Abstract group data - 64.85

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '32.21', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [4, 4, 4, 4, 4], 'aut_gens': [[1, 2, 8], [37, 18, 63], [1, 6, 59], [37, 2, 45], [1, 22, 62], [33, 6, 41]], 'aut_group': '1024.dhy', 'aut_hash': 8313881968751267222, 'aut_nilpotency_class': 3, 'aut_nilpotent': True, 'aut_order': 1024, 'aut_permdeg': 20, 'aut_perms': [881269872814206737, 751238352260903527, 1127934642117427201, 1649940671046091096, 288951677944473600], 'aut_phi_ratio': 32.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 2, 1], [4, 1, 4, 1], [4, 1, 8, 1], [4, 2, 2, 1], [4, 2, 4, 1], [8, 2, 16, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^5.C_2^5', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '512.301254', 'autcent_hash': 3537108304499242570, 'autcent_nilpotent': True, 'autcent_order': 512, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6:D_4', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 2, 'autcentquo_group': '2.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 2, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [4, 1, 12], [4, 2, 6], [8, 2, 16]], 'center_label': '16.2', 'center_order': 16, 'central_product': True, 'central_quotient': '4.2', 'commutator_count': 1, 'commutator_label': '2.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 85, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['16.6', 1], ['4.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [4, 1, 2, 6], [4, 2, 1, 2], [4, 2, 2, 2], [8, 2, 2, 8]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 84, 'exponent': 8, 'exponents_of_order': [6], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '8.5', 'hash': 85, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 1, 2], 'inner_gens': [[1, 2, 40], [1, 2, 8], [33, 2, 8]], 'inner_hash': 2, 'inner_nilpotent': True, 'inner_order': 4, 'inner_split': False, 'inner_tex': 'C_2^2', 'inner_used': [1, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 8]], 'label': '64.85', 'linC_count': 128, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 32, 'linQ_dim': 6, 'linQ_dim_count': 32, 'linR_count': 32, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C4*OD16', 'ngens': 3, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 9, 'number_characteristic_subgroups': 11, 'number_conjugacy_classes': 40, 'number_divisions': 24, 'number_normal_subgroups': 61, 'number_subgroup_autclasses': 31, 'number_subgroup_classes': 71, 'number_subgroups': 81, 'old_label': None, 'order': 64, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 7], [4, 24], [8, 32]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 1, 0, 0, 0, 0], 'outer_gens': [[1, 18, 24], [5, 2, 58], [1, 2, 24], [1, 34, 29], [5, 34, 12], [1, 6, 24], [1, 34, 8], [1, 2, 12]], 'outer_group': '256.28668', 'outer_hash': 28668, 'outer_nilpotent': True, 'outer_order': 256, 'outer_permdeg': 16, 'outer_perms': [1313941703470, 5786825962344, 1313941680821, 4103646986880, 8396027157821, 2789792421916, 5329, 2789792409600], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3.C_2^5', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 12, 'pgroup': 2, 'primary_abelian_invariants': [2, 4, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [4, 4]], 'representations': {'PC': {'code': 279315480730, 'gens': [1, 2, 4], 'pres': [6, 2, 2, 2, 2, 2, 2, 31, 963, 69, 88]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [58438776791336234, 125101738392040930, 125101749995522276]}, 'GLFp': {'d': 3, 'p': 5, 'gens': [1173753, 106892, 496574, 1692709, 518956, 1565004]}, 'Perm': {'d': 12, 'gens': [48439447, 95443337, 18553680, 141608880, 178981927, 178981920]}}, 'schur_multiplier': [2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4, 4], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4\\times \\OD_{16}', 'transitive_degree': 32, '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: 105739269
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 85, 'group_order': 64, 'label': '1A', 'order': 1, 'powers': [1], 'representative': 0, 'size': 1}
  • id: 105739280
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 85, 'group_order': 64, 'label': '2A', 'order': 2, 'powers': [1], 'representative': 4, 'size': 1}
  • id: 105739291
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 85, 'group_order': 64, 'label': '2B', 'order': 2, 'powers': [1], 'representative': 36, 'size': 1}
  • id: 105739302
    {'aut_label': '2C', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 85, 'group_order': 64, 'label': '2C', 'order': 2, 'powers': [1], 'representative': 32, 'size': 1}
  • id: 105739304
    {'aut_label': '2D', 'centralizer': '2.a1.a1', 'counter': 5, 'group_counter': 85, 'group_order': 64, 'label': '2D', 'order': 2, 'powers': [1], 'representative': 1, 'size': 2}
  • id: 105739305
    {'aut_label': '2D', 'centralizer': '2.a1.a1', 'counter': 6, 'group_counter': 85, 'group_order': 64, 'label': '2E', 'order': 2, 'powers': [1], 'representative': 5, 'size': 2}
  • id: 105739306
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 7, 'group_counter': 85, 'group_order': 64, 'label': '4A1', 'order': 4, 'powers': [2], 'representative': 2, 'size': 1}
  • id: 105739307
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 8, 'group_counter': 85, 'group_order': 64, 'label': '4A-1', 'order': 4, 'powers': [2], 'representative': 6, 'size': 1}
  • id: 105739308
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 9, 'group_counter': 85, 'group_order': 64, 'label': '4B1', 'order': 4, 'powers': [2], 'representative': 34, 'size': 1}
  • id: 105739270
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 10, 'group_counter': 85, 'group_order': 64, 'label': '4B-1', 'order': 4, 'powers': [2], 'representative': 38, 'size': 1}
  • id: 105739271
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 11, 'group_counter': 85, 'group_order': 64, 'label': '4C1', 'order': 4, 'powers': [3], 'representative': 18, 'size': 1}
  • id: 105739272
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 12, 'group_counter': 85, 'group_order': 64, 'label': '4C-1', 'order': 4, 'powers': [3], 'representative': 54, 'size': 1}
  • id: 105739273
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 13, 'group_counter': 85, 'group_order': 64, 'label': '4D1', 'order': 4, 'powers': [3], 'representative': 50, 'size': 1}
  • id: 105739274
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 14, 'group_counter': 85, 'group_order': 64, 'label': '4D-1', 'order': 4, 'powers': [3], 'representative': 22, 'size': 1}
  • id: 105739275
    {'aut_label': '4E1', 'centralizer': '1.a1.a1', 'counter': 15, 'group_counter': 85, 'group_order': 64, 'label': '4E1', 'order': 4, 'powers': [4], 'representative': 16, 'size': 1}
  • id: 105739276
    {'aut_label': '4E1', 'centralizer': '1.a1.a1', 'counter': 16, 'group_counter': 85, 'group_order': 64, 'label': '4E-1', 'order': 4, 'powers': [4], 'representative': 48, 'size': 1}
  • id: 105739277
    {'aut_label': '4E1', 'centralizer': '1.a1.a1', 'counter': 17, 'group_counter': 85, 'group_order': 64, 'label': '4F1', 'order': 4, 'powers': [4], 'representative': 20, 'size': 1}
  • id: 105739278
    {'aut_label': '4E1', 'centralizer': '1.a1.a1', 'counter': 18, 'group_counter': 85, 'group_order': 64, 'label': '4F-1', 'order': 4, 'powers': [4], 'representative': 52, 'size': 1}
  • id: 105739279
    {'aut_label': '4G', 'centralizer': '2.a1.a1', 'counter': 19, 'group_counter': 85, 'group_order': 64, 'label': '4G', 'order': 4, 'powers': [4], 'representative': 17, 'size': 2}
  • id: 105739281
    {'aut_label': '4G', 'centralizer': '2.a1.a1', 'counter': 20, 'group_counter': 85, 'group_order': 64, 'label': '4H', 'order': 4, 'powers': [4], 'representative': 21, 'size': 2}
  • id: 105739282
    {'aut_label': '4I1', 'centralizer': '2.a1.a1', 'counter': 21, 'group_counter': 85, 'group_order': 64, 'label': '4I1', 'order': 4, 'powers': [2], 'representative': 3, 'size': 2}
  • id: 105739283
    {'aut_label': '4I1', 'centralizer': '2.a1.a1', 'counter': 22, 'group_counter': 85, 'group_order': 64, 'label': '4I-1', 'order': 4, 'powers': [2], 'representative': 7, 'size': 2}
  • id: 105739284
    {'aut_label': '4I1', 'centralizer': '2.a1.a1', 'counter': 23, 'group_counter': 85, 'group_order': 64, 'label': '4J1', 'order': 4, 'powers': [3], 'representative': 19, 'size': 2}
  • id: 105739285
    {'aut_label': '4I1', 'centralizer': '2.a1.a1', 'counter': 24, 'group_counter': 85, 'group_order': 64, 'label': '4J-1', 'order': 4, 'powers': [3], 'representative': 23, 'size': 2}
  • id: 105739286
    {'aut_label': '8A1', 'centralizer': '2.c1.a1', 'counter': 25, 'group_counter': 85, 'group_order': 64, 'label': '8A1', 'order': 8, 'powers': [15], 'representative': 8, 'size': 2}
  • id: 105739287
    {'aut_label': '8A1', 'centralizer': '2.c1.a1', 'counter': 26, 'group_counter': 85, 'group_order': 64, 'label': '8A-1', 'order': 8, 'powers': [16], 'representative': 24, 'size': 2}
  • id: 105739288
    {'aut_label': '8A1', 'centralizer': '2.c1.a1', 'counter': 27, 'group_counter': 85, 'group_order': 64, 'label': '8B1', 'order': 8, 'powers': [15], 'representative': 12, 'size': 2}
  • id: 105739289
    {'aut_label': '8A1', 'centralizer': '2.c1.a1', 'counter': 28, 'group_counter': 85, 'group_order': 64, 'label': '8B-1', 'order': 8, 'powers': [16], 'representative': 28, 'size': 2}
  • id: 105739290
    {'aut_label': '8A1', 'centralizer': '2.c1.a1', 'counter': 29, 'group_counter': 85, 'group_order': 64, 'label': '8C1', 'order': 8, 'powers': [17], 'representative': 10, 'size': 2}
  • id: 105739292
    {'aut_label': '8A1', 'centralizer': '2.c1.a1', 'counter': 30, 'group_counter': 85, 'group_order': 64, 'label': '8C-1', 'order': 8, 'powers': [18], 'representative': 30, 'size': 2}
  • id: 105739293
    {'aut_label': '8A1', 'centralizer': '2.c1.b1', 'counter': 31, 'group_counter': 85, 'group_order': 64, 'label': '8D1', 'order': 8, 'powers': [16], 'representative': 9, 'size': 2}
  • id: 105739294
    {'aut_label': '8A1', 'centralizer': '2.c1.b1', 'counter': 32, 'group_counter': 85, 'group_order': 64, 'label': '8D-1', 'order': 8, 'powers': [15], 'representative': 25, 'size': 2}
  • id: 105739295
    {'aut_label': '8A1', 'centralizer': '2.c1.a1', 'counter': 33, 'group_counter': 85, 'group_order': 64, 'label': '8E1', 'order': 8, 'powers': [18], 'representative': 26, 'size': 2}
  • id: 105739296
    {'aut_label': '8A1', 'centralizer': '2.c1.a1', 'counter': 34, 'group_counter': 85, 'group_order': 64, 'label': '8E-1', 'order': 8, 'powers': [17], 'representative': 14, 'size': 2}
  • id: 105739297
    {'aut_label': '8A1', 'centralizer': '2.c1.b1', 'counter': 35, 'group_counter': 85, 'group_order': 64, 'label': '8F1', 'order': 8, 'powers': [16], 'representative': 13, 'size': 2}
  • id: 105739298
    {'aut_label': '8A1', 'centralizer': '2.c1.b1', 'counter': 36, 'group_counter': 85, 'group_order': 64, 'label': '8F-1', 'order': 8, 'powers': [15], 'representative': 29, 'size': 2}
  • id: 105739299
    {'aut_label': '8A1', 'centralizer': '2.c1.b1', 'counter': 37, 'group_counter': 85, 'group_order': 64, 'label': '8G1', 'order': 8, 'powers': [18], 'representative': 11, 'size': 2}
  • id: 105739300
    {'aut_label': '8A1', 'centralizer': '2.c1.b1', 'counter': 38, 'group_counter': 85, 'group_order': 64, 'label': '8G-1', 'order': 8, 'powers': [17], 'representative': 31, 'size': 2}
  • id: 105739301
    {'aut_label': '8A1', 'centralizer': '2.c1.b1', 'counter': 39, 'group_counter': 85, 'group_order': 64, 'label': '8H1', 'order': 8, 'powers': [17], 'representative': 27, 'size': 2}
  • id: 105739303
    {'aut_label': '8A1', 'centralizer': '2.c1.b1', 'counter': 40, 'group_counter': 85, 'group_order': 64, 'label': '8H-1', 'order': 8, 'powers': [18], 'representative': 15, 'size': 2}
• 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: 3573473
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '64.85', 'group_order': 64, 'image': None, 'label': '64.85.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3573484
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '64.85', 'group_order': 64, 'image': None, 'label': '64.85.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1], 'schur_index': 1}
  • id: 3573490
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '64.85', 'group_order': 64, 'image': None, 'label': '64.85.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1], 'schur_index': 1}
  • id: 3573491
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '64.85', 'group_order': 64, 'image': None, 'label': '64.85.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1], 'schur_index': 1}
  • id: 3573492
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '64.85', 'group_order': 64, 'image': None, 'label': '64.85.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1], 'schur_index': 1}
  • id: 3573493
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '64.85', 'group_order': 64, 'image': None, 'label': '64.85.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 3573494
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '64.85', 'group_order': 64, 'image': None, 'label': '64.85.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3573495
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '64.85', 'group_order': 64, 'image': None, 'label': '64.85.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 3573496
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '64.85', 'group_order': 64, 'image': None, 'label': '64.85.1i', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, -2, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 2, -2, 2, 2], 'schur_index': 1}
  • id: 3573474
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '64.85', 'group_order': 64, 'image': None, 'label': '64.85.1j', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, -2, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, -2, 2, -2, -2], 'schur_index': 1}
  • id: 3573475
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '64.85', 'group_order': 64, 'image': None, 'label': '64.85.1k', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, -2, -2, 0, -2, 0, 2, 0, 0, 0, 0, 0, -2, 2, -2, 2, -2, -2, 2, 0, 0, 2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3573476
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '64.85', 'group_order': 64, 'image': None, 'label': '64.85.1l', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, -2, -2, 0, -2, 0, 2, 0, 0, 0, 0, 0, 2, -2, 2, -2, 2, 2, -2, 0, 0, -2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3573477
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '64.85', 'group_order': 64, 'image': None, 'label': '64.85.1m', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 2, 2, 0, -2, 0, 2, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 2, 2, -2, -2], 'schur_index': 1}
  • id: 3573478
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '64.85', 'group_order': 64, 'image': None, 'label': '64.85.1n', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 2, 2, 0, -2, 0, 2, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, -2, -2, 2, 2], 'schur_index': 1}
  • id: 3573479
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '64.85', 'group_order': 64, 'image': None, 'label': '64.85.1o', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, 0, 0, 2, 2, 0, 0, 0, 0, 0, -2, -2, 0, 2, 0, -2, 0, 0, 0, 0, 0, -2, -2, 2, 2, -2, 2, -2, 0, 0, 2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3573480
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '64.85', 'group_order': 64, 'image': None, 'label': '64.85.1p', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, 0, 0, 2, 2, 0, 0, 0, 0, 0, -2, -2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 2, 2, -2, -2, 2, -2, 2, 0, 0, -2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3573481
    {'cdim': 1, 'counter': 17, 'faithful': False, 'group': '64.85', 'group_order': 64, 'image': None, 'label': '64.85.1q', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 2, 2, 2, -2, 2, -2, -2, -2, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3573482
    {'cdim': 1, 'counter': 18, 'faithful': False, 'group': '64.85', 'group_order': 64, 'image': None, 'label': '64.85.1r', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, 2, -2, -2, -2, -2, -2, 2, -2, -2, -2, 2, 2, -2, 2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3573483
    {'cdim': 1, 'counter': 19, 'faithful': False, 'group': '64.85', 'group_order': 64, 'image': None, 'label': '64.85.1s', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 2, -2, 2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3573485
    {'cdim': 1, 'counter': 20, 'faithful': False, 'group': '64.85', 'group_order': 64, 'image': None, 'label': '64.85.1t', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, 2, -2, -2, -2, 2, -2, 2, -2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3573486
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '64.85', 'group_order': 64, 'image': None, 'label': '64.85.2a', 'multiplicity': 2, 'nt': [8, 7], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, 0, 0, -4, 4, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3573487
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '64.85', 'group_order': 64, 'image': None, 'label': '64.85.2b', 'multiplicity': 2, 'nt': [8, 7], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 4, -4, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3573488
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '64.85', 'group_order': 64, 'image': None, 'label': '64.85.2c', 'multiplicity': 2, 'nt': [8, 7], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, -4, 4, 0, 0, 0, 0, 0, -4, 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], 'schur_index': 1}
  • id: 3573489
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '64.85', 'group_order': 64, 'image': None, 'label': '64.85.2d', 'multiplicity': 2, 'nt': [8, 7], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 4, -4, 0, 0, 0, 0, 0, 4, 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], 'schur_index': 1}
• gps_char •

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

  
  
  • id: 5144019
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 64, 'label': '64.85.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5144030
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.b1', 'kernel_order': 32, 'label': '64.85.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5144041
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 32, 'label': '64.85.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5144052
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.b1', 'kernel_order': 32, 'label': '64.85.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5144054
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 32, 'label': '64.85.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5144055
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.b1', 'kernel_order': 32, 'label': '64.85.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5144056
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 32, 'label': '64.85.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5144057
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 32, 'label': '64.85.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5144058
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 9, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.g1.f1', 'kernel_order': 16, 'label': '64.85.1i1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 0]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5144020
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 10, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.g1.f1', 'kernel_order': 16, 'label': '64.85.1i2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5144021
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 11, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.g1.e1', 'kernel_order': 16, 'label': '64.85.1j1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 0]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5144022
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 12, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.g1.e1', 'kernel_order': 16, 'label': '64.85.1j2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5144023
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 13, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.g1.g1', 'kernel_order': 16, 'label': '64.85.1k1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 5144024
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 14, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.g1.g1', 'kernel_order': 16, 'label': '64.85.1k2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 5144025
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 15, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.g1.h1', 'kernel_order': 16, 'label': '64.85.1l1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 5144026
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 16, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.g1.h1', 'kernel_order': 16, 'label': '64.85.1l2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 5144027
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 17, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.g1.b1', 'kernel_order': 16, 'label': '64.85.1m1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5144028
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 18, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.g1.b1', 'kernel_order': 16, 'label': '64.85.1m2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 0]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5144029
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 19, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.g1.a1', 'kernel_order': 16, 'label': '64.85.1n1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5144031
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 20, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.g1.a1', 'kernel_order': 16, 'label': '64.85.1n2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 0]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5144032
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 21, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.g1.c1', 'kernel_order': 16, 'label': '64.85.1o1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 5144033
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 22, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.g1.c1', 'kernel_order': 16, 'label': '64.85.1o2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 5144034
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 23, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.g1.d1', 'kernel_order': 16, 'label': '64.85.1p1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 5144035
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 24, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.g1.d1', 'kernel_order': 16, 'label': '64.85.1p2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 5144036
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 25, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.c1.b1', 'kernel_order': 16, 'label': '64.85.1q1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 5144037
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 26, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.c1.b1', 'kernel_order': 16, 'label': '64.85.1q2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 5144038
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 27, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.c1.a1', 'kernel_order': 16, 'label': '64.85.1r1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 5144039
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 28, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.c1.a1', 'kernel_order': 16, 'label': '64.85.1r2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 5144040
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 29, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.b1', 'kernel_order': 16, 'label': '64.85.1s1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 5144042
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 30, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.b1', 'kernel_order': 16, 'label': '64.85.1s2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 5144043
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 31, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 16, 'label': '64.85.1t1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 5144044
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 32, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 16, 'label': '64.85.1t2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 5144045
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 16, 'counter': 33, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '16.6', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.d1', 'kernel_order': 4, 'label': '64.85.2a1', 'nt': [8, 7], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[-2, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5144046
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 16, 'counter': 34, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '16.6', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.d1', 'kernel_order': 4, 'label': '64.85.2a2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 1]], [[-2, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5144047
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 16, 'counter': 35, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '16.6', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.c1', 'kernel_order': 4, 'label': '64.85.2b1', 'nt': [8, 7], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 1]], [[2, 0]], [[2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5144048
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 16, 'counter': 36, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '16.6', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.c1', 'kernel_order': 4, 'label': '64.85.2b2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[2, 0]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5144049
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 16, 'counter': 37, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '16.6', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 4, 'label': '64.85.2c1', 'nt': [8, 7], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 0]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5144050
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 16, 'counter': 38, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '16.6', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 4, 'label': '64.85.2c2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[-2, 0]], [[2, 1]], [[-2, 1]], [[2, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5144051
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 16, 'counter': 39, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '16.6', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.b1', 'kernel_order': 4, 'label': '64.85.2d1', 'nt': [8, 7], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 0]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5144053
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 16, 'counter': 40, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '64.85', 'group_counter': 85, 'group_order': 64, 'image': None, 'image_isoclass': '16.6', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.b1', 'kernel_order': 4, 'label': '64.85.2d2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[2, 0]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• 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: 59434709
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '64.85.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['F', 'R', 'U0', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.85', 'subgroup_hash': 85, 'subgroup_order': 64, 'subgroup_tex': 'C_4\\times \\OD_{16}', 'supersolvable': True, 'sylow': 2}
  • id: 59434720
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 59434731
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': True, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 59434742
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': True, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.2.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 59434753
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 32, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, '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: 59434764
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 32, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.2.c1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 59434775
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': True, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 59434778
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': True, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.2.d1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 59434779
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59434710
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.4.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59434711
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59434712
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 59434713
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.4.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 59434714
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U1'], '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: 59434715
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': 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: 59434716
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], '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: 59434717
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.4.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 59434718
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.4.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.f1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 59434719
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.4.f1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.f1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 59434721
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': True, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 20, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '64.85.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 59434722
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': True, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 21, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '64.85.4.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 59434723
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': True, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 22, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '64.85.4.g1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.g1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 59434724
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': True, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 23, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '64.85.4.g1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.g1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 59434725
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': True, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 24, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '64.85.4.g1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.g1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 59434726
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': True, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 25, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '64.85.4.g1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.g1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 59434727
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': True, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 26, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '64.85.4.g1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.g1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 59434728
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': True, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 27, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '64.85.4.g1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.g1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 59434729
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59434730
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59434732
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.8.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59434733
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'C3'], '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: 59434734
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59434735
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59434736
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.8.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59434737
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59434738
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.8.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59434739
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.8.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59434740
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.8.f1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59434741
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 39, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.85.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 59434743
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 40, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.85.8.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 59434744
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 41, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.85.8.g1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.g1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 59434745
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 42, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.85.8.g1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.g1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 59434746
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 43, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.85.8.g1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.g1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 59434747
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 44, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.85.8.g1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.g1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 59434748
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 45, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.85.8.g1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.g1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 59434749
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 46, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.85.8.g1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.g1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 59434750
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.85.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59434751
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.85.8.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59434752
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.85.8.h1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.h1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59434754
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.85.8.h1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.h1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59434755
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 51, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '64.85.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\OD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59434756
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 52, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '64.85.16.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\OD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59434757
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 53, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '64.85.16.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\OD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59434758
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 54, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '64.85.16.a1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\OD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59434759
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 4, 'counter': 55, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59434760
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 56, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59434761
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 57, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.85.16.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59434762
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 58, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.85.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['C4'], '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: 59434763
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 59, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.85.16.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59434765
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 60, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.85.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2', '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: 59434766
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 61, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.85.16.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2', '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: 59434767
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.85.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59434768
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.85.16.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59434769
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 64, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '64.85.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59434770
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 65, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '64.85.16.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59434771
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 66, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.85.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.37', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 37, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times \\OD_{16}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59434772
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 67, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.85.32.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.37', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 37, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times \\OD_{16}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59434773
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 2, 'counter': 68, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.85.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '32.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.21', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 21, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4^2', 'simple': True, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C5'], '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: 59434774
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 69, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '64.85.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59434776
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 70, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '64.85.32.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59434777
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.85', 'ambient_counter': 85, 'ambient_order': 64, 'ambient_tex': 'C_4\\times \\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 1, 'counter': 71, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '64.85.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '64.85', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 85, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times \\OD_{16}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'L2', 'D2', 'C6'], '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: 59434709
    {'ambient': '64.85', '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': '4.d1.a1', 'complements': ['64.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.b1.b1', '2.c1.a1', '2.c1.b1', '2.d1.a1', '2.d1.b1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6128, 5259, 6736, 4109, 6246, 5491, 6781, 4164], 'generators': [1, 2, 8], 'label': '64.85.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.b1.b1', '2.c1.a1', '2.c1.b1', '2.d1.a1', '2.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '4.2', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59434710
    {'ambient': '64.85', 'aut_centralizer_order': 32, 'aut_label': '4.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.b1.b1', '8.e1.b1', '8.h1.c1', '8.h1.d1'], 'core': '4.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2145, 1026, 2974, 322, 2200, 1148, 2994, 327], 'generators': [1, 18, 32], 'label': '64.85.4.a1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1.b1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.b1', '8.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.b1', 'projective_image': '8.2', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434711
    {'ambient': '64.85', 'aut_centralizer_order': 32, 'aut_label': '4.b1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'contains': ['8.a1.a1', '8.c1.a1', '8.d1.a1', '8.f1.a1', '8.f1.b1', '8.f1.c1', '8.f1.d1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6250, 5790, 6219, 5961, 6413, 5929, 6261, 6040], 'generators': [1, 4, 16], 'label': '64.85.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'normal_contains': ['8.a1.a1', '8.c1.a1', '8.d1.a1', '8.f1.b1', '8.f1.a1', '8.f1.d1', '8.f1.c1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '8.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434712
    {'ambient': '64.85', 'aut_centralizer_order': 32, 'aut_label': '4.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.a1', '8.d1.a1', '8.e1.b1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3364, 2442, 3414, 1607, 3452, 2568, 3436, 1629], 'generators': [17, 2], 'label': '64.85.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.b1.a1', '8.e1.b1', '8.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '8.2', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434713
    {'ambient': '64.85', 'aut_centralizer_order': 32, 'aut_label': '4.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.b1', '8.d1.a1', '8.e1.a1'], 'core': '4.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3364, 2442, 3714, 1988, 3452, 2568, 3739, 2015], 'generators': [17, 18], 'label': '64.85.4.c1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.b1.b1', '8.e1.a1', '8.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.b1', 'projective_image': '8.2', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434714
    {'ambient': '64.85', 'aut_centralizer_order': 32, 'aut_label': '4.d1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.c1.a1', '2.c1.b1'], 'contains': ['8.b1.a1', '8.b1.b1', '8.c1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5031, 3408, 4014, 2368, 5162, 3539, 4041, 2401], 'generators': [2, 16], 'label': '64.85.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.a1.a1', '2.c1.a1', '2.c1.b1'], 'normal_contains': ['8.b1.a1', '8.b1.b1', '8.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '4.2', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59434715
    {'ambient': '64.85', 'aut_centralizer_order': 32, 'aut_label': '4.e1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.d1.b1'], 'contains': ['8.c1.a1', '8.e1.a1', '8.e1.b1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4198, 4375, 4315, 2749, 4307, 4509, 4344, 2786], 'generators': [3, 16], 'label': '64.85.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.a1.a1', '2.d1.a1', '2.d1.b1'], 'normal_contains': ['8.c1.a1', '8.e1.a1', '8.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '8.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434716
    {'ambient': '64.85', 'aut_centralizer_order': 16, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.c1.a1', '2.d1.a1'], 'contains': ['8.c1.a1', '8.g1.a1', '8.g1.b1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7744, 7524, 8619, 3886, 7946, 7669, 8676, 3938], 'generators': [8, 4], 'label': '64.85.4.f1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.b1.a1', '2.c1.a1', '2.d1.a1'], 'normal_contains': ['8.c1.a1', '8.g1.b1', '8.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '8.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434717
    {'ambient': '64.85', 'aut_centralizer_order': 16, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '2.c1.a1', '2.d1.b1'], 'contains': ['8.c1.a1', '8.g1.e1', '8.g1.f1'], 'core': '4.f1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7744, 7524, 7257, 7106, 7946, 7669, 7305, 7202], 'generators': [10, 16], 'label': '64.85.4.f1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.b1', 'normal_contained_in': ['2.b1.b1', '2.c1.a1', '2.d1.b1'], 'normal_contains': ['8.c1.a1', '8.g1.f1', '8.g1.e1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.b1', 'projective_image': '8.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.f1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434718
    {'ambient': '64.85', 'aut_centralizer_order': 16, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '2.c1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.c1.b1', '2.d1.b1'], 'contains': ['8.c1.a1', '8.g1.c1', '8.g1.d1'], 'core': '4.f1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [7744, 7524, 7755, 3255, 7946, 7669, 7806, 3299], 'generators': [9, 4], 'label': '64.85.4.f1.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.c1', 'normal_contained_in': ['2.b1.a1', '2.c1.b1', '2.d1.b1'], 'normal_contains': ['8.c1.a1', '8.g1.d1', '8.g1.c1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.c1', 'projective_image': '8.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.f1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434719
    {'ambient': '64.85', 'aut_centralizer_order': 16, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '2.c1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '2.c1.b1', '2.d1.a1'], 'contains': ['8.c1.a1', '8.g1.g1', '8.g1.h1'], 'core': '4.f1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [7744, 7524, 6758, 7738, 7946, 7669, 6803, 7842], 'generators': [11, 16], 'label': '64.85.4.f1.d1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.d1', 'normal_contained_in': ['2.b1.b1', '2.c1.b1', '2.d1.a1'], 'normal_contains': ['8.c1.a1', '8.g1.h1', '8.g1.g1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.d1', 'projective_image': '8.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.f1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434720
    {'ambient': '64.85', 'aut_centralizer_order': 8, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 8, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.a1.b1', '4.b1.a1', '4.c1.a1', '4.c1.b1', '4.d1.a1', '4.e1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3618, 2594, 3864, 1970, 3681, 2828, 3890, 1996], 'generators': [1, 2, 16], 'label': '64.85.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.a1.b1', '4.b1.a1', '4.c1.a1', '4.c1.b1', '4.d1.a1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '4.2', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434721
    {'ambient': '64.85', 'aut_centralizer_order': 8, 'aut_label': '4.g1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '4.d1.a1', 'complements': ['16.a1.a1', '16.a1.b1', '16.a1.c1', '16.a1.d1', '16.g1.a1', '16.g1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.f1.a1', '8.g1.a1', '8.g1.c1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8943, 8916, 9051, 4434, 9176, 9065, 9111, 4493], 'generators': [1, 8], 'label': '64.85.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['8.f1.a1', '8.g1.a1', '8.g1.c1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '16.10', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59434722
    {'ambient': '64.85', 'aut_centralizer_order': 8, 'aut_label': '4.g1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '4.d1.a1', 'complements': ['16.a1.a1', '16.a1.b1', '16.a1.c1', '16.a1.d1', '16.g1.a1', '16.g1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.f1.a1', '8.g1.b1', '8.g1.d1'], 'core': '4.g1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8943, 8916, 9417, 5362, 9176, 9065, 9480, 5434], 'generators': [1, 12], 'label': '64.85.4.g1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.g1.b1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['8.f1.a1', '8.g1.b1', '8.g1.d1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.b1', 'projective_image': '16.10', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.g1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59434723
    {'ambient': '64.85', 'aut_centralizer_order': 8, 'aut_label': '4.g1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '4.d1.a1', 'complements': ['16.a1.c1', '16.a1.d1', '16.a1.a1', '16.a1.b1', '16.g1.b1', '16.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1'], 'contains': ['8.f1.b1', '8.g1.e1', '8.g1.g1'], 'core': '4.g1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [8943, 8916, 5381, 8286, 9176, 9065, 5417, 8396], 'generators': [1, 10], 'label': '64.85.4.g1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.g1.c1', 'normal_contained_in': ['2.b1.b1'], 'normal_contains': ['8.f1.b1', '8.g1.g1', '8.g1.e1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.c1', 'projective_image': '16.10', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.g1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59434724
    {'ambient': '64.85', 'aut_centralizer_order': 8, 'aut_label': '4.g1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '4.d1.a1', 'complements': ['16.a1.a1', '16.a1.b1', '16.a1.d1', '16.a1.c1', '16.g1.a1', '16.g1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1'], 'contains': ['8.f1.b1', '8.g1.f1', '8.g1.h1'], 'core': '4.g1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [8943, 8916, 5747, 9678, 9176, 9065, 5785, 9807], 'generators': [1, 26], 'label': '64.85.4.g1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.g1.d1', 'normal_contained_in': ['2.b1.b1'], 'normal_contains': ['8.f1.b1', '8.g1.h1', '8.g1.f1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.d1', 'projective_image': '16.10', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.g1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59434725
    {'ambient': '64.85', 'aut_centralizer_order': 8, 'aut_label': '4.g1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '4.d1.a1', 'complements': ['16.a1.a1', '16.a1.b1', '16.a1.c1', '16.a1.d1', '16.g1.a1', '16.g1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.f1.c1', '8.g1.a1', '8.g1.d1'], 'core': '4.g1.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [8943, 8916, 9784, 6560, 9176, 9065, 9849, 6647], 'generators': [5, 8], 'label': '64.85.4.g1.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.g1.e1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['8.f1.c1', '8.g1.a1', '8.g1.d1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.e1', 'projective_image': '16.10', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.g1.e1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59434726
    {'ambient': '64.85', 'aut_centralizer_order': 8, 'aut_label': '4.g1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '4.d1.a1', 'complements': ['16.a1.a1', '16.a1.b1', '16.a1.c1', '16.a1.d1', '16.g1.a1', '16.g1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.f1.c1', '8.g1.b1', '8.g1.c1'], 'core': '4.g1.f1', 'coset_action_label': None, 'count': 1, 'diagramx': [8943, 8916, 8187, 4898, 9176, 9065, 8241, 4964], 'generators': [5, 12], 'label': '64.85.4.g1.f1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.g1.f1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['8.f1.c1', '8.g1.b1', '8.g1.c1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.f1', 'projective_image': '16.10', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.g1.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59434727
    {'ambient': '64.85', 'aut_centralizer_order': 8, 'aut_label': '4.g1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '4.d1.a1', 'complements': ['16.a1.c1', '16.a1.d1', '16.a1.a1', '16.a1.b1', '16.g1.a1', '16.g1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1'], 'contains': ['8.f1.d1', '8.g1.e1', '8.g1.h1'], 'core': '4.g1.g1', 'coset_action_label': None, 'count': 1, 'diagramx': [8943, 8916, 5014, 8749, 9176, 9065, 5048, 8867], 'generators': [17, 10], 'label': '64.85.4.g1.g1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.g1.g1', 'normal_contained_in': ['2.b1.b1'], 'normal_contains': ['8.f1.d1', '8.g1.h1', '8.g1.e1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.g1', 'projective_image': '16.10', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.g1.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59434728
    {'ambient': '64.85', 'aut_centralizer_order': 8, 'aut_label': '4.g1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '4.d1.a1', 'complements': ['16.a1.a1', '16.a1.b1', '16.a1.d1', '16.a1.c1', '16.g1.b1', '16.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1'], 'contains': ['8.f1.d1', '8.g1.f1', '8.g1.g1'], 'core': '4.g1.h1', 'coset_action_label': None, 'count': 1, 'diagramx': [8943, 8916, 4648, 9213, 9176, 9065, 4679, 9337], 'generators': [17, 26], 'label': '64.85.4.g1.h1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.g1.h1', 'normal_contained_in': ['2.b1.b1'], 'normal_contains': ['8.f1.d1', '8.g1.f1', '8.g1.g1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.h1', 'projective_image': '16.10', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.g1.h1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59434729
    {'ambient': '64.85', 'aut_centralizer_order': 128, 'aut_label': '8.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.a1.b1', '4.b1.a1'], 'contains': ['16.b1.a1', '16.c1.a1', '16.c1.b1', '16.f1.a1', '16.f1.b1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4472, 3585, 3107, 2749, 4588, 3598, 3127, 2786], 'generators': [1, 4, 32], 'label': '64.85.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.a1.b1', '4.b1.a1'], 'normal_contains': ['16.b1.a1', '16.c1.a1', '16.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '16.10', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434730
    {'ambient': '64.85', 'aut_centralizer_order': 128, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.c1.a1', '4.d1.a1'], 'contains': ['16.a1.a1', '16.a1.b1', '16.b1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3364, 696, 1212, 981, 3452, 698, 1220, 995], 'generators': [2, 32], 'label': '64.85.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1', '4.c1.a1', '4.d1.a1'], 'normal_contains': ['16.b1.a1', '16.a1.b1', '16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '8.2', 'quotient_action_image': '1.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59434731
    {'ambient': '64.85', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 8, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.f1.a1', '4.f1.c1', '4.g1.a1', '4.g1.b1', '4.g1.e1', '4.g1.f1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8740, 8538, 8619, 5765, 8937, 8793, 8676, 5843], 'generators': [1, 8, 4], 'label': '64.85.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.f1.a1', '4.f1.c1', '4.g1.b1', '4.g1.a1', '4.g1.f1', '4.g1.e1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '8.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59434732
    {'ambient': '64.85', 'aut_centralizer_order': 128, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '4.c1.b1', '4.d1.a1'], 'contains': ['16.a1.c1', '16.a1.d1', '16.b1.a1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3364, 696, 4004, 350, 3452, 698, 4030, 355], 'generators': [18, 32], 'label': '64.85.8.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': ['4.a1.b1', '4.c1.b1', '4.d1.a1'], 'normal_contains': ['16.b1.a1', '16.a1.c1', '16.a1.d1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.b1', 'projective_image': '8.2', 'quotient_action_image': '1.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '8.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59434733
    {'ambient': '64.85', 'aut_centralizer_order': 128, 'aut_label': '8.c1', 'aut_quo_index': 42, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.f1.b1', '4.f1.c1', '4.f1.d1'], 'contains': ['16.b1.a1', '16.d1.a1', '16.d1.b1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6962, 6474, 7052, 3886, 7143, 6497, 7098, 3938], 'generators': [4, 16], 'label': '64.85.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.b1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.f1.d1', '4.f1.b1', '4.f1.c1'], 'normal_contains': ['16.b1.a1', '16.d1.b1', '16.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '8.5', 'quotient_action_image': '1.1', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59434734
    {'ambient': '64.85', 'aut_centralizer_order': 128, 'aut_label': '8.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.c1.a1', '4.c1.b1'], 'contains': ['16.b1.a1', '16.e1.a1', '16.e1.b1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5580, 4871, 4502, 3255, 5725, 4888, 4532, 3299], 'generators': [17, 4], 'label': '64.85.8.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': ['4.b1.a1', '4.c1.a1', '4.c1.b1'], 'normal_contains': ['16.b1.a1', '16.e1.a1', '16.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '16.10', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434735
    {'ambient': '64.85', 'aut_centralizer_order': 128, 'aut_label': '8.e1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.c1.b1', '4.e1.a1'], 'contains': ['16.b1.a1', '16.g1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1981, 2300, 2707, 2244, 2033, 2308, 2725, 2274], 'generators': [3, 32], 'label': '64.85.8.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': ['4.a1.a1', '4.c1.b1', '4.e1.a1'], 'normal_contains': ['16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.a1', 'projective_image': '16.10', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434736
    {'ambient': '64.85', 'aut_centralizer_order': 128, 'aut_label': '8.e1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '4.c1.a1', '4.e1.a1'], 'contains': ['16.b1.a1', '16.g1.b1'], 'core': '8.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1981, 2300, 3505, 1613, 2033, 2308, 3529, 1634], 'generators': [19, 32], 'label': '64.85.8.e1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.e1.b1', 'normal_contained_in': ['4.a1.b1', '4.c1.a1', '4.e1.a1'], 'normal_contains': ['16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.b1', 'projective_image': '16.10', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.e1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434737
    {'ambient': '64.85', 'aut_centralizer_order': 64, 'aut_label': '8.f1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.g1.a1', '4.g1.b1'], 'contains': ['16.c1.a1', '16.d1.a1', '16.e1.a1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8344, 8078, 7550, 5854, 8561, 8107, 7599, 5932], 'generators': [1, 16], 'label': '64.85.8.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': ['4.b1.a1', '4.g1.b1', '4.g1.a1'], 'normal_contains': ['16.c1.a1', '16.d1.a1', '16.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.a1', 'projective_image': '16.10', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434738
    {'ambient': '64.85', 'aut_centralizer_order': 64, 'aut_label': '8.f1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.g1.c1', '4.g1.d1'], 'contains': ['16.c1.a1', '16.d1.b1', '16.e1.b1'], 'core': '8.f1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8344, 8078, 6553, 7116, 8561, 8107, 6596, 7211], 'generators': [1, 20], 'label': '64.85.8.f1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.f1.b1', 'normal_contained_in': ['4.b1.a1', '4.g1.d1', '4.g1.c1'], 'normal_contains': ['16.c1.a1', '16.d1.b1', '16.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.b1', 'projective_image': '16.10', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.f1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434739
    {'ambient': '64.85', 'aut_centralizer_order': 64, 'aut_label': '8.f1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.g1.e1', '4.g1.f1'], 'contains': ['16.c1.b1', '16.d1.a1', '16.e1.b1'], 'core': '8.f1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [8344, 8078, 8048, 6485, 8561, 8107, 8101, 6572], 'generators': [5, 16], 'label': '64.85.8.f1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.f1.c1', 'normal_contained_in': ['4.b1.a1', '4.g1.f1', '4.g1.e1'], 'normal_contains': ['16.c1.b1', '16.d1.a1', '16.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.c1', 'projective_image': '16.10', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.f1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434740
    {'ambient': '64.85', 'aut_centralizer_order': 64, 'aut_label': '8.f1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.g1.g1', '4.g1.h1'], 'contains': ['16.c1.b1', '16.d1.b1', '16.e1.a1'], 'core': '8.f1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [8344, 8078, 5000, 7747, 8561, 8107, 5033, 7851], 'generators': [17, 20], 'label': '64.85.8.f1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.f1.d1', 'normal_contained_in': ['4.b1.a1', '4.g1.g1', '4.g1.h1'], 'normal_contains': ['16.c1.b1', '16.d1.b1', '16.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.d1', 'projective_image': '16.10', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.f1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434741
    {'ambient': '64.85', 'aut_centralizer_order': 32, 'aut_label': '8.g1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '2.c1.a1', 'complements': ['8.h1.a1', '8.h1.b1', '8.h1.c1', '8.h1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.g1.a1', '4.g1.e1'], 'contains': ['16.d1.a1'], 'core': '8.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9401, 9304, 9004, 5371, 9646, 9337, 9063, 5443], 'generators': [8], 'label': '64.85.8.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': ['4.f1.a1', '4.g1.a1', '4.g1.e1'], 'normal_contains': ['16.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.g1.a1', 'projective_image': '16.10', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434742
    {'ambient': '64.85', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 8, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.f1.b1', '4.f1.d1', '4.g1.c1', '4.g1.d1', '4.g1.g1', '4.g1.h1'], 'core': '2.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8740, 8538, 5505, 8012, 8937, 8793, 5542, 8119], 'generators': [1, 10, 16], 'label': '64.85.2.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.f1.d1', '4.f1.b1', '4.g1.d1', '4.g1.c1', '4.g1.g1', '4.g1.h1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.b1', 'projective_image': '8.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59434743
    {'ambient': '64.85', 'aut_centralizer_order': 32, 'aut_label': '8.g1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '2.c1.a1', 'complements': ['8.h1.a1', '8.h1.b1', '8.h1.c1', '8.h1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.g1.b1', '4.g1.f1'], 'contains': ['16.d1.a1'], 'core': '8.g1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9401, 9304, 8693, 4703, 9646, 9337, 8750, 4766], 'generators': [12], 'label': '64.85.8.g1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.g1.b1', 'normal_contained_in': ['4.f1.a1', '4.g1.b1', '4.g1.f1'], 'normal_contains': ['16.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.g1.b1', 'projective_image': '16.10', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.g1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434744
    {'ambient': '64.85', 'aut_centralizer_order': 32, 'aut_label': '8.g1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '2.c1.b1', 'complements': ['8.h1.a1', '8.h1.b1', '8.h1.c1', '8.h1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.c1', '4.g1.a1', '4.g1.f1'], 'contains': ['16.d1.a1'], 'core': '8.g1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [9401, 9304, 8429, 4369, 9646, 9337, 8484, 4427], 'generators': [9], 'label': '64.85.8.g1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.g1.c1', 'normal_contained_in': ['4.f1.c1', '4.g1.a1', '4.g1.f1'], 'normal_contains': ['16.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.g1.c1', 'projective_image': '16.10', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.g1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434745
    {'ambient': '64.85', 'aut_centralizer_order': 32, 'aut_label': '8.g1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '2.c1.b1', 'complements': ['8.h1.a1', '8.h1.b1', '8.h1.c1', '8.h1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.c1', '4.g1.b1', '4.g1.e1'], 'contains': ['16.d1.a1'], 'core': '8.g1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [9401, 9304, 9366, 5037, 9646, 9337, 9428, 5104], 'generators': [13], 'label': '64.85.8.g1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.g1.d1', 'normal_contained_in': ['4.f1.c1', '4.g1.b1', '4.g1.e1'], 'normal_contains': ['16.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.g1.d1', 'projective_image': '16.10', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.g1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434746
    {'ambient': '64.85', 'aut_centralizer_order': 32, 'aut_label': '8.g1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '2.c1.a1', 'complements': ['8.h1.c1', '8.h1.d1', '8.h1.a1', '8.h1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '4.g1.c1', '4.g1.g1'], 'contains': ['16.d1.b1'], 'core': '8.g1.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [9401, 9304, 5645, 8229, 9646, 9337, 5682, 8340], 'generators': [10], 'label': '64.85.8.g1.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.g1.e1', 'normal_contained_in': ['4.f1.b1', '4.g1.c1', '4.g1.g1'], 'normal_contains': ['16.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.g1.e1', 'projective_image': '16.10', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.g1.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434747
    {'ambient': '64.85', 'aut_centralizer_order': 32, 'aut_label': '8.g1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '2.c1.a1', 'complements': ['8.h1.a1', '8.h1.b1', '8.h1.d1', '8.h1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '4.g1.d1', '4.g1.h1'], 'contains': ['16.d1.b1'], 'core': '8.g1.f1', 'coset_action_label': None, 'count': 1, 'diagramx': [9401, 9304, 5909, 9232, 9646, 9337, 5948, 9356], 'generators': [26], 'label': '64.85.8.g1.f1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.g1.f1', 'normal_contained_in': ['4.f1.b1', '4.g1.d1', '4.g1.h1'], 'normal_contains': ['16.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.g1.f1', 'projective_image': '16.10', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.g1.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434748
    {'ambient': '64.85', 'aut_centralizer_order': 32, 'aut_label': '8.g1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '2.c1.b1', 'complements': ['8.h1.a1', '8.h1.b1', '8.h1.d1', '8.h1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.d1', '4.g1.c1', '4.g1.h1'], 'contains': ['16.d1.b1'], 'core': '8.g1.g1', 'coset_action_label': None, 'count': 1, 'diagramx': [9401, 9304, 5381, 8564, 9646, 9337, 5417, 8679], 'generators': [11], 'label': '64.85.8.g1.g1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.g1.g1', 'normal_contained_in': ['4.f1.d1', '4.g1.c1', '4.g1.h1'], 'normal_contains': ['16.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.g1.g1', 'projective_image': '16.10', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.g1.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434749
    {'ambient': '64.85', 'aut_centralizer_order': 32, 'aut_label': '8.g1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '2.c1.b1', 'complements': ['8.h1.a1', '8.h1.b1', '8.h1.d1', '8.h1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.d1', '4.g1.d1', '4.g1.g1'], 'contains': ['16.d1.b1'], 'core': '8.g1.h1', 'coset_action_label': None, 'count': 1, 'diagramx': [9401, 9304, 6172, 8898, 9646, 9337, 6213, 9017], 'generators': [27], 'label': '64.85.8.g1.h1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.g1.h1', 'normal_contained_in': ['4.f1.d1', '4.g1.d1', '4.g1.g1'], 'normal_contains': ['16.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.g1.h1', 'projective_image': '16.10', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.g1.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434750
    {'ambient': '64.85', 'aut_centralizer_order': 32, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.a1.a1', '16.f1.a1', '16.g1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [599, -1, 216, -1, 615, -1, 218, -1], 'generators': [1, 2], 'label': '64.85.8.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.h1.a1', 'projective_image': '16.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59434751
    {'ambient': '64.85', 'aut_centralizer_order': 32, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.a1.b1', '16.f1.a1', '16.g1.a1'], 'core': '16.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [599, -1, 714, -1, 615, -1, 719, -1], 'generators': [1, 34], 'label': '64.85.8.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.h1.b1', 'projective_image': '16.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59434752
    {'ambient': '64.85', 'aut_centralizer_order': 32, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1'], 'contains': ['16.a1.c1', '16.f1.b1', '16.g1.b1'], 'core': '16.a1.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [599, -1, 2209, -1, 615, -1, 2223, -1], 'generators': [1, 18], 'label': '64.85.8.h1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.h1.c1', 'projective_image': '16.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59434753
    {'ambient': '64.85', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.753', 'aut_weyl_index': 8, 'centralizer': '2.c1.a1', 'complements': ['32.c1.a1', '32.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.d1.a1', '4.f1.a1', '4.f1.b1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6921, 4328, 7964, 3478, 7070, 4568, 8016, 3525], 'generators': [2, 8], 'label': '64.85.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.d1.a1', '4.f1.a1', '4.f1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '4.2', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434754
    {'ambient': '64.85', 'aut_centralizer_order': 32, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1'], 'contains': ['16.a1.d1', '16.f1.b1', '16.g1.b1'], 'core': '16.a1.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [599, -1, 1710, -1, 615, -1, 1722, -1], 'generators': [1, 50], 'label': '64.85.8.h1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.h1.d1', 'projective_image': '16.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59434755
    {'ambient': '64.85', 'aut_centralizer_order': 128, 'aut_label': '16.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '1.a1.a1', 'complements': ['4.g1.a1', '4.g1.e1', '4.g1.b1', '4.g1.f1', '4.g1.c1', '4.g1.g1', '4.g1.d1', '4.g1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.h1.a1'], 'contains': ['32.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2856, 1687, 791, 1353, 2930, 1692, 796, 1371], 'generators': [2], 'label': '64.85.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.b1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '16.6', 'quotient_action_image': '1.1', 'quotient_action_kernel': '16.6', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59434756
    {'ambient': '64.85', 'aut_centralizer_order': 128, 'aut_label': '16.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '1.a1.a1', 'complements': ['4.g1.a1', '4.g1.e1', '4.g1.b1', '4.g1.f1', '4.g1.c1', '4.g1.g1', '4.g1.d1', '4.g1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.h1.b1'], 'contains': ['32.a1.a1'], 'core': '16.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2856, 1687, 1319, 1019, 2930, 1692, 1327, 1032], 'generators': [34], 'label': '64.85.16.a1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.b1', 'normal_contained_in': ['8.b1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.b1', 'projective_image': '16.6', 'quotient_action_image': '1.1', 'quotient_action_kernel': '16.6', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '16.a1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59434757
    {'ambient': '64.85', 'aut_centralizer_order': 128, 'aut_label': '16.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '1.a1.a1', 'complements': ['4.g1.a1', '4.g1.e1', '4.g1.b1', '4.g1.f1', '4.g1.d1', '4.g1.h1', '4.g1.c1', '4.g1.g1'], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '8.h1.c1'], 'contains': ['32.a1.b1'], 'core': '16.a1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [2856, 1687, 3019, 350, 2930, 1692, 3038, 355], 'generators': [18], 'label': '64.85.16.a1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.c1', 'normal_contained_in': ['8.b1.b1'], 'normal_contains': ['32.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.c1', 'projective_image': '16.6', 'quotient_action_image': '1.1', 'quotient_action_kernel': '16.6', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '16.a1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59434758
    {'ambient': '64.85', 'aut_centralizer_order': 128, 'aut_label': '16.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '1.a1.a1', 'complements': ['4.g1.a1', '4.g1.e1', '4.g1.b1', '4.g1.f1', '4.g1.d1', '4.g1.h1', '4.g1.c1', '4.g1.g1'], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '8.h1.d1'], 'contains': ['32.a1.b1'], 'core': '16.a1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [2856, 1687, 2755, 684, 2930, 1692, 2773, 694], 'generators': [50], 'label': '64.85.16.a1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.d1', 'normal_contained_in': ['8.b1.b1'], 'normal_contains': ['32.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.d1', 'projective_image': '16.6', 'quotient_action_image': '1.1', 'quotient_action_kernel': '16.6', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '16.a1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59434759
    {'ambient': '64.85', 'aut_centralizer_order': 512, 'aut_label': '16.b1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '8.c1.a1', '8.d1.a1', '8.e1.a1', '8.e1.b1'], 'contains': ['32.a1.a1', '32.a1.b1', '32.b1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4472, 3585, 3403, 1980, 4588, 3598, 3426, 2006], 'generators': [4, 32], 'label': '64.85.16.b1.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '8.c1.a1', '8.e1.a1', '8.e1.b1', '8.d1.a1'], 'normal_contains': ['32.b1.a1', '32.a1.a1', '32.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '16.10', 'quotient_action_image': '1.1', 'quotient_action_kernel': '16.10', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59434760
    {'ambient': '64.85', 'aut_centralizer_order': 256, 'aut_label': '16.c1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.f1.a1', '8.f1.b1'], 'contains': ['32.b1.a1', '32.c1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5305, 4552, 5927, 5399, 5443, 4568, 5966, 5471], 'generators': [1, 32], 'label': '64.85.16.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.a1.a1', '8.f1.b1', '8.f1.a1'], 'normal_contains': ['32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.a1', 'projective_image': '32.21', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434761
    {'ambient': '64.85', 'aut_centralizer_order': 256, 'aut_label': '16.c1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.f1.c1', '8.f1.d1'], 'contains': ['32.b1.a1', '32.c1.b1'], 'core': '16.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5305, 4552, 5000, 5780, 5443, 4568, 5033, 5857], 'generators': [5, 32], 'label': '64.85.16.c1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1.b1', 'normal_contained_in': ['8.a1.a1', '8.f1.d1', '8.f1.c1'], 'normal_contains': ['32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.b1', 'projective_image': '32.21', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434762
    {'ambient': '64.85', 'aut_centralizer_order': 256, 'aut_label': '16.d1', 'aut_quo_index': 12, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.f1.a1', '8.f1.c1', '8.g1.a1', '8.g1.b1', '8.g1.c1', '8.g1.d1'], 'contains': ['32.b1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7653, 7277, 8238, 5042, 7852, 7302, 8293, 5109], 'generators': [16], 'label': '64.85.16.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': ['8.c1.a1', '8.f1.a1', '8.f1.c1', '8.g1.b1', '8.g1.a1', '8.g1.d1', '8.g1.c1'], 'normal_contains': ['32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.d1.a1', 'projective_image': '16.10', 'quotient_action_image': '1.1', 'quotient_action_kernel': '16.10', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59434763
    {'ambient': '64.85', 'aut_centralizer_order': 256, 'aut_label': '16.d1', 'aut_quo_index': 12, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.f1.b1', '8.f1.d1', '8.g1.e1', '8.g1.f1', '8.g1.g1', '8.g1.h1'], 'contains': ['32.b1.a1'], 'core': '16.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7653, 7277, 5645, 7988, 7852, 7302, 5682, 8095], 'generators': [20], 'label': '64.85.16.d1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1.b1', 'normal_contained_in': ['8.c1.a1', '8.f1.b1', '8.f1.d1', '8.g1.h1', '8.g1.f1', '8.g1.g1', '8.g1.e1'], 'normal_contains': ['32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.d1.b1', 'projective_image': '16.10', 'quotient_action_image': '1.1', 'quotient_action_kernel': '16.10', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '16.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59434764
    {'ambient': '64.85', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.753', 'aut_weyl_index': 8, 'centralizer': '2.c1.b1', 'complements': ['32.c1.a1', '32.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.d1.a1', '4.f1.c1', '4.f1.d1'], 'core': '2.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6921, 4328, 6161, 4109, 7070, 4568, 6202, 4164], 'generators': [9, 2], 'label': '64.85.2.c1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.d1.a1', '4.f1.d1', '4.f1.c1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.b1', 'projective_image': '4.2', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434765
    {'ambient': '64.85', 'aut_centralizer_order': 256, 'aut_label': '16.e1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.f1.a1', '8.f1.d1'], 'contains': ['32.b1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6088, 5460, 5329, 6137, 6246, 5479, 5365, 6219], 'generators': [17], 'label': '64.85.16.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': ['8.d1.a1', '8.f1.a1', '8.f1.d1'], 'normal_contains': ['32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.e1.a1', 'projective_image': '32.21', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434766
    {'ambient': '64.85', 'aut_centralizer_order': 256, 'aut_label': '16.e1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.f1.b1', '8.f1.c1'], 'contains': ['32.b1.a1'], 'core': '16.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6088, 5460, 6381, 6475, 6246, 5479, 6423, 6562], 'generators': [21], 'label': '64.85.16.e1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.e1.b1', 'normal_contained_in': ['8.d1.a1', '8.f1.b1', '8.f1.c1'], 'normal_contains': ['32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.e1.b1', 'projective_image': '32.21', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.e1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59434767
    {'ambient': '64.85', 'aut_centralizer_order': 128, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.h1.a1', '8.h1.b1'], 'contains': ['32.a1.a1', '32.c1.a1', '32.c1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3639, -1, 1703, -1, 3733, -1, 1818, -1], 'generators': [1, 4], 'label': '64.85.16.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.f1.a1', 'projective_image': '32.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59434768
    {'ambient': '64.85', 'aut_centralizer_order': 128, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.h1.c1', '8.h1.d1'], 'contains': ['32.a1.b1', '32.c1.a1', '32.c1.b1'], 'core': '32.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3639, -1, 2209, -1, 3733, -1, 2223, -1], 'generators': [1, 36], 'label': '64.85.16.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.f1.b1', 'projective_image': '32.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59434769
    {'ambient': '64.85', 'aut_centralizer_order': 128, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.h1.a1', '8.h1.b1'], 'contains': ['32.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1981, -1, 1055, -1, 2033, -1, 1062, -1], 'generators': [3], 'label': '64.85.16.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.g1.a1', 'projective_image': '32.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59434770
    {'ambient': '64.85', 'aut_centralizer_order': 128, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.b1', '8.h1.c1', '8.h1.d1'], 'contains': ['32.a1.b1'], 'core': '32.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1981, -1, 2491, -1, 2033, -1, 2507, -1], 'generators': [19], 'label': '64.85.16.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.g1.b1', 'projective_image': '32.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59434771
    {'ambient': '64.85', 'aut_centralizer_order': 512, 'aut_label': '32.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.a1.b1', '16.b1.a1', '16.f1.a1', '16.g1.a1'], 'contains': ['64.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3639, 3585, 1512, 1353, 3733, 3598, 1574, 1371], 'generators': [4], 'label': '64.85.32.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.b1.a1', '16.a1.b1', '16.a1.a1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '32.37', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.37', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59434772
    {'ambient': '64.85', 'aut_centralizer_order': 512, 'aut_label': '32.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.c1', '16.a1.d1', '16.b1.a1', '16.f1.b1', '16.g1.b1'], 'contains': ['64.a1.a1'], 'core': '32.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3639, 3585, 2747, 852, 3733, 3598, 2766, 863], 'generators': [36], 'label': '64.85.32.a1.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '32.a1.b1', 'normal_contained_in': ['16.b1.a1', '16.a1.c1', '16.a1.d1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.b1', 'projective_image': '32.37', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.37', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.a1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59434773
    {'ambient': '64.85', 'aut_centralizer_order': 1024, 'aut_label': '32.b1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.c1.a1', '16.c1.b1', '16.d1.a1', '16.d1.b1', '16.e1.a1', '16.e1.b1'], 'contains': ['64.a1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5305, 4552, 5488, 5590, 5443, 4568, 5524, 5664], 'generators': [32], 'label': '64.85.32.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': ['16.b1.a1', '16.c1.a1', '16.c1.b1', '16.d1.b1', '16.d1.a1', '16.e1.a1', '16.e1.b1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.b1.a1', 'projective_image': '32.21', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.21', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59434774
    {'ambient': '64.85', 'aut_centralizer_order': 256, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.f1.a1', '16.f1.b1'], 'contains': ['64.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': '32T185', 'count': 2, 'diagramx': [4472, -1, 2472, -1, 4588, -1, 2489, -1], 'generators': [1], 'label': '64.85.32.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.c1.a1', 'projective_image': '64.85', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59434775
    {'ambient': '64.85', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.753', 'aut_weyl_index': 8, 'centralizer': '4.d1.a1', 'complements': ['32.c1.a1', '32.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.e1.a1', '4.f1.a1', '4.f1.d1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5326, 6179, 6736, 4838, 5433, 6426, 6781, 4902], 'generators': [3, 8], 'label': '64.85.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.e1.a1', '4.f1.a1', '4.f1.d1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '8.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59434776
    {'ambient': '64.85', 'aut_centralizer_order': 256, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.b1', '16.f1.a1', '16.f1.b1'], 'contains': ['64.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': '32T185', 'count': 2, 'diagramx': [4472, -1, 2209, -1, 4588, -1, 2223, -1], 'generators': [5], 'label': '64.85.32.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.c1.b1', 'projective_image': '64.85', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59434777
    {'ambient': '64.85', '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.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.a1.b1', '32.b1.a1', '32.c1.a1', '32.c1.b1'], 'contains': [], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4472, 4068, 2472, 1353, 4588, 4083, 2489, 1371], 'generators': [], 'label': '64.85.64.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': ['32.b1.a1', '32.a1.a1', '32.a1.b1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '64.a1.a1', 'projective_image': '64.85', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59434778
    {'ambient': '64.85', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.753', 'aut_weyl_index': 8, 'centralizer': '4.d1.a1', 'complements': ['32.c1.a1', '32.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.e1.a1', '4.f1.b1', '4.f1.c1'], 'core': '2.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5326, 6179, 7388, 2749, 5433, 6426, 7437, 2786], 'generators': [9, 10], 'label': '64.85.2.d1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.e1.a1', '4.f1.b1', '4.f1.c1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.b1', 'projective_image': '8.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59434779
    {'ambient': '64.85', 'aut_centralizer_order': 32, 'aut_label': '4.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.e1.a1', '8.h1.a1', '8.h1.b1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2145, 1026, 1805, 1051, 2200, 1148, 1818, 1065], 'generators': [1, 2, 32], 'label': '64.85.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '8.2', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}