Abstract group data - 128.1917

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 8, 'aut_gen_orders': [2, 2, 2, 2, 4, 2, 4, 2, 2, 4, 8, 2], 'aut_gens': [[1, 2, 4, 16], [73, 10, 68, 24], [65, 66, 4, 80], [1, 74, 4, 80], [65, 74, 68, 80], [9, 15, 12, 16], [1, 66, 4, 80], [1, 34, 4, 80], [1, 106, 12, 56], [1, 10, 4, 24], [73, 71, 76, 21], [1, 95, 108, 56], [73, 2, 76, 24]], 'aut_group': '8192.xq', 'aut_hash': 8991148268851618933, 'aut_nilpotency_class': 4, 'aut_nilpotent': True, 'aut_order': 8192, 'aut_permdeg': 36, 'aut_perms': [75302273716909615271960763230078446378193, 361382855943358522477072211495594662091830, 2173808815075069792917600172957963677513, 353805027417558580328086984262847969257824, 107459751327124951780846674718952341475584, 10064499879159401947281346042768455445833, 5475905681104974183818096683466185678563, 7259928714175205736318551700019552058719, 3039770480138774579443892877283454323353, 73001745424831816965358506343041179296271, 4680793991640602713787356016432551651639, 72638602376390965617713513113776398864792], 'aut_phi_ratio': 128.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 4, 1, 1], [4, 2, 2, 1], [4, 2, 4, 2], [4, 4, 1, 1], [4, 8, 4, 2], [8, 4, 4, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_2^4.C_2^4\\wr C_2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '256.56092', 'autcent_hash': 56092, 'autcent_nilpotent': True, 'autcent_order': 256, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^8', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 4, 'autcentquo_group': '32.27', 'autcentquo_hash': 27, 'autcentquo_nilpotent': True, 'autcentquo_order': 32, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^2\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 4, 1], [4, 2, 10], [4, 4, 1], [4, 8, 8], [8, 4, 8]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '32.46', 'commutator_count': 1, 'commutator_label': '8.2', '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': 1917, '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, 2, 1, 6], [4, 2, 2, 2], [4, 4, 1, 1], [4, 8, 1, 8], [8, 4, 1, 4], [8, 4, 2, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 10080, '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': 1917, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [2, 2, 2, 4], 'inner_gens': [[1, 10, 4, 80], [9, 2, 4, 48], [1, 2, 4, 80], [65, 98, 68, 16]], 'inner_hash': 46, 'inner_nilpotent': True, 'inner_order': 32, 'inner_split': False, 'inner_tex': 'C_2^2\\times D_4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 12], [4, 4]], 'label': '128.1917', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C4^2.D4', 'ngens': 4, 'nilpotency_class': 3, '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': 12, 'number_characteristic_subgroups': 16, 'number_conjugacy_classes': 32, 'number_divisions': 28, 'number_normal_subgroups': 92, 'number_subgroup_autclasses': 69, 'number_subgroup_classes': 179, 'number_subgroups': 292, 'old_label': None, 'order': 128, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 7], [4, 88], [8, 32]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4, 2, 4], 'outer_gen_pows': [0, 0, 5, 0, 5, 0], 'outer_gens': [[73, 2, 12, 16], [65, 2, 76, 21], [73, 79, 76, 16], [73, 2, 76, 21], [73, 111, 12, 16], [73, 23, 36, 16]], 'outer_group': '256.7703', 'outer_hash': 7703, 'outer_nilpotent': True, 'outer_order': 256, 'outer_permdeg': 16, 'outer_perms': [17885, 4103730462355, 2789705356979, 2789785517916, 18619, 2702654428388], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5:D_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 24, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 4], [4, 8]], 'representations': {'PC': {'code': 9748149912466071381918326, 'gens': [1, 2, 3, 5], 'pres': [7, 2, 2, 2, 2, 2, 2, 2, 141, 512, 58, 2804, 851, 718, 102, 2028, 124]}, 'Perm': {'d': 24, 'gens': [29553120853647265689989, 360249526062556709455, 56629125756642252844800, 360249526062556717294, 17764, 83644056104331310519680, 110526798351795787180800]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4^2.D_4', '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: 43234445
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 1917, 'group_order': 128, 'label': '1A', 'order': 1, 'powers': [1], 'representative': 0, 'size': 1}
  • id: 43234456
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 1917, 'group_order': 128, 'label': '2A', 'order': 2, 'powers': [1], 'representative': 8, 'size': 1}
  • id: 43234467
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 3, 'group_counter': 1917, 'group_order': 128, 'label': '2B', 'order': 2, 'powers': [1], 'representative': 72, 'size': 1}
  • id: 43234471
    {'aut_label': '2C', 'centralizer': '1.a1', 'counter': 4, 'group_counter': 1917, 'group_order': 128, 'label': '2C', 'order': 2, 'powers': [1], 'representative': 64, 'size': 1}
  • id: 43234472
    {'aut_label': '2D', 'centralizer': '4.a1', 'counter': 5, 'group_counter': 1917, 'group_order': 128, 'label': '2D', 'order': 2, 'powers': [1], 'representative': 1, 'size': 4}
  • id: 43234473
    {'aut_label': '4A', 'centralizer': '2.b1', 'counter': 6, 'group_counter': 1917, 'group_order': 128, 'label': '4A', 'order': 4, 'powers': [2], 'representative': 5, 'size': 2}
  • id: 43234474
    {'aut_label': '4A', 'centralizer': '2.b1', 'counter': 7, 'group_counter': 1917, 'group_order': 128, 'label': '4B', 'order': 4, 'powers': [2], 'representative': 69, 'size': 2}
  • id: 43234475
    {'aut_label': '4A', 'centralizer': '2.b1', 'counter': 8, 'group_counter': 1917, 'group_order': 128, 'label': '4C', 'order': 4, 'powers': [3], 'representative': 37, 'size': 2}
  • id: 43234476
    {'aut_label': '4A', 'centralizer': '2.b1', 'counter': 9, 'group_counter': 1917, 'group_order': 128, 'label': '4D', 'order': 4, 'powers': [3], 'representative': 101, 'size': 2}
  • id: 43234446
    {'aut_label': '4E', 'centralizer': '2.b1', 'counter': 10, 'group_counter': 1917, 'group_order': 128, 'label': '4E', 'order': 4, 'powers': [4], 'representative': 32, 'size': 2}
  • id: 43234447
    {'aut_label': '4E', 'centralizer': '2.b1', 'counter': 11, 'group_counter': 1917, 'group_order': 128, 'label': '4F', 'order': 4, 'powers': [4], 'representative': 40, 'size': 2}
  • id: 43234448
    {'aut_label': '4G1', 'centralizer': '2.a1', 'counter': 12, 'group_counter': 1917, 'group_order': 128, 'label': '4G1', 'order': 4, 'powers': [2], 'representative': 4, 'size': 2}
  • id: 43234449
    {'aut_label': '4G1', 'centralizer': '2.a1', 'counter': 13, 'group_counter': 1917, 'group_order': 128, 'label': '4G-1', 'order': 4, 'powers': [2], 'representative': 12, 'size': 2}
  • id: 43234450
    {'aut_label': '4G1', 'centralizer': '2.a1', 'counter': 14, 'group_counter': 1917, 'group_order': 128, 'label': '4H1', 'order': 4, 'powers': [3], 'representative': 36, 'size': 2}
  • id: 43234451
    {'aut_label': '4G1', 'centralizer': '2.a1', 'counter': 15, 'group_counter': 1917, 'group_order': 128, 'label': '4H-1', 'order': 4, 'powers': [3], 'representative': 44, 'size': 2}
  • id: 43234452
    {'aut_label': '4I', 'centralizer': '4.a1', 'counter': 16, 'group_counter': 1917, 'group_order': 128, 'label': '4I', 'order': 4, 'powers': [4], 'representative': 33, 'size': 4}
  • id: 43234453
    {'aut_label': '4J', 'centralizer': '8.m1', 'counter': 17, 'group_counter': 1917, 'group_order': 128, 'label': '4J', 'order': 4, 'powers': [3], 'representative': 2, 'size': 8}
  • id: 43234454
    {'aut_label': '4J', 'centralizer': '8.m1', 'counter': 18, 'group_counter': 1917, 'group_order': 128, 'label': '4K', 'order': 4, 'powers': [2], 'representative': 18, 'size': 8}
  • id: 43234455
    {'aut_label': '4L', 'centralizer': '8.m1', 'counter': 19, 'group_counter': 1917, 'group_order': 128, 'label': '4L', 'order': 4, 'powers': [4], 'representative': 6, 'size': 8}
  • id: 43234457
    {'aut_label': '4L', 'centralizer': '8.m1', 'counter': 20, 'group_counter': 1917, 'group_order': 128, 'label': '4M', 'order': 4, 'powers': [4], 'representative': 3, 'size': 8}
  • id: 43234458
    {'aut_label': '4L', 'centralizer': '8.m1', 'counter': 21, 'group_counter': 1917, 'group_order': 128, 'label': '4N', 'order': 4, 'powers': [4], 'representative': 22, 'size': 8}
  • id: 43234459
    {'aut_label': '4L', 'centralizer': '8.m1', 'counter': 22, 'group_counter': 1917, 'group_order': 128, 'label': '4O', 'order': 4, 'powers': [4], 'representative': 19, 'size': 8}
  • id: 43234460
    {'aut_label': '4J', 'centralizer': '8.m1', 'counter': 23, 'group_counter': 1917, 'group_order': 128, 'label': '4P', 'order': 4, 'powers': [3], 'representative': 7, 'size': 8}
  • id: 43234461
    {'aut_label': '4J', 'centralizer': '8.m1', 'counter': 24, 'group_counter': 1917, 'group_order': 128, 'label': '4Q', 'order': 4, 'powers': [2], 'representative': 23, 'size': 8}
  • id: 43234462
    {'aut_label': '8A', 'centralizer': '4.f1', 'counter': 25, 'group_counter': 1917, 'group_order': 128, 'label': '8A', 'order': 8, 'powers': [10], 'representative': 16, 'size': 4}
  • id: 43234463
    {'aut_label': '8A', 'centralizer': '4.f1', 'counter': 26, 'group_counter': 1917, 'group_order': 128, 'label': '8B', 'order': 8, 'powers': [10], 'representative': 24, 'size': 4}
  • id: 43234464
    {'aut_label': '8A', 'centralizer': '4.f1', 'counter': 27, 'group_counter': 1917, 'group_order': 128, 'label': '8C', 'order': 8, 'powers': [11], 'representative': 21, 'size': 4}
  • id: 43234465
    {'aut_label': '8A', 'centralizer': '4.f1', 'counter': 28, 'group_counter': 1917, 'group_order': 128, 'label': '8D', 'order': 8, 'powers': [11], 'representative': 53, 'size': 4}
  • id: 43234466
    {'aut_label': '8E1', 'centralizer': '4.g1', 'counter': 29, 'group_counter': 1917, 'group_order': 128, 'label': '8E1', 'order': 8, 'powers': [11], 'representative': 20, 'size': 4}
  • id: 43234468
    {'aut_label': '8E1', 'centralizer': '4.g1', 'counter': 30, 'group_counter': 1917, 'group_order': 128, 'label': '8E-1', 'order': 8, 'powers': [11], 'representative': 28, 'size': 4}
  • id: 43234469
    {'aut_label': '8E1', 'centralizer': '4.g1', 'counter': 31, 'group_counter': 1917, 'group_order': 128, 'label': '8F1', 'order': 8, 'powers': [10], 'representative': 17, 'size': 4}
  • id: 43234470
    {'aut_label': '8E1', 'centralizer': '4.g1', 'counter': 32, 'group_counter': 1917, 'group_order': 128, 'label': '8F-1', 'order': 8, 'powers': [10], 'representative': 49, '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: 85470
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '128.1917', 'group_order': 128, 'image': None, 'label': '128.1917.1a', '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], 'schur_index': 1}
  • id: 85481
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '128.1917', 'group_order': 128, 'image': None, 'label': '128.1917.1b', '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], 'schur_index': 1}
  • id: 85491
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '128.1917', 'group_order': 128, 'image': None, 'label': '128.1917.1c', '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], 'schur_index': 1}
  • id: 85492
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '128.1917', 'group_order': 128, 'image': None, 'label': '128.1917.1d', '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], 'schur_index': 1}
  • id: 85493
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '128.1917', 'group_order': 128, 'image': None, 'label': '128.1917.1e', '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], 'schur_index': 1}
  • id: 85494
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '128.1917', 'group_order': 128, 'image': None, 'label': '128.1917.1f', '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], 'schur_index': 1}
  • id: 85495
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '128.1917', 'group_order': 128, 'image': None, 'label': '128.1917.1g', '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], 'schur_index': 1}
  • id: 85496
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '128.1917', 'group_order': 128, 'image': None, 'label': '128.1917.1h', '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], 'schur_index': 1}
  • id: 85497
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '128.1917', 'group_order': 128, 'image': None, 'label': '128.1917.1i', '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], 'schur_index': 1}
  • id: 85471
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '128.1917', 'group_order': 128, 'image': None, 'label': '128.1917.1j', '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], 'schur_index': 1}
  • id: 85472
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '128.1917', 'group_order': 128, 'image': None, 'label': '128.1917.1k', '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], 'schur_index': 1}
  • id: 85473
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '128.1917', 'group_order': 128, 'image': None, 'label': '128.1917.1l', '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], 'schur_index': 1}
  • id: 85474
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '128.1917', 'group_order': 128, 'image': None, 'label': '128.1917.1m', '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], 'schur_index': 1}
  • id: 85475
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '128.1917', 'group_order': 128, 'image': None, 'label': '128.1917.1n', '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], 'schur_index': 1}
  • id: 85476
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '128.1917', 'group_order': 128, 'image': None, 'label': '128.1917.1o', '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], 'schur_index': 1}
  • id: 85477
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '128.1917', 'group_order': 128, 'image': None, 'label': '128.1917.1p', '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], 'schur_index': 1}
  • id: 85478
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '128.1917', 'group_order': 128, 'image': None, 'label': '128.1917.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [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], 'schur_index': 1}
  • id: 85479
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '128.1917', 'group_order': 128, 'image': None, 'label': '128.1917.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [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], 'schur_index': 1}
  • id: 85480
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '128.1917', 'group_order': 128, 'image': None, 'label': '128.1917.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [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], 'schur_index': 1}
  • id: 85482
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '128.1917', 'group_order': 128, 'image': None, 'label': '128.1917.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [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], 'schur_index': 1}
  • id: 85483
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '128.1917', 'group_order': 128, 'image': None, 'label': '128.1917.2e', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0], 'schur_index': 1}
  • id: 85484
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '128.1917', 'group_order': 128, 'image': None, 'label': '128.1917.2f', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0], 'schur_index': 1}
  • id: 85485
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '128.1917', 'group_order': 128, 'image': None, 'label': '128.1917.2g', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4], 'schur_index': 1}
  • id: 85486
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '128.1917', 'group_order': 128, 'image': None, 'label': '128.1917.2h', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -4], 'schur_index': 1}
  • id: 85487
    {'cdim': 4, 'counter': 25, 'faithful': False, 'group': '128.1917', 'group_order': 128, 'image': None, 'label': '128.1917.4a', 'multiplicity': 1, 'nt': [16, 32], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 85488
    {'cdim': 4, 'counter': 26, 'faithful': False, 'group': '128.1917', 'group_order': 128, 'image': None, 'label': '128.1917.4b', 'multiplicity': 1, 'nt': [16, 32], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 85489
    {'cdim': 4, 'counter': 27, 'faithful': False, 'group': '128.1917', 'group_order': 128, 'image': None, 'label': '128.1917.4c', 'multiplicity': 1, 'nt': [16, 32], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 85490
    {'cdim': 4, 'counter': 28, 'faithful': False, 'group': '128.1917', 'group_order': 128, 'image': None, 'label': '128.1917.4d', 'multiplicity': 1, 'nt': [16, 32], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
• gps_char •

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

  
  
  • id: 75488
    {'center': '1.a1', 'center_index': 1, 'center_order': 128, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 128, 'label': '128.1917.1a', '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]]]}
  • id: 75499
    {'center': '1.a1', 'center_index': 1, 'center_order': 128, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 64, 'label': '128.1917.1b', '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]]]}
  • id: 75510
    {'center': '1.a1', 'center_index': 1, 'center_order': 128, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 64, 'label': '128.1917.1c', '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]]]}
  • id: 75514
    {'center': '1.a1', 'center_index': 1, 'center_order': 128, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 64, 'label': '128.1917.1d', '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]]]}
  • id: 75515
    {'center': '1.a1', 'center_index': 1, 'center_order': 128, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1', 'kernel_order': 64, 'label': '128.1917.1e', '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]]]}
  • id: 75516
    {'center': '1.a1', 'center_index': 1, 'center_order': 128, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1', 'kernel_order': 64, 'label': '128.1917.1f', '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]]]}
  • id: 75517
    {'center': '1.a1', 'center_index': 1, 'center_order': 128, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1', 'kernel_order': 64, 'label': '128.1917.1g', '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]]]}
  • id: 75518
    {'center': '1.a1', 'center_index': 1, 'center_order': 128, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1', 'kernel_order': 64, 'label': '128.1917.1h', '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]]]}
  • id: 75519
    {'center': '1.a1', 'center_index': 1, 'center_order': 128, 'counter': 9, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1', 'kernel_order': 64, 'label': '128.1917.1i', '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]]]}
  • id: 75489
    {'center': '1.a1', 'center_index': 1, 'center_order': 128, 'counter': 10, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 64, 'label': '128.1917.1j', '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]]]}
  • id: 75490
    {'center': '1.a1', 'center_index': 1, 'center_order': 128, 'counter': 11, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 64, 'label': '128.1917.1k', '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]]]}
  • id: 75491
    {'center': '1.a1', 'center_index': 1, 'center_order': 128, 'counter': 12, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 64, 'label': '128.1917.1l', '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]]]}
  • id: 75492
    {'center': '1.a1', 'center_index': 1, 'center_order': 128, 'counter': 13, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 64, 'label': '128.1917.1m', '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]]]}
  • id: 75493
    {'center': '1.a1', 'center_index': 1, 'center_order': 128, 'counter': 14, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 64, 'label': '128.1917.1n', '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]]]}
  • id: 75494
    {'center': '1.a1', 'center_index': 1, 'center_order': 128, 'counter': 15, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 64, 'label': '128.1917.1o', '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]]]}
  • id: 75495
    {'center': '1.a1', 'center_index': 1, 'center_order': 128, 'counter': 16, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 64, 'label': '128.1917.1p', '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]]]}
  • id: 75496
    {'center': '4.a1', 'center_index': 4, 'center_order': 32, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.c1', 'kernel_order': 16, 'label': '128.1917.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 75497
    {'center': '4.a1', 'center_index': 4, 'center_order': 32, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.c1', 'kernel_order': 16, 'label': '128.1917.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 75498
    {'center': '4.a1', 'center_index': 4, 'center_order': 32, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 16, 'label': '128.1917.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 75500
    {'center': '4.a1', 'center_index': 4, 'center_order': 32, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 16, 'label': '128.1917.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 75501
    {'center': '4.i1', 'center_index': 4, 'center_order': 32, 'counter': 21, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.f1', 'kernel_order': 8, 'label': '128.1917.2e1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[2, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]]]}
  • id: 75502
    {'center': '4.i1', 'center_index': 4, 'center_order': 32, 'counter': 22, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.f1', 'kernel_order': 8, 'label': '128.1917.2e2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[2, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]]]}
  • id: 75503
    {'center': '4.i1', 'center_index': 4, 'center_order': 32, 'counter': 23, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.f1', 'kernel_order': 8, 'label': '128.1917.2f1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[2, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]]]}
  • id: 75504
    {'center': '4.i1', 'center_index': 4, 'center_order': 32, 'counter': 24, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.f1', 'kernel_order': 8, 'label': '128.1917.2f2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[2, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]]]}
  • id: 75505
    {'center': '4.i1', 'center_index': 4, 'center_order': 32, 'counter': 25, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.f1', 'kernel_order': 8, 'label': '128.1917.2g1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[2, 1]], [[0, 0]], [[-2, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 0]], [[0, 0]], [[2, 0]]]}
  • id: 75506
    {'center': '4.i1', 'center_index': 4, 'center_order': 32, 'counter': 26, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.f1', 'kernel_order': 8, 'label': '128.1917.2g2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[-2, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 0]], [[0, 0]], [[2, 0]]]}
  • id: 75507
    {'center': '4.i1', 'center_index': 4, 'center_order': 32, 'counter': 27, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.f1', 'kernel_order': 8, 'label': '128.1917.2h1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[2, 1]], [[0, 0]], [[-2, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 0]], [[0, 0]], [[-2, 0]]]}
  • id: 75508
    {'center': '4.i1', 'center_index': 4, 'center_order': 32, 'counter': 28, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.f1', 'kernel_order': 8, 'label': '128.1917.2h2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[-2, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 0]], [[0, 0]], [[-2, 0]]]}
  • id: 75509
    {'center': '16.b1', 'center_index': 16, 'center_order': 8, 'counter': 29, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '32.44', 'image_order': 32, 'indicator': -1, 'kernel': '32.a1', 'kernel_order': 4, 'label': '128.1917.4a', 'nt': [16, 32], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 75511
    {'center': '16.b1', 'center_index': 16, 'center_order': 8, 'counter': 30, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '32.44', 'image_order': 32, 'indicator': -1, 'kernel': '32.a1', 'kernel_order': 4, 'label': '128.1917.4b', 'nt': [16, 32], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 75512
    {'center': '16.b1', 'center_index': 16, 'center_order': 8, 'counter': 31, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '32.44', 'image_order': 32, 'indicator': -1, 'kernel': '32.a1', 'kernel_order': 4, 'label': '128.1917.4c', 'nt': [16, 32], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 75513
    {'center': '16.b1', 'center_index': 16, 'center_order': 8, 'counter': 32, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '128.1917', 'group_counter': 1917, 'group_order': 128, 'image': None, 'image_isoclass': '32.44', 'image_order': 32, 'indicator': -1, 'kernel': '32.a1', 'kernel_order': 4, 'label': '128.1917.4d', 'nt': [16, 32], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 8017189
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '128.1917.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['F', 'R', 'U0', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1917', 'subgroup_hash': 1917, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 2}
  • id: 8017200
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': 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: 8017211
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.85', 'subgroup_hash': 85, 'subgroup_order': 64, 'subgroup_tex': 'C_4\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 8017222
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.151', 'subgroup_hash': 151, 'subgroup_order': 64, 'subgroup_tex': 'C_8.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 8017233
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.2.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.168', 'subgroup_hash': 168, 'subgroup_order': 64, 'subgroup_tex': 'C_4.Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 8017244
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.2.e1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.179', 'subgroup_hash': 179, 'subgroup_order': 64, 'subgroup_tex': 'C_8:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 8017255
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.2.f1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.175', 'subgroup_hash': 175, 'subgroup_order': 64, 'subgroup_tex': 'C_4:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 8017256
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.2.g1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.122', 'subgroup_hash': 122, 'subgroup_order': 64, 'subgroup_tex': 'Q_{16}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8017257
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['U1'], '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: 8017190
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 8017191
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 8017192
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.4.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 8017193
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.4.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 8017194
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.4.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8017195
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.4.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8017196
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.4.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 8017197
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.4.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], '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: 8017198
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.4.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8017199
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.4.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.13', 'subgroup_hash': 13, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8017201
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.4.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.41', 'subgroup_hash': 41, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 8017202
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1917.4.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 8017203
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1917.4.m2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.m2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 8017204
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1917.4.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.32', 'subgroup_hash': 32, 'subgroup_order': 32, 'subgroup_tex': 'C_4.Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 8017205
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1917.4.n2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.n2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 8017206
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8017207
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.8.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8017208
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.8.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 8017209
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.8.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], '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: 8017210
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.8.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 8017212
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.8.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8017213
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.8.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 8017214
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.8.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8017215
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.8.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8017216
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1917.8.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8017217
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1917.8.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8017218
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1917.8.k2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.k2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 8017219
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1917.8.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8017220
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1917.8.l2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.l2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8017221
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1917.8.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 8017223
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1917.8.m2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.m2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8017224
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1917.8.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8017225
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1917.8.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 8017226
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1917.8.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 8017227
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 8017228
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.16.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8017229
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.16.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'Phi', 'L1', 'D1', '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: 8017230
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.16.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8017231
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.16.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8017232
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 49, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.1917.16.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8017234
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1917.16.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 8017235
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1917.16.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 8017236
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1917.16.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 8017237
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1917.16.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 8017238
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1917.16.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 8017239
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1917.16.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 8017240
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 56, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.1917.16.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8017241
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 57, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.1917.32.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.44', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 44, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_{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: 8017242
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 58, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.1917.32.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.46', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'S', 'U2'], '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: 8017243
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 59, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.1917.32.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', '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: 8017245
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1917.32.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 8017246
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 61, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.1917.32.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 8017247
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 62, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.1917.32.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 8017248
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.1917.32.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 8017249
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 64, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.1917.32.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 8017250
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 65, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.1917.32.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 8017251
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 66, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.1917.64.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '64.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '64.255', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 255, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_{16}:C_2^2', '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: 8017252
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 2, 'counter': 67, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.1917.64.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '64.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '64.213', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 213, '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': ['L2', '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: 8017253
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 68, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.1917.64.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 8017254
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.1917', 'ambient_counter': 1917, 'ambient_order': 128, 'ambient_tex': 'C_4^2.D_4', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 1, 'counter': 69, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '128.1917.128.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '128.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '128.1917', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1917, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2.D_4', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U3', 'L3', '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: 8017238
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.b1', '8.o1'], 'contains': ['32.c1', '32.g1', '32.h1'], 'core': '32.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [6279, -1, 6241, -1], 'generators': [1, 40], 'label': '128.1917.16.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '16.k1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017239
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.g1', '8.p1'], 'contains': ['32.c1', '32.i1'], 'core': '32.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [6766, -1, 6726, -1], 'generators': [3, 40], 'label': '128.1917.16.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1', 'old_label': '16.l1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017240
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.i1', '8.o1'], 'contains': ['32.c1'], 'core': '32.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [7422, -1, 7377, -1], 'generators': [17], 'label': '128.1917.16.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '16.m1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017189
    {'ambient': '128.1917', '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': '32.b1', 'complements': ['128.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '2.d1', '2.e1', '2.f1', '2.g1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5849, 4985, 5814, 5186], 'generators': [1, 2, 4, 16], 'label': '128.1917.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1', '2.d1', '2.e1', '2.f1', '2.g1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017190
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['2.a1', '2.c1'], 'contains': ['8.b1', '8.f1', '8.g1', '8.j1', '8.n1'], 'core': '4.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [5234, 2393, 5203, 2441], 'generators': [1, 6, 32], 'label': '128.1917.4.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': ['2.a1', '2.c1'], 'normal_contains': ['8.b1', '8.f1', '8.g1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017191
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.d1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '2.c1'], 'contains': ['8.b1', '8.h1', '8.i1', '8.o1'], 'core': '4.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [8858, 6508, 8805, 6640], 'generators': [1, 20, 32], 'label': '128.1917.4.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': ['2.b1', '2.c1'], 'normal_contains': ['8.b1', '8.h1', '8.i1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017192
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '2.d1', '2.e1'], 'contains': ['8.d1', '8.f1', '8.k1', '8.k2'], 'core': '4.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [3021, 1760, 3002, 1796], 'generators': [5, 2, 32], 'label': '128.1917.4.d1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1', 'normal_contained_in': ['2.a1', '2.d1', '2.e1'], 'normal_contains': ['8.d1', '8.f1'], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017193
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '4.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '2.d1', '2.f1'], 'contains': ['8.d1', '8.g1', '8.l1', '8.l2'], 'core': '4.e1', 'coset_action_label': None, 'count': 2, 'diagramx': [4150, 1195, 4125, 1219], 'generators': [3, 6, 32], 'label': '128.1917.4.e1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1', 'normal_contained_in': ['2.a1', '2.d1', '2.f1'], 'normal_contains': ['8.d1', '8.g1'], 'normalizer': '1.a1', 'old_label': '4.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017194
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.f1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '2.e1', '2.f1'], 'contains': ['8.d1', '8.h1'], 'core': '4.f1', 'coset_action_label': None, 'count': 1, 'diagramx': [6413, 4843, 6375, 4942], 'generators': [5, 16], 'label': '128.1917.4.f1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1', 'normal_contained_in': ['2.b1', '2.e1', '2.f1'], 'normal_contains': ['8.d1', '8.h1'], 'normalizer': '1.a1', 'old_label': '4.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017195
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.g1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '2.d1'], 'contains': ['8.d1', '8.i1'], 'core': '4.g1', 'coset_action_label': None, 'count': 1, 'diagramx': [5799, 3160, 5764, 3225], 'generators': [17, 20], 'label': '128.1917.4.g1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1', 'normal_contained_in': ['2.b1', '2.d1'], 'normal_contains': ['8.d1', '8.i1'], 'normalizer': '1.a1', 'old_label': '4.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017196
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['2.a1', '2.g1'], 'contains': ['8.e1', '8.f1', '8.g1', '8.m1', '8.m2'], 'core': '4.h1', 'coset_action_label': None, 'count': 4, 'diagramx': [4669, 4002, 4642, 4083], 'generators': [3, 4, 32], 'label': '128.1917.4.h1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.h1', 'normal_contained_in': ['2.a1', '2.g1'], 'normal_contains': ['8.e1', '8.f1', '8.g1'], 'normalizer': '1.a1', 'old_label': '4.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017197
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.d1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '2.g1'], 'contains': ['8.e1', '8.h1', '8.i1'], 'core': '4.i1', 'coset_action_label': None, 'count': 2, 'diagramx': [7539, 7737, 7494, 7894], 'generators': [17, 4], 'label': '128.1917.4.i1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.i1', 'normal_contained_in': ['2.b1', '2.g1'], 'normal_contains': ['8.e1', '8.h1', '8.i1'], 'normalizer': '1.a1', 'old_label': '4.i1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017198
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 8, 'contained_in': ['2.c1', '2.d1', '2.g1'], 'contains': ['8.f1', '8.g1', '8.i1'], 'core': '4.j1', 'coset_action_label': None, 'count': 8, 'diagramx': [6929, 5544, 6888, 5657], 'generators': [17, 6], 'label': '128.1917.4.j1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.j1', 'normal_contained_in': ['2.c1', '2.d1', '2.g1'], 'normal_contains': ['8.f1', '8.g1', '8.i1'], 'normalizer': '1.a1', 'old_label': '4.j1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017199
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '4.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['2.c1', '2.e1', '2.g1'], 'contains': ['8.f1', '8.h1'], 'core': '4.k1', 'coset_action_label': None, 'count': 4, 'diagramx': [8149, 9573, 8100, 9768], 'generators': [21, 2], 'label': '128.1917.4.k1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.k1', 'normal_contained_in': ['2.c1', '2.e1', '2.g1'], 'normal_contains': ['8.f1', '8.h1'], 'normalizer': '1.a1', 'old_label': '4.k1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.k1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017200
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '2.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.d1', '4.e1', '4.h1', '4.m1', '4.m2', '4.n1', '4.n2'], 'core': '2.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3306, 1299, 3285, 1426], 'generators': [1, 2, 4, 32], 'label': '128.1917.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '4.d1', '4.e1', '4.h1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017201
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '4.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['2.c1', '2.f1', '2.g1'], 'contains': ['8.g1', '8.h1', '8.p1'], 'core': '4.l1', 'coset_action_label': None, 'count': 4, 'diagramx': [9731, 8787, 9672, 8966], 'generators': [19, 6, 32], 'label': '128.1917.4.l1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.l1', 'normal_contained_in': ['2.c1', '2.f1', '2.g1'], 'normal_contains': ['8.g1', '8.h1'], 'normalizer': '1.a1', 'old_label': '4.l1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.l1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017202
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '4.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1'], 'contains': ['8.a1', '8.j1', '8.k1', '8.l1', '8.m1'], 'core': '8.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1376, -1, 1368, -1], 'generators': [1, 2, 4], 'label': '128.1917.4.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.m1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.m1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017203
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '4.m2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1'], 'contains': ['8.a1', '8.j1', '8.k2', '8.l2', '8.m2'], 'core': '8.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [721, -1, 716, -1], 'generators': [1, 2, 36], 'label': '128.1917.4.m2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.m2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.m2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017204
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '4.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1'], 'contains': ['8.c1', '8.k1', '8.l1', '8.m2', '8.n1'], 'core': '8.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [2605, -1, 2589, -1], 'generators': [33, 2, 36], 'label': '128.1917.4.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.n1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.n1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017205
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '4.n2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1'], 'contains': ['8.c1', '8.k2', '8.l2', '8.m1', '8.n1'], 'core': '8.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [2085, -1, 2073, -1], 'generators': [33, 2, 4], 'label': '128.1917.4.n2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.n2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.n2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017206
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.m1', '4.m2'], 'contains': ['16.a1', '16.b1', '16.d1', '16.g1'], 'core': '8.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [933, 568, 927, 573], 'generators': [1, 4, 64], 'label': '128.1917.8.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1'], 'normal_contains': ['16.a1', '16.b1', '16.d1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017207
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.b1', '4.c1'], 'contains': ['16.a1', '16.c1', '16.e1', '16.k1'], 'core': '8.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6139, 2546, 6101, 2592], 'generators': [1, 8, 32], 'label': '128.1917.8.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1', 'normal_contained_in': ['4.a1', '4.b1', '4.c1'], 'normal_contains': ['16.a1', '16.c1', '16.e1'], 'normalizer': '1.a1', 'old_label': '8.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017208
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.n1', '4.n2'], 'contains': ['16.b1', '16.d1', '16.e1'], 'core': '8.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [2723, 1306, 2706, 1326], 'generators': [33, 4], 'label': '128.1917.8.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': ['4.a1'], 'normal_contains': ['16.b1', '16.d1', '16.e1'], 'normalizer': '1.a1', 'old_label': '8.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017209
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.d1', '4.e1', '4.f1', '4.g1'], 'contains': ['16.b1', '16.c1'], 'core': '8.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [4810, 1809, 4781, 1840], 'generators': [5, 32], 'label': '128.1917.8.d1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.d1', 'normal_contained_in': ['4.a1', '4.d1', '4.e1', '4.f1', '4.g1'], 'normal_contains': ['16.b1', '16.c1'], 'normalizer': '1.a1', 'old_label': '8.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017210
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.h1', '4.i1'], 'contains': ['16.c1', '16.d1'], 'core': '8.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [5180, 3283, 5149, 3344], 'generators': [4, 32], 'label': '128.1917.8.e1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.e1', 'normal_contained_in': ['4.a1', '4.h1', '4.i1'], 'normal_contains': ['16.c1', '16.d1'], 'normalizer': '1.a1', 'old_label': '8.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017211
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '2.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.d1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.c1', '4.f1', '4.g1', '4.i1'], 'core': '2.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5849, 3677, 5814, 3851], 'generators': [1, 4, 16], 'label': '128.1917.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.c1', '4.f1', '4.g1', '4.i1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017212
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '4.d1', '4.h1', '4.j1', '4.k1'], 'contains': ['16.c1', '16.i1'], 'core': '8.f1', 'coset_action_label': None, 'count': 4, 'diagramx': [5574, 4666, 5540, 4754], 'generators': [7, 32], 'label': '128.1917.8.f1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.f1', 'normal_contained_in': ['4.b1', '4.d1', '4.h1', '4.j1', '4.k1'], 'normal_contains': ['16.c1'], 'normalizer': '1.a1', 'old_label': '8.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017213
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '4.e1', '4.h1', '4.j1', '4.l1'], 'contains': ['16.c1', '16.j1', '16.l1'], 'core': '8.g1', 'coset_action_label': None, 'count': 4, 'diagramx': [6802, 3959, 6762, 4033], 'generators': [3, 8, 32], 'label': '128.1917.8.g1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.g1', 'normal_contained_in': ['4.b1', '4.e1', '4.h1', '4.j1', '4.l1'], 'normal_contains': ['16.c1'], 'normalizer': '1.a1', 'old_label': '8.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017214
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.f1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '4.f1', '4.i1', '4.k1', '4.l1'], 'contains': ['16.c1', '16.f1'], 'core': '8.h1', 'coset_action_label': None, 'count': 2, 'diagramx': [8035, 6508, 7988, 6640], 'generators': [21, 32], 'label': '128.1917.8.h1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.h1', 'normal_contained_in': ['4.c1', '4.f1', '4.i1', '4.k1', '4.l1'], 'normal_contains': ['16.c1', '16.f1'], 'normalizer': '1.a1', 'old_label': '8.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017215
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.g1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '4.g1', '4.i1', '4.j1'], 'contains': ['16.c1', '16.m1'], 'core': '8.i1', 'coset_action_label': None, 'count': 2, 'diagramx': [7422, 5544, 7377, 5657], 'generators': [17, 8], 'label': '128.1917.8.i1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.i1', 'normal_contained_in': ['4.c1', '4.g1', '4.i1', '4.j1'], 'normal_contains': ['16.c1'], 'normalizer': '1.a1', 'old_label': '8.i1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017216
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '4.m1', '4.m2'], 'contains': ['16.a1', '16.i1', '16.j1'], 'core': '16.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3951, -1, 3928, -1], 'generators': [1, 6], 'label': '128.1917.8.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.j1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017217
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.d1', '4.m1', '4.n1'], 'contains': ['16.b1', '16.i1'], 'core': '16.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [1498, -1, 1489, -1], 'generators': [5, 2], 'label': '128.1917.8.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.k1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017218
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '8.k2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.d1', '4.m2', '4.n2'], 'contains': ['16.b1', '16.h1', '16.i1'], 'core': '16.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [269, -1, 267, -1], 'generators': [37, 2, 64], 'label': '128.1917.8.k2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.k2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017219
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.e1', '4.m1', '4.n1'], 'contains': ['16.b1', '16.j1'], 'core': '16.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [2329, -1, 2315, -1], 'generators': [3, 6], 'label': '128.1917.8.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.l1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017220
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '8.l2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.e1', '4.m2', '4.n2'], 'contains': ['16.b1', '16.j1'], 'core': '16.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [1914, -1, 1902, -1], 'generators': [35, 6], 'label': '128.1917.8.l2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.l2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017221
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.m1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.h1', '4.m1', '4.n2'], 'contains': ['16.d1', '16.i1', '16.j1'], 'core': '16.d1', 'coset_action_label': None, 'count': 8, 'diagramx': [3508, -1, 3488, -1], 'generators': [3, 4], 'label': '128.1917.8.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.m1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017222
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '2.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.c1', '4.j1', '4.k1', '4.l1'], 'core': '2.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [8145, 6625, 8096, 6860], 'generators': [1, 2, 20], 'label': '128.1917.2.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.c1', '4.j1', '4.k1', '4.l1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017223
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '8.m2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.h1', '4.m2', '4.n1'], 'contains': ['16.d1', '16.i1', '16.j1'], 'core': '16.d1', 'coset_action_label': None, 'count': 8, 'diagramx': [3115, -1, 3097, -1], 'generators': [3, 36], 'label': '128.1917.8.m2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.m2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017224
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '4.n1', '4.n2'], 'contains': ['16.e1', '16.i1', '16.j1'], 'core': '16.e1', 'coset_action_label': None, 'count': 8, 'diagramx': [4417, -1, 4390, -1], 'generators': [33, 6], 'label': '128.1917.8.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.n1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017225
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '8.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.c1'], 'contains': ['16.f1', '16.k1', '16.m1'], 'core': '16.f1', 'coset_action_label': None, 'count': 8, 'diagramx': [8569, -1, 8518, -1], 'generators': [1, 20], 'label': '128.1917.8.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '8.o1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.o1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017226
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '8.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['4.l1'], 'contains': ['16.f1', '16.l1'], 'core': '16.f1', 'coset_action_label': None, 'count': 16, 'diagramx': [8998, -1, 8945, -1], 'generators': [19, 6], 'label': '128.1917.8.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1', 'old_label': '8.p1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.p1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017227
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '8.b1', '8.j1'], 'contains': ['32.b1', '32.d1', '32.g1'], 'core': '16.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3924, 1336, 3901, 1451], 'generators': [1, 8, 64], 'label': '128.1917.16.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': ['8.a1', '8.b1'], 'normal_contains': ['32.b1'], 'normalizer': '1.a1', 'old_label': '16.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017228
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '8.c1', '8.d1', '8.k1', '8.k2', '8.l1', '8.l2'], 'contains': ['32.a1', '32.b1'], 'core': '16.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2203, 666, 2189, 768], 'generators': [5, 64], 'label': '128.1917.16.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': ['8.a1', '8.c1', '8.d1'], 'normal_contains': ['32.a1', '32.b1'], 'normalizer': '1.a1', 'old_label': '16.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017229
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '8.d1', '8.e1', '8.f1', '8.g1', '8.h1', '8.i1'], 'contains': ['32.b1', '32.c1'], 'core': '16.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [5664, 3768, 5630, 3933], 'generators': [8, 32], 'label': '128.1917.16.c1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.c1', 'normal_contained_in': ['8.b1', '8.d1', '8.e1', '8.f1', '8.g1', '8.h1', '8.i1'], 'normal_contains': ['32.b1', '32.c1'], 'normalizer': '1.a1', 'old_label': '16.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017230
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '8.c1', '8.e1', '8.m1', '8.m2'], 'contains': ['32.b1', '32.e1'], 'core': '16.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [2817, 2005, 2800, 2134], 'generators': [4, 64], 'label': '128.1917.16.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1', 'normal_contained_in': ['8.a1', '8.c1', '8.e1'], 'normal_contains': ['32.b1'], 'normalizer': '1.a1', 'old_label': '16.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017231
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '8.c1', '8.n1'], 'contains': ['32.b1', '32.h1'], 'core': '16.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [5031, 2841, 5001, 2987], 'generators': [33, 8], 'label': '128.1917.16.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.e1', 'normal_contained_in': ['8.b1', '8.c1'], 'normal_contains': ['32.b1'], 'normalizer': '1.a1', 'old_label': '16.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017232
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.f1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['8.h1', '8.o1', '8.p1'], 'contains': ['32.c1'], 'core': '16.f1', 'coset_action_label': None, 'count': 4, 'diagramx': [8303, 5483, 8253, 5631], 'generators': [21], 'label': '128.1917.16.f1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': ['8.h1'], 'normal_contains': ['32.c1'], 'normalizer': '1.a1', 'old_label': '16.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017233
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '2.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': ['64.c1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.d1', '4.e1', '4.g1', '4.j1'], 'core': '2.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [4529, 2454, 4503, 2604], 'generators': [17, 2, 20], 'label': '128.1917.2.d1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.d1', '4.e1', '4.g1', '4.j1'], 'normalizer': '1.a1', 'old_label': '2.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017234
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.a1'], 'contains': ['32.a1', '32.d1', '32.e1'], 'core': '32.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1588, -1, 1579, -1], 'generators': [1, 4], 'label': '128.1917.16.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017235
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.k2'], 'contains': ['32.a1', '32.f1'], 'core': '32.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1119, -1, 1112, -1], 'generators': [37, 2], 'label': '128.1917.16.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.n2', 'old_label': '16.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017236
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.m1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.f1', '8.j1', '8.k1', '8.k2', '8.m1', '8.m2', '8.n1'], 'contains': ['32.b1', '32.f1'], 'core': '32.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [3432, -1, 3411, -1], 'generators': [7, 64], 'label': '128.1917.16.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.i1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017237
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.m1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.g1', '8.j1', '8.l1', '8.l2', '8.m1', '8.m2', '8.n1'], 'contains': ['32.b1', '32.i1'], 'core': '32.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [4417, -1, 4390, -1], 'generators': [3, 8], 'label': '128.1917.16.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.j1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017241
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['16.b1', '16.g1', '16.h1'], 'contains': ['64.a1'], 'core': '32.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1896, 1102, 1884, 1213], 'generators': [5], 'label': '128.1917.32.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': ['16.b1'], 'normal_contains': ['64.a1'], 'normalizer': '1.a1', 'old_label': '32.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017242
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.b1', '16.c1', '16.d1', '16.e1', '16.i1', '16.j1'], 'contains': ['64.a1', '64.b1'], 'core': '32.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3861, 2005, 3788, 2134], 'generators': [8, 64], 'label': '128.1917.32.b1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '32.b1', 'normal_contained_in': ['16.a1', '16.b1', '16.c1', '16.d1', '16.e1'], 'normal_contains': ['64.a1', '64.b1'], 'normalizer': '1.a1', 'old_label': '32.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017243
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['16.c1', '16.f1', '16.k1', '16.l1', '16.m1'], 'contains': ['64.b1'], 'core': '32.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [6522, 3768, 6483, 3933], 'generators': [40], 'label': '128.1917.32.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.c1', 'normal_contained_in': ['16.c1', '16.f1'], 'normal_contains': ['64.b1'], 'normalizer': '1.a1', 'old_label': '32.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017244
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '2.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': ['64.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.d1', '4.f1', '4.k1'], 'core': '2.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [5140, 5900, 5109, 6120], 'generators': [5, 2, 16], 'label': '128.1917.2.e1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.d1', '4.f1', '4.k1'], 'normalizer': '1.a1', 'old_label': '2.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.e1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017245
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.a1', '16.g1'], 'contains': ['64.a1', '64.c1'], 'core': '64.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3404, -1, 3389, -1], 'generators': [1, 8], 'label': '128.1917.32.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017246
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.d1', '16.g1'], 'contains': ['64.a1'], 'core': '64.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2881, -1, 2980, -1], 'generators': [4], 'label': '128.1917.32.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017247
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.m1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.h1', '16.i1'], 'contains': ['64.a1'], 'core': '64.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2555, -1, 2657, -1], 'generators': [7], 'label': '128.1917.32.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.n2', 'old_label': '32.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.f1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017248
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '32.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.k1'], 'contains': ['64.b1', '64.c1'], 'core': '64.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4231, -1, 4157, -1], 'generators': [1, 64], 'label': '128.1917.32.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '32.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.g1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017249
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '32.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1', '16.k1'], 'contains': ['64.b1'], 'core': '64.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5031, -1, 5001, -1], 'generators': [33], 'label': '128.1917.32.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '32.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.h1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017250
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.m1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.j1', '16.l1'], 'contains': ['64.b1'], 'core': '64.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [4579, -1, 4503, -1], 'generators': [3], 'label': '128.1917.32.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '32.i1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.i1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017251
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['32.a1', '32.b1', '32.d1', '32.e1', '32.f1'], 'contains': ['128.a1'], 'core': '64.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3142, 1784, 3223, 1908], 'generators': [8], 'label': '128.1917.64.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '64.a1', 'normal_contained_in': ['32.a1', '32.b1'], 'normal_contains': ['128.a1'], 'normalizer': '1.a1', 'old_label': '64.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017252
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '64.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.b1', '32.c1', '32.g1', '32.h1', '32.i1'], 'contains': ['128.a1'], 'core': '64.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4571, 2227, 4327, 2360], 'generators': [64], 'label': '128.1917.64.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '64.b1', 'normal_contained_in': ['32.b1', '32.c1'], 'normal_contains': ['128.a1'], 'normalizer': '1.a1', 'old_label': '64.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017253
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '64.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1', '32.g1'], 'contains': ['128.a1'], 'core': '128.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3852, -1, 3555, -1], 'generators': [1], 'label': '128.1917.64.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '64.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017254
    {'ambient': '128.1917', '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', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['64.a1', '64.b1', '64.c1'], 'contains': [], 'core': '128.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3852, 2005, 3555, 2134], 'generators': [], 'label': '128.1917.128.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '128.a1', 'normal_contained_in': ['64.a1', '64.b1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '128.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017255
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '2.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': ['64.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.e1', '4.f1', '4.l1'], 'core': '2.f1', 'coset_action_label': None, 'count': 1, 'diagramx': [6812, 4985, 6771, 5186], 'generators': [3, 6, 16], 'label': '128.1917.2.f1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.f1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.e1', '4.f1', '4.l1'], 'normalizer': '1.a1', 'old_label': '2.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.f1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017256
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '2.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': ['64.c1'], 'conjugacy_class_count': 4, 'contained_in': ['1.a1'], 'contains': ['4.h1', '4.i1', '4.j1', '4.k1', '4.l1'], 'core': '2.g1', 'coset_action_label': None, 'count': 4, 'diagramx': [7543, 7534, 7498, 7787], 'generators': [17, 2, 4], 'label': '128.1917.2.g1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.h1', '4.i1', '4.j1', '4.k1', '4.l1'], 'normalizer': '1.a1', 'old_label': '2.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.g1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 8017257
    {'ambient': '128.1917', 'aut_centralizer_order': None, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.b1'], 'contains': ['8.a1', '8.b1', '8.c1', '8.d1', '8.e1'], 'core': '4.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3586, 427, 3564, 436], 'generators': [1, 4, 32], 'label': '128.1917.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1'], 'normal_contains': ['8.a1', '8.b1', '8.c1', '8.d1', '8.e1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': None}