759, 3302, 7552], 'generators': [5, 22], 'label': '128.1717.4.o1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.o1.b1', 'normal_contained_in': ['2.c1.a1', '2.g1.c1', '2.g1.b1'], 'normal_contains': ['8.g1.a1', '8.i1.b1', '8.i1.c1'], 'normalizer': '1.a1.a1', 'old_label': '4.o1.b1', 'projective_image': '16.14', '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': '16.14'}
  • id: 7995219
    {'ambient': '128.1717', 'aut_centralizer_order': 8, 'aut_label': '4.p1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 8, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.k1.a1', '8.k1.b1', '8.m1.a1', '8.q1.a1', '8.q1.b1', '8.r1.a1', '8.r1.b1'], 'core': '4.p1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2790, 9038, 8929, 2352, 2803, 9114, 8928, 2353], 'generators': [33, 2, 36], 'label': '128.1717.4.p1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.p1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.k1.b1', '8.k1.a1', '8.m1.a1', '8.r1.b1', '8.r1.a1', '8.q1.a1', '8.q1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.p1.a1', 'projective_image': '32.45', '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': '16.14'}
  • id: 7995220
    {'ambient': '128.1717', 'aut_centralizer_order': 8, 'aut_label': '4.q1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 8, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.l1.a1', '8.l1.b1', '8.m1.a1', '8.s1.a1', '8.s1.b1', '8.t1.a1', '8.t1.b1'], 'core': '4.q1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1537, 8268, 7236, 1712, 1544, 8337, 7236, 1712], 'generators': [33, 34, 36], 'label': '128.1717.4.q1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.q1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.l1.b1', '8.l1.a1', '8.m1.a1', '8.t1.a1', '8.t1.b1', '8.s1.b1', '8.s1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.q1.a1', 'projective_image': '32.45', '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': '16.14'}
  • id: 7995221
    {'ambient': '128.1717', 'aut_centralizer_order': 8, 'aut_label': '4.r1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 16, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.n1.a1', '8.n1.d1', '8.o1.a1', '8.p1.a1', '8.p1.c1', '8.q1.a1', '8.s1.b1'], 'core': '4.r1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3127, 7925, 7951, 2201, 3141, 7990, 7950, 2202], 'generators': [33, 2, 4], 'label': '128.1717.4.r1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.r1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.n1.d1', '8.n1.a1', '8.o1.a1', '8.p1.c1', '8.p1.a1', '8.q1.a1', '8.s1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.r1.a1', 'projective_image': '32.45', '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': '16.14'}
  • id: 7995222
    {'ambient': '128.1717', 'aut_centralizer_order': 8, 'aut_label': '4.r1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 16, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.n1.b1', '8.n1.c1', '8.o1.a1', '8.p1.b1', '8.p1.d1', '8.q1.b1', '8.s1.a1'], 'core': '4.r1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3127, 7925, 7800, 2051, 3141, 7990, 7799, 2051], 'generators': [33, 34, 4], 'label': '128.1717.4.r1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.r1.b1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.n1.c1', '8.n1.b1', '8.o1.a1', '8.p1.d1', '8.p1.b1', '8.q1.b1', '8.s1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.r1.b1', 'projective_image': '32.45', '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': '16.14'}
  • id: 7995223
    {'ambient': '128.1717', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 16, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.b1', '4.d1.b1', '4.k1.a1', '4.k2.c1', '4.l1.a1', '4.l2.c1'], 'core': '2.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7889, 2356, 2753, 6329, 7928, 2376, 2752, 6329], 'generators': [1, 2, 20], 'label': '128.1717.2.d1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.c1.b1', '4.d1.b1', '4.k1.a1', '4.k2.c1', '4.l1.a1', '4.l2.c1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.b1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.d1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 7995224
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '8.a1', 'aut_quo_index': 42, 'aut_stab_index': 1, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '4.c1.a1', '4.c1.b1', '4.d1.a1', '4.d1.b1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.g1.a1', '16.n1.a1', '16.n1.b1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6347, 4035, 4354, 5646, 6375, 4069, 4354, 5646], 'generators': [1, 72, 32], 'label': '128.1717.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '4.c1.a1', '4.c1.b1', '4.d1.a1', '4.d1.b1'], 'normal_contains': ['16.a1.a1', '16.b1.a1', '16.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995225
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.e1.a1', '4.e1.b1'], 'contains': ['16.a1.a1', '16.c1.a1', '16.i1.a1', '16.j1.a1', '16.j1.b1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4871, 4932, 9437, 491, 4892, 4974, 9436, 491], 'generators': [1, 36, 64], 'label': '128.1717.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1', '4.e1.b1', '4.e1.a1'], 'normal_contains': ['16.a1.a1', '16.c1.a1', '16.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '32.45', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995226
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '8.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.f1.a1', '4.f1.b1'], 'contains': ['16.a1.a1', '16.d1.a1', '16.h1.a1', '16.l1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1431, 7034, 6103, 4410, 1437, 7093, 6102, 4410], 'generators': [1, 4, 64], 'label': '128.1717.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.a1.a1', '4.f1.b1', '4.f1.a1'], 'normal_contains': ['16.a1.a1', '16.d1.a1', '16.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '32.45', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995227
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '8.d1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.e1.a1', '4.f1.a1'], 'contains': ['16.a1.a1', '16.e1.a1', '16.f1.c1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1924, 7539, 8270, 3472, 1933, 7602, 8269, 3472], 'generators': [1, 2], 'label': '128.1717.8.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': ['4.b1.a1', '4.f1.a1', '4.e1.a1'], 'normal_contains': ['16.a1.a1', '16.e1.a1', '16.f1.c1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '32.45', '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': '16.14'}
  • id: 7995228
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '8.d1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.e1.b1', '4.f1.b1'], 'contains': ['16.a1.a1', '16.e1.c1', '16.f1.a1'], 'core': '8.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1924, 7539, 6988, 866, 1933, 7602, 6988, 866], 'generators': [1, 34], 'label': '128.1717.8.d1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': ['4.b1.a1', '4.f1.b1', '4.e1.b1'], 'normal_contains': ['16.a1.a1', '16.e1.c1', '16.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.b1', 'projective_image': '32.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 7995229
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '8.d1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '4.e1.b1', '4.f1.a1'], 'contains': ['16.a1.a1', '16.e1.d1', '16.f1.b1'], 'core': '8.d1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [1924, 7539, 8609, 4188, 1933, 7602, 8608, 4188], 'generators': [1, 6], 'label': '128.1717.8.d1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1.c1', 'normal_contained_in': ['4.b1.b1', '4.f1.a1', '4.e1.b1'], 'normal_contains': ['16.a1.a1', '16.e1.d1', '16.f1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.c1', 'projective_image': '32.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.c1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 7995230
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '8.d1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '4.e1.a1', '4.f1.b1'], 'contains': ['16.a1.a1', '16.e1.b1', '16.f1.d1'], 'core': '8.d1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [1924, 7539, 7781, 1277, 1933, 7602, 7779, 1277], 'generators': [1, 38], 'label': '128.1717.8.d1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1.d1', 'normal_contained_in': ['4.b1.b1', '4.f1.b1', '4.e1.a1'], 'normal_contains': ['16.a1.a1', '16.e1.b1', '16.f1.d1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.d1', 'projective_image': '32.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.d1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 7995231
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '8.e1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.g1.a1', '4.g1.b1', '4.h1.a1', '4.i1.a1', '4.i1.b1', '4.j1.a1'], 'contains': ['16.b1.a1', '16.c1.a1', '16.d1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5908, 3280, 4157, 5179, 5934, 3307, 4157, 5179], 'generators': [4, 32], 'label': '128.1717.8.e1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.e1.a1', 'normal_contained_in': ['4.a1.a1', '4.g1.b1', '4.g1.a1', '4.h1.a1', '4.i1.a1', '4.i1.b1', '4.j1.a1'], 'normal_contains': ['16.b1.a1', '16.d1.a1', '16.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.a1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 7995232
    {'ambient': '128.1717', 'aut_centralizer_order': 64, 'aut_label': '8.f1', 'aut_quo_index': 168, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 256, 'centralizer': '4.k2.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.g1.a1', '4.k1.a1', '4.k2.a1', '4.l1.a1', '4.l2.a1', '4.m1.a1'], 'contains': ['16.b1.a1', '16.e1.a1', '16.f1.a1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5609, 3587, 4552, 4910, 5633, 3616, 4551, 4910], 'generators': [2, 32], 'label': '128.1717.8.f1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.f1.a1', 'normal_contained_in': ['4.b1.a1', '4.g1.a1', '4.k1.a1', '4.k2.a1', '4.l1.a1', '4.l2.a1', '4.m1.a1'], 'normal_contains': ['16.b1.a1', '16.e1.a1', '16.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.a1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995233
    {'ambient': '128.1717', 'aut_centralizer_order': 64, 'aut_label': '8.f1', 'aut_quo_index': 168, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 256, 'centralizer': '4.k2.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '4.g1.a1', '4.k1.b1', '4.k2.b1', '4.l1.b1', '4.l2.b1', '4.m1.b1'], 'contains': ['16.b1.a1', '16.e1.b1', '16.f1.b1'], 'core': '8.f1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5609, 3587, 4821, 5448, 5633, 3616, 4820, 5449], 'generators': [6, 32], 'label': '128.1717.8.f1.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.f1.b1', 'normal_contained_in': ['4.b1.b1', '4.g1.a1', '4.k1.b1', '4.k2.b1', '4.l1.b1', '4.l2.b1', '4.m1.b1'], 'normal_contains': ['16.b1.a1', '16.e1.b1', '16.f1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.b1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.f1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995234
    {'ambient': '128.1717', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 16, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.b1', '4.c1.a1', '4.d1.b1', '4.k1.d1', '4.k2.b1', '4.l1.d1', '4.l2.b1'], 'core': '2.d1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [7889, 2356, 2427, 5711, 7928, 2376, 2427, 5711], 'generators': [1, 6, 16], 'label': '128.1717.2.d1.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.c1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.b1', '4.c1.a1', '4.d1.b1', '4.k1.d1', '4.k2.b1', '4.l1.d1', '4.l2.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.c1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.d1.c1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 7995235
    {'ambient': '128.1717', 'aut_centralizer_order': 64, 'aut_label': '8.f1', 'aut_quo_index': 168, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 256, 'centralizer': '4.k2.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.g1.b1', '4.k1.c1', '4.k2.c1', '4.l1.c1', '4.l2.c1', '4.m1.b1'], 'contains': ['16.b1.a1', '16.e1.c1', '16.f1.c1'], 'core': '8.f1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [5609, 3587, 5090, 5044, 5633, 3616, 5090, 5044], 'generators': [3, 32], 'label': '128.1717.8.f1.c1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.f1.c1', 'normal_contained_in': ['4.b1.a1', '4.g1.b1', '4.k1.c1', '4.k2.c1', '4.l1.c1', '4.l2.c1', '4.m1.b1'], 'normal_contains': ['16.b1.a1', '16.e1.c1', '16.f1.c1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.c1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.f1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995236
    {'ambient': '128.1717', 'aut_centralizer_order': 64, 'aut_label': '8.f1', 'aut_quo_index': 168, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 256, 'centralizer': '4.k2.d1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '4.g1.b1', '4.k1.d1', '4.k2.d1', '4.l1.d1', '4.l2.d1', '4.m1.a1'], 'contains': ['16.b1.a1', '16.e1.d1', '16.f1.d1'], 'core': '8.f1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [5609, 3587, 4956, 5843, 5633, 3616, 4955, 5843], 'generators': [7, 32], 'label': '128.1717.8.f1.d1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.f1.d1', 'normal_contained_in': ['4.b1.b1', '4.g1.b1', '4.k1.d1', '4.k2.d1', '4.l1.d1', '4.l2.d1', '4.m1.a1'], 'normal_contains': ['16.b1.a1', '16.e1.d1', '16.f1.d1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.d1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.f1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995237
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '8.g1', 'aut_quo_index': 42, 'aut_stab_index': 1, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.m1.a1', '4.m1.b1', '4.n1.a1', '4.n1.b1', '4.o1.a1', '4.o1.b1'], 'contains': ['16.b1.a1', '16.h1.a1', '16.i1.a1'], 'core': '8.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5309, 4484, 4686, 5314, 5332, 4521, 4686, 5314], 'generators': [5, 32], 'label': '128.1717.8.g1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.g1.a1', 'normal_contained_in': ['4.a1.a1', '4.m1.b1', '4.m1.a1', '4.n1.a1', '4.n1.b1', '4.o1.a1', '4.o1.b1'], 'normal_contains': ['16.b1.a1', '16.h1.a1', '16.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.g1.a1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995238
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '8.h1', 'aut_quo_index': 84, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 256, 'centralizer': '2.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.h1.a1', '4.k1.c1', '4.k1.d1', '4.k2.a1', '4.k2.b1', '4.n1.a1'], 'contains': ['16.b1.a1', '16.o1.a1'], 'core': '8.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7995, 1245, 1785, 8576, 8031, 1256, 1707, 8575], 'generators': [16, 72], 'label': '128.1717.8.h1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.h1.a1', 'normal_contained_in': ['4.c1.a1', '4.h1.a1', '4.k1.c1', '4.k1.d1', '4.k2.b1', '4.k2.a1', '4.n1.a1'], 'normal_contains': ['16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.h1.a1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 7995239
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '8.h1', 'aut_quo_index': 84, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 256, 'centralizer': '2.e1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '4.h1.a1', '4.k1.a1', '4.k1.b1', '4.k2.c1', '4.k2.d1', '4.n1.b1'], 'contains': ['16.b1.a1', '16.o1.b1'], 'core': '8.h1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7995, 1245, 3526, 7496, 8031, 1256, 3526, 7522], 'generators': [20, 32], 'label': '128.1717.8.h1.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.h1.b1', 'normal_contained_in': ['4.c1.b1', '4.h1.a1', '4.k1.b1', '4.k1.a1', '4.k2.c1', '4.k2.d1', '4.n1.b1'], 'normal_contains': ['16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.h1.b1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.h1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 7995240
    {'ambient': '128.1717', 'aut_centralizer_order': 64, 'aut_label': '8.i1', 'aut_quo_index': 168, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 256, 'centralizer': '4.k2.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.i1.a1', '4.k1.b1', '4.k2.a1', '4.l1.c1', '4.l2.d1', '4.o1.a1'], 'contains': ['16.b1.a1', '16.p1.c1'], 'core': '8.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6884, 2872, 3978, 7198, 6915, 2896, 3978, 7263], 'generators': [18, 32], 'label': '128.1717.8.i1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.i1.a1', 'normal_contained_in': ['4.d1.a1', '4.i1.a1', '4.k1.b1', '4.k2.a1', '4.l1.c1', '4.l2.d1', '4.o1.a1'], 'normal_contains': ['16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.i1.a1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995241
    {'ambient': '128.1717', 'aut_centralizer_order': 64, 'aut_label': '8.i1', 'aut_quo_index': 168, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 256, 'centralizer': '4.k2.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1', '4.i1.a1', '4.k1.a1', '4.k2.b1', '4.l1.d1', '4.l2.c1', '4.o1.b1'], 'contains': ['16.b1.a1', '16.p1.d1'], 'core': '8.i1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6884, 2872, 3753, 6550, 6915, 2896, 3751, 6594], 'generators': [22, 32], 'label': '128.1717.8.i1.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.i1.b1', 'normal_contained_in': ['4.d1.b1', '4.i1.a1', '4.k1.a1', '4.k2.b1', '4.l1.d1', '4.l2.c1', '4.o1.b1'], 'normal_contains': ['16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.i1.b1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.i1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995242
    {'ambient': '128.1717', 'aut_centralizer_order': 64, 'aut_label': '8.i1', 'aut_quo_index': 168, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 256, 'centralizer': '4.k2.d1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.i1.b1', '4.k1.c1', '4.k2.d1', '4.l1.b1', '4.l2.a1', '4.o1.b1'], 'contains': ['16.b1.a1', '16.p1.a1'], 'core': '8.i1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [6884, 2872, 2821, 7756, 6915, 2896, 2821, 7764], 'generators': [19, 72], 'label': '128.1717.8.i1.c1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.i1.c1', 'normal_contained_in': ['4.d1.a1', '4.i1.b1', '4.k1.c1', '4.k2.d1', '4.l1.b1', '4.l2.a1', '4.o1.b1'], 'normal_contains': ['16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.i1.c1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.i1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995243
    {'ambient': '128.1717', 'aut_centralizer_order': 64, 'aut_label': '8.i1', 'aut_quo_index': 168, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 256, 'centralizer': '4.k2.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1', '4.i1.b1', '4.k1.d1', '4.k2.c1', '4.l1.a1', '4.l2.b1', '4.o1.a1'], 'contains': ['16.b1.a1', '16.p1.b1'], 'core': '8.i1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [6884, 2872, 2598, 6303, 6915, 2896, 2598, 6303], 'generators': [23, 72], 'label': '128.1717.8.i1.d1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.i1.d1', 'normal_contained_in': ['4.d1.b1', '4.i1.b1', '4.k1.d1', '4.k2.c1', '4.l1.a1', '4.l2.b1', '4.o1.a1'], 'normal_contains': ['16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.i1.d1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.i1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995244
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '8.j1', 'aut_quo_index': 84, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 256, 'centralizer': '4.j1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.j1.a1', '4.l1.c1', '4.l1.d1', '4.l2.a1', '4.l2.b1', '4.n1.b1'], 'contains': ['16.b1.a1', '16.q1.b1'], 'core': '8.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7381, 2359, 3302, 6022, 7414, 2376, 3302, 6022], 'generators': [17, 32], 'label': '128.1717.8.j1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.j1.a1', 'normal_contained_in': ['4.c1.a1', '4.j1.a1', '4.l1.c1', '4.l1.d1', '4.l2.b1', '4.l2.a1', '4.n1.b1'], 'normal_contains': ['16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.j1.a1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995245
    {'ambient': '128.1717', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 16, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.b1', '4.c1.b1', '4.d1.a1', '4.k1.b1', '4.k2.d1', '4.l1.b1', '4.l2.d1'], 'core': '2.d1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [7889, 2356, 3988, 8442, 7928, 2376, 3987, 8441], 'generators': [1, 18, 20], 'label': '128.1717.2.d1.d1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.d1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.b1', '4.c1.b1', '4.d1.a1', '4.k1.b1', '4.k2.d1', '4.l1.b1', '4.l2.d1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.d1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.d1.d1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 7995246
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '8.j1', 'aut_quo_index': 84, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 256, 'centralizer': '4.j1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '4.j1.a1', '4.l1.a1', '4.l1.b1', '4.l2.c1', '4.l2.d1', '4.n1.a1'], 'contains': ['16.b1.a1', '16.q1.a1'], 'core': '8.j1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7381, 2359, 1560, 6799, 7414, 2376, 1484, 6965], 'generators': [21, 72], 'label': '128.1717.8.j1.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.j1.b1', 'normal_contained_in': ['4.c1.b1', '4.j1.a1', '4.l1.b1', '4.l1.a1', '4.l2.c1', '4.l2.d1', '4.n1.a1'], 'normal_contains': ['16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.j1.b1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.j1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995247
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '8.k1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 64, 'centralizer': '8.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.g1.a1', '4.p1.a1'], 'contains': ['16.c1.a1', '16.e1.a1', '16.e1.b1', '16.k1.a1', '16.k1.c1'], 'core': '8.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3057, 6137, 9903, 250, 3071, 6188, 9902, 250], 'generators': [2, 36, 64], 'label': '128.1717.8.k1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.k1.a1', 'normal_contained_in': ['4.e1.a1', '4.g1.a1', '4.p1.a1'], 'normal_contains': ['16.c1.a1', '16.e1.a1', '16.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.k1.a1', 'projective_image': '32.45', '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': '8.5'}
  • id: 7995248
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '8.k1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 64, 'centralizer': '8.h1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '4.g1.b1', '4.p1.a1'], 'contains': ['16.c1.a1', '16.e1.c1', '16.e1.d1', '16.k1.b1', '16.k1.d1'], 'core': '8.k1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3057, 6137, 9678, 2542, 3071, 6188, 9677, 2542], 'generators': [35, 36, 64], 'label': '128.1717.8.k1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.k1.b1', 'normal_contained_in': ['4.e1.b1', '4.g1.b1', '4.p1.a1'], 'normal_contains': ['16.c1.a1', '16.e1.c1', '16.e1.d1'], 'normalizer': '1.a1.a1', 'old_label': '8.k1.b1', 'projective_image': '32.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 7995249
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '8.l1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 64, 'centralizer': '8.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '4.g1.a1', '4.q1.a1'], 'contains': ['16.c1.a1', '16.f1.a1', '16.f1.b1'], 'core': '8.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2301, 5706, 6308, 696, 2311, 5754, 6307, 697], 'generators': [34, 36], 'label': '128.1717.8.l1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.l1.a1', 'normal_contained_in': ['4.e1.b1', '4.g1.a1', '4.q1.a1'], 'normal_contains': ['16.c1.a1', '16.f1.b1', '16.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.l1.a1', 'projective_image': '32.45', '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': '8.5'}
  • id: 7995250
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '8.l1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 64, 'centralizer': '8.h1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.g1.b1', '4.q1.a1'], 'contains': ['16.c1.a1', '16.f1.c1', '16.f1.d1'], 'core': '8.l1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2301, 5706, 7309, 61, 2311, 5754, 7308, 61], 'generators': [3, 36], 'label': '128.1717.8.l1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.l1.b1', 'normal_contained_in': ['4.e1.a1', '4.g1.b1', '4.q1.a1'], 'normal_contains': ['16.c1.a1', '16.f1.d1', '16.f1.c1'], 'normalizer': '1.a1.a1', 'old_label': '8.l1.b1', 'projective_image': '32.45', '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': '8.5'}
  • id: 7995251
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '8.m1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.p1.a1', '4.q1.a1'], 'contains': ['16.c1.a1', '16.g1.a1', '16.h1.a1'], 'core': '8.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3460, 8937, 6602, 2723, 3475, 9012, 6602, 2723], 'generators': [33, 36], 'label': '128.1717.8.m1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.m1.a1', 'normal_contained_in': ['4.a1.a1', '4.p1.a1', '4.q1.a1'], 'normal_contains': ['16.c1.a1', '16.h1.a1', '16.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.m1.a1', 'projective_image': '32.45', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.m1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995252
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '8.n1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '8.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.g1.a1', '4.r1.a1'], 'contains': ['16.d1.a1', '16.e1.a1', '16.f1.b1'], 'core': '8.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [974, 7925, 7158, 4019, 978, 7990, 7157, 4019], 'generators': [2, 4], 'label': '128.1717.8.n1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.n1.a1', 'normal_contained_in': ['4.f1.a1', '4.g1.a1', '4.r1.a1'], 'normal_contains': ['16.d1.a1', '16.e1.a1', '16.f1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.n1.a1', 'projective_image': '32.45', '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': '8.5'}
  • id: 7995253
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '8.n1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '8.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '4.g1.a1', '4.r1.b1'], 'contains': ['16.d1.a1', '16.e1.b1', '16.f1.a1'], 'core': '8.n1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [974, 7925, 5611, 1446, 978, 7990, 5611, 1446], 'generators': [34, 4], 'label': '128.1717.8.n1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.n1.b1', 'normal_contained_in': ['4.f1.b1', '4.g1.a1', '4.r1.b1'], 'normal_contains': ['16.d1.a1', '16.e1.b1', '16.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.n1.b1', 'projective_image': '32.45', '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': '8.5'}
  • id: 7995254
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '8.n1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '8.h1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.g1.b1', '4.r1.b1'], 'contains': ['16.d1.a1', '16.e1.d1', '16.f1.c1'], 'core': '8.n1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [974, 7925, 7459, 4767, 978, 7990, 7459, 4767], 'generators': [3, 4], 'label': '128.1717.8.n1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.n1.c1', 'normal_contained_in': ['4.f1.a1', '4.g1.b1', '4.r1.b1'], 'normal_contains': ['16.d1.a1', '16.e1.d1', '16.f1.c1'], 'normalizer': '1.a1.a1', 'old_label': '8.n1.c1', 'projective_image': '32.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 7995255
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '8.n1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '8.h1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '4.g1.b1', '4.r1.a1'], 'contains': ['16.d1.a1', '16.e1.c1', '16.f1.d1'], 'core': '8.n1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [974, 7925, 6459, 2352, 978, 7990, 6459, 2353], 'generators': [35, 4], 'label': '128.1717.8.n1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.n1.d1', 'normal_contained_in': ['4.f1.b1', '4.g1.b1', '4.r1.a1'], 'normal_contains': ['16.d1.a1', '16.e1.c1', '16.f1.d1'], 'normalizer': '1.a1.a1', 'old_label': '8.n1.d1', 'projective_image': '32.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1.d1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 7995256
    {'ambient': '128.1717', 'aut_centralizer_order': 4, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '256.55643', 'aut_weyl_index': 8, 'centralizer': '8.h1.a1', 'complements': ['64.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.g1.a1', '4.h1.a1', '4.i1.a1', '4.k1.a1', '4.k1.b1', '4.k2.a1', '4.k2.b1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7275, 1728, 4450, 8049, 7311, 1742, 4449, 8050], 'generators': [2, 4, 16], 'label': '128.1717.2.e1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.g1.a1', '4.h1.a1', '4.i1.a1', '4.k1.b1', '4.k1.a1', '4.k2.b1', '4.k2.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 7995257
    {'ambient': '128.1717', 'aut_centralizer_order': 128, 'aut_label': '8.o1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.r1.a1', '4.r1.b1'], 'contains': ['16.d1.a1', '16.g1.a1', '16.i1.a1'], 'core': '8.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4432, 5381, 5754, 3160, 4451, 5426, 5754, 3160], 'generators': [33, 4], 'label': '128.1717.8.o1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.o1.a1', 'normal_contained_in': ['4.a1.a1', '4.r1.a1', '4.r1.b1'], 'normal_contains': ['16.d1.a1', '16.g1.a1', '16.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.o1.a1', 'projective_image': '32.45', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.o1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 7995258
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '8.p1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.m1.a1', '4.r1.a1'], 'contains': ['16.e1.a1', '16.f1.d1', '16.i1.a1'], 'core': '8.p1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2637, 6567, 8101, 2051, 2649, 6622, 8100, 2051], 'generators': [37, 2], 'label': '128.1717.8.p1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': ['4.e1.a1', '4.m1.a1', '4.r1.a1'], 'normal_contains': ['16.e1.a1', '16.f1.d1', '16.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.p1.a1', 'projective_image': '32.45', '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': '16.14'}
  • id: 7995259
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '8.p1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '4.m1.a1', '4.r1.b1'], 'contains': ['16.e1.d1', '16.f1.a1', '16.i1.a1'], 'core': '8.p1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2637, 6567, 7611, 1749, 2649, 6622, 7610, 1748], 'generators': [37, 34], 'label': '128.1717.8.p1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.p1.b1', 'normal_contained_in': ['4.e1.b1', '4.m1.a1', '4.r1.b1'], 'normal_contains': ['16.e1.d1', '16.f1.a1', '16.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.p1.b1', 'projective_image': '32.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.p1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 7995260
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '8.p1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '4.m1.b1', '4.r1.a1'], 'contains': ['16.e1.c1', '16.f1.b1', '16.i1.a1'], 'core': '8.p1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [2637, 6567, 7949, 2201, 2649, 6622, 7949, 2202], 'generators': [37, 6], 'label': '128.1717.8.p1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.p1.c1', 'normal_contained_in': ['4.e1.b1', '4.m1.b1', '4.r1.a1'], 'normal_contains': ['16.e1.c1', '16.f1.b1', '16.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.p1.c1', 'projective_image': '32.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.p1.c1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 7995261
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '8.p1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.m1.b1', '4.r1.b1'], 'contains': ['16.e1.b1', '16.f1.c1', '16.i1.a1'], 'core': '8.p1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [2637, 6567, 8929, 1597, 2649, 6622, 8928, 1597], 'generators': [37, 38], 'label': '128.1717.8.p1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.p1.d1', 'normal_contained_in': ['4.e1.a1', '4.m1.b1', '4.r1.b1'], 'normal_contains': ['16.e1.b1', '16.f1.c1', '16.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.p1.d1', 'projective_image': '32.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.p1.d1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 7995262
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '8.q1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.p1.a1', '4.r1.a1'], 'contains': ['16.e1.a1', '16.e1.c1', '16.g1.a1'], 'core': '8.q1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4114, 8612, 8440, 3303, 4132, 8684, 8438, 3303], 'generators': [33, 2], 'label': '128.1717.8.q1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': ['4.b1.a1', '4.r1.a1', '4.p1.a1'], 'normal_contains': ['16.e1.c1', '16.e1.a1', '16.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.q1.a1', 'projective_image': '32.45', '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': '16.14'}
  • id: 7995263
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '8.q1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '4.p1.a1', '4.r1.b1'], 'contains': ['16.e1.b1', '16.e1.d1', '16.g1.a1'], 'core': '8.q1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4114, 8612, 9231, 3641, 4132, 8684, 9230, 3641], 'generators': [33, 38], 'label': '128.1717.8.q1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.q1.b1', 'normal_contained_in': ['4.b1.b1', '4.r1.b1', '4.p1.a1'], 'normal_contains': ['16.e1.d1', '16.e1.b1', '16.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.q1.b1', 'projective_image': '32.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.q1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 7995264
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '8.r1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.m1.a1', '4.p1.a1'], 'contains': ['16.e1.a1', '16.e1.d1', '16.h1.a1'], 'core': '8.r1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [637, 9779, 8777, 4615, 641, 9860, 8777, 4616], 'generators': [5, 2], 'label': '128.1717.8.r1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.r1.a1', 'normal_contained_in': ['4.f1.a1', '4.m1.a1', '4.p1.a1'], 'normal_contains': ['16.e1.a1', '16.e1.d1', '16.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.r1.a1', 'projective_image': '32.45', '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': '16.14'}
  • id: 7995265
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '8.r1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '4.m1.b1', '4.p1.a1'], 'contains': ['16.e1.b1', '16.e1.c1', '16.h1.a1'], 'core': '8.r1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [637, 9779, 9080, 3016, 641, 9860, 9079, 3017], 'generators': [5, 38], 'label': '128.1717.8.r1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.r1.b1', 'normal_contained_in': ['4.f1.b1', '4.m1.b1', '4.p1.a1'], 'normal_contains': ['16.e1.c1', '16.e1.b1', '16.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.r1.b1', 'projective_image': '32.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.r1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 7995266
    {'ambient': '128.1717', 'aut_centralizer_order': 32, 'aut_label': '8.s1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.q1.a1', '4.r1.b1'], 'contains': ['16.f1.a1', '16.f1.c1', '16.g1.a1'], 'core': '8.s1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3777, 8268, 5460, 1900, 3794, 8337, 5460, 1899], 'generators': [33, 34], 'label': '128.1717.8.s1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.s1.a1', 'normal_contained_in': ['4.b1.a1', '4.r1.b1', '4.q1.a1'], 'normal_contains': ['16.f1.c1', '16.f1.a1', '16.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.s1.a1', 'projective_image': '32.45', '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': '16.14'}