Abstract group data - 3072.bgb

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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': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [6, 8, 8, 4, 8], 'aut_gens': [[108118421696801471190456, 134021529040297499210286, 378358649363678452761737], [25903485430815165863622, 324355901221310116838376, 458378079904529944161840], [162070200542086092753977, 187973307870272318862697, 432475093514187725718960], [108118421698102958822263, 296092500499408867062462, 51347412416128147182], [25903485430815165863622, 486477963656030037513479, 350259008905189606486342], [108118542986214492206143, 108169512647396423714639, 270189392814047393584566]], 'aut_group': '2500.ch', 'aut_hash': 2330610246365708940, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6144, 'aut_permdeg': 64, 'aut_perms': [110330436900984887806891726145468238558279182527011692157727386333230871492415239751216396, 114177996654955268543746459680675728127644244317203085598788485932186610784398235340294851, 116768451223344476476129242497380884569707776920417289329217727109397305727605871441046099, 17961790815183306806527358515508211983461042269498153799502376525749682676680718150285546, 78392228702411424516736910756198750099163927728810263000215655255012543977291174290603640], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 4, 1, 1], [2, 8, 1, 1], [2, 12, 2, 1], [2, 24, 1, 3], [2, 24, 2, 1], [2, 32, 1, 1], [2, 48, 1, 2], [3, 128, 1, 1], [4, 6, 1, 2], [4, 8, 1, 1], [4, 12, 1, 1], [4, 24, 1, 4], [4, 24, 2, 1], [4, 48, 1, 3], [4, 96, 1, 1], [4, 96, 2, 2], [4, 192, 1, 1], [6, 128, 1, 1], [6, 256, 1, 2], [8, 48, 2, 3], [8, 96, 1, 3], [8, 192, 1, 1], [12, 256, 1, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_5\\wr C_4', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': None, 'autcentquo_hash': 2330610246365708940, 'autcentquo_nilpotent': False, 'autcentquo_order': 6144, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_4^2.(D_4\\times S_4).C_2', 'cc_stats': [[1, 1, 1], [2, 3, 1], [2, 4, 1], [2, 8, 1], [2, 12, 2], [2, 24, 5], [2, 32, 1], [2, 48, 2], [3, 128, 1], [4, 6, 2], [4, 8, 1], [4, 12, 1], [4, 24, 6], [4, 48, 3], [4, 96, 5], [4, 192, 1], [6, 128, 1], [6, 256, 2], [8, 48, 6], [8, 96, 3], [8, 192, 1], [12, 256, 1]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '3072.bgb', 'commutator_count': 1, 'commutator_label': '384.18236', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 11, 'conjugacy_classes_known': True, 'counter': 834, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 4, 1, 1], [2, 8, 1, 1], [2, 12, 1, 2], [2, 24, 1, 5], [2, 32, 1, 1], [2, 48, 1, 2], [3, 128, 1, 1], [4, 6, 1, 2], [4, 8, 1, 1], [4, 12, 1, 1], [4, 24, 1, 6], [4, 48, 1, 3], [4, 96, 1, 5], [4, 192, 1, 1], [6, 128, 1, 1], [6, 256, 1, 2], [8, 48, 1, 6], [8, 96, 1, 3], [8, 192, 1, 1], [12, 256, 1, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 1290240, 'exponent': 24, 'exponents_of_order': [10, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 1, 8], [24, 1, 2]], 'familial': False, 'frattini_label': '32.21', 'frattini_quotient': '96.226', 'hash': 7983714371117797868, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [8, 4, 8], 'inner_gens': [[108118421696801471190456, 133970559733522671655552, 242089631071724762738046], [108169634288197880657302, 134021529040297499210286, 540644350052627126634952], [377746962634166272, 458378079908654274953039, 378358649363678452761737]], 'inner_hash': 7983714371117797868, 'inner_nilpotent': False, 'inner_order': 3072, 'inner_split': True, 'inner_tex': 'C_4^3:(C_2\\times S_4)', 'inner_used': [1, 2, 3], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 8], [2, 6], [3, 8], [4, 1], [6, 14], [12, 9], [24, 2]], 'label': '3072.bgb', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'C4^3:(C2*S4)', 'ngens': 3, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 40, 'number_characteristic_subgroups': 33, 'number_conjugacy_classes': 48, 'number_divisions': 48, 'number_normal_subgroups': 35, 'number_subgroup_autclasses': 2088, 'number_subgroup_classes': 2726, 'number_subgroups': 46946, 'old_label': None, 'order': 3072, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 287], [3, 128], [4, 992], [6, 640], [8, 768], [12, 256]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[134021529377858197555056, 108118543358714709115566, 404159696449804700702662]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': 7, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 6], [3, 8], [4, 1], [6, 14], [12, 9], [24, 2]], 'representations': {'PC': {'code': '774422807212385769657039556353229452322262062652520179914371389460600381544469886761758479987368434958461297654232303647750021408820794322176480853774801967360', 'gens': [1, 2, 4, 5, 6, 7, 9], 'pres': [11, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 28248, 20021, 56, 5018, 112467, 39086, 19693, 96364, 42915, 2996, 8067, 110885, 52684, 25569, 709, 125670, 96113, 46228, 10511, 523, 226, 67602, 38045, 216224, 27343, 69231, 24593, 7972, 4221, 2054, 294, 116169, 142580, 50191, 8842, 5784, 328, 209098, 104565, 5840]}, 'Perm': {'d': 24, 'gens': [108118421696801471190456, 134021529040297499210286, 378358649363678452761737]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_4^3:(C_2\\times S_4)', 'transitive_degree': 24, '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: 157946513
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 834, 'group_order': 3072, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 157946524
    {'aut_label': '2A', 'centralizer': '3.a1', 'counter': 2, 'group_counter': 834, 'group_order': 3072, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 1313941673647, 'size': 3}
  • id: 157946535
    {'aut_label': '2B', 'centralizer': '4.H', 'counter': 3, 'group_counter': 834, 'group_order': 3072, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 122000787877207687, 'size': 4}
  • id: 157946546
    {'aut_label': '2C', 'centralizer': '8.C', 'counter': 4, 'group_counter': 834, 'group_order': 3072, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 25852017094578671678641, 'size': 8}
  • id: 157946556
    {'aut_label': '2D', 'centralizer': '12.CG', 'counter': 5, 'group_counter': 834, 'group_order': 3072, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 5612462138742, 'size': 12}
  • id: 157946557
    {'aut_label': '2D', 'centralizer': '12.CG', 'counter': 6, 'group_counter': 834, 'group_order': 3072, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 25903229687456985141817, 'size': 12}
  • id: 157946558
    {'aut_label': '2F', 'centralizer': '24.E', 'counter': 7, 'group_counter': 834, 'group_order': 3072, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 375302543248078, 'size': 24}
  • id: 157946559
    {'aut_label': '2G', 'centralizer': '24.CP', 'counter': 8, 'group_counter': 834, 'group_order': 3072, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 51091300648929957136, 'size': 24}
  • id: 157946560
    {'aut_label': '2F', 'centralizer': '24.E', 'counter': 9, 'group_counter': 834, 'group_order': 3072, 'label': '2H', 'order': 2, 'powers': [1, 9], 'representative': 51212956968387221062, 'size': 24}
  • id: 157946514
    {'aut_label': '2I', 'centralizer': '24.GA', 'counter': 10, 'group_counter': 834, 'group_order': 3072, 'label': '2I', 'order': 2, 'powers': [1, 10], 'representative': 187973685954795477134032, 'size': 24}
  • id: 157946515
    {'aut_label': '2J', 'centralizer': '24.GO', 'counter': 11, 'group_counter': 834, 'group_order': 3072, 'label': '2J', 'order': 2, 'powers': [1, 11], 'representative': 133970303630145059516752, 'size': 24}
  • id: 157946516
    {'aut_label': '2K', 'centralizer': '32.D', 'counter': 12, 'group_counter': 834, 'group_order': 3072, 'label': '2K', 'order': 2, 'powers': [1, 12], 'representative': 53952156579733379227566, 'size': 32}
  • id: 157946517
    {'aut_label': '2L', 'centralizer': '48.CK', 'counter': 13, 'group_counter': 834, 'group_order': 3072, 'label': '2L', 'order': 2, 'powers': [1, 13], 'representative': 256106167364275336, 'size': 48}
  • id: 157946518
    {'aut_label': '2M', 'centralizer': '48.H', 'counter': 14, 'group_counter': 834, 'group_order': 3072, 'label': '2M', 'order': 2, 'powers': [1, 14], 'representative': 51212959784829545017, 'size': 48}
  • id: 157946519
    {'aut_label': '3A', 'centralizer': '128.H', 'counter': 15, 'group_counter': 834, 'group_order': 3072, 'label': '3A', 'order': 3, 'powers': [15, 1], 'representative': 296092756602747121212846, 'size': 128}
  • id: 157946520
    {'aut_label': '4A', 'centralizer': '6.K', 'counter': 16, 'group_counter': 834, 'group_order': 3072, 'label': '4A', 'order': 4, 'powers': [2, 16], 'representative': 25903229684640542817862, 'size': 6}
  • id: 157946521
    {'aut_label': '4B', 'centralizer': '6.I', 'counter': 17, 'group_counter': 834, 'group_order': 3072, 'label': '4B', 'order': 4, 'powers': [2, 17], 'representative': 2796019804937, 'size': 6}
  • id: 157946522
    {'aut_label': '4C', 'centralizer': '8.I', 'counter': 18, 'group_counter': 834, 'group_order': 3072, 'label': '4C', 'order': 4, 'powers': [3, 18], 'representative': 25903364133006371697982, 'size': 8}
  • id: 157946523
    {'aut_label': '4D', 'centralizer': '12.W', 'counter': 19, 'group_counter': 834, 'group_order': 3072, 'label': '4D', 'order': 4, 'powers': [2, 19], 'representative': 122003583896286862, 'size': 12}
  • id: 157946525
    {'aut_label': '4E', 'centralizer': '24.DG', 'counter': 20, 'group_counter': 834, 'group_order': 3072, 'label': '4E', 'order': 4, 'powers': [2, 20], 'representative': 372506524168903, 'size': 24}
  • id: 157946526
    {'aut_label': '4F', 'centralizer': '24.FL', 'counter': 21, 'group_counter': 834, 'group_order': 3072, 'label': '4F', 'order': 4, 'powers': [2, 21], 'representative': 122006400338620657, 'size': 24}
  • id: 157946527
    {'aut_label': '4G', 'centralizer': '24.D', 'counter': 22, 'group_counter': 834, 'group_order': 3072, 'label': '4G', 'order': 4, 'powers': [3, 22], 'representative': 256450635784229177, 'size': 24}
  • id: 157946528
    {'aut_label': '4H', 'centralizer': '24.FS', 'counter': 23, 'group_counter': 834, 'group_order': 3072, 'label': '4H', 'order': 4, 'powers': [2, 23], 'representative': 51091306261392095878, 'size': 24}
  • id: 157946529
    {'aut_label': '4E', 'centralizer': '24.D', 'counter': 24, 'group_counter': 834, 'group_order': 3072, 'label': '4I', 'order': 4, 'powers': [2, 24], 'representative': 51212954172367416367, 'size': 24}
  • id: 157946530
    {'aut_label': '4J', 'centralizer': '24.GI', 'counter': 25, 'group_counter': 834, 'group_order': 3072, 'label': '4J', 'order': 4, 'powers': [2, 25], 'representative': 162121547575114918571536, 'size': 24}
  • id: 157946531
    {'aut_label': '4K', 'centralizer': '48.MB', 'counter': 26, 'group_counter': 834, 'group_order': 3072, 'label': '4K', 'order': 4, 'powers': [2, 26], 'representative': 366906516081841, 'size': 48}
  • id: 157946532
    {'aut_label': '4L', 'centralizer': '48.DA', 'counter': 27, 'group_counter': 834, 'group_order': 3072, 'label': '4L', 'order': 4, 'powers': [2, 27], 'representative': 25903363787224090639936, 'size': 48}
  • id: 157946533
    {'aut_label': '4M', 'centralizer': '48.E', 'counter': 28, 'group_counter': 834, 'group_order': 3072, 'label': '4M', 'order': 4, 'powers': [2, 28], 'representative': 54003382331745037000319, 'size': 48}
  • id: 157946534
    {'aut_label': '4N', 'centralizer': '96.HA', 'counter': 29, 'group_counter': 834, 'group_order': 3072, 'label': '4N', 'order': 4, 'powers': [10, 29], 'representative': 620397310434072627420726, 'size': 96}
  • id: 157946536
    {'aut_label': '4O', 'centralizer': '96.HA', 'counter': 30, 'group_counter': 834, 'group_order': 3072, 'label': '4O', 'order': 4, 'powers': [10, 30], 'representative': 324355644769192388380656, 'size': 96}
  • id: 157946537
    {'aut_label': '4N', 'centralizer': '96.GZ', 'counter': 31, 'group_counter': 834, 'group_order': 3072, 'label': '4P', 'order': 4, 'powers': [10, 31], 'representative': 620397189141863626903096, 'size': 96}
  • id: 157946538
    {'aut_label': '4O', 'centralizer': '96.GZ', 'counter': 32, 'group_counter': 834, 'group_order': 3072, 'label': '4Q', 'order': 4, 'powers': [10, 32], 'representative': 324355523478477960292536, 'size': 96}
  • id: 157946539
    {'aut_label': '4R', 'centralizer': '96.CM', 'counter': 33, 'group_counter': 834, 'group_order': 3072, 'label': '4R', 'order': 4, 'powers': [3, 33], 'representative': 486426751059060618928681, 'size': 96}
  • id: 157946540
    {'aut_label': '4S', 'centralizer': '192.KS', 'counter': 34, 'group_counter': 834, 'group_order': 3072, 'label': '4S', 'order': 4, 'powers': [11, 34], 'representative': 458378079908654274953039, 'size': 192}
  • id: 157946541
    {'aut_label': '6A', 'centralizer': '128.H', 'counter': 35, 'group_counter': 834, 'group_order': 3072, 'label': '6A', 'order': 6, 'powers': [15, 3], 'representative': 458377823799676695369617, 'size': 128}
  • id: 157946542
    {'aut_label': '6B', 'centralizer': '256.B', 'counter': 36, 'group_counter': 834, 'group_order': 3072, 'label': '6B', 'order': 6, 'powers': [15, 4], 'representative': 270189770926602388412879, 'size': 256}
  • id: 157946543
    {'aut_label': '6C', 'centralizer': '256.D', 'counter': 37, 'group_counter': 834, 'group_order': 3072, 'label': '6C', 'order': 6, 'powers': [15, 12], 'representative': 378358649016414227493241, 'size': 256}
  • id: 157946544
    {'aut_label': '8A', 'centralizer': '48.BU', 'counter': 38, 'group_counter': 834, 'group_order': 3072, 'label': '8A', 'order': 8, 'powers': [17, 38], 'representative': 256111767411926393, 'size': 48}
  • id: 157946545
    {'aut_label': '8B', 'centralizer': '48.BU', 'counter': 39, 'group_counter': 834, 'group_order': 3072, 'label': '8B', 'order': 8, 'powers': [19, 39], 'representative': 256456248206078152, 'size': 48}
  • id: 157946547
    {'aut_label': '8A', 'centralizer': '48.CD', 'counter': 40, 'group_counter': 834, 'group_order': 3072, 'label': '8C', 'order': 8, 'powers': [17, 40], 'representative': 25903363792824058447313, 'size': 48}
  • id: 157946548
    {'aut_label': '8B', 'centralizer': '48.MO', 'counter': 41, 'group_counter': 834, 'group_order': 3072, 'label': '8D', 'order': 8, 'powers': [19, 41], 'representative': 25903364137304932442752, 'size': 48}
  • id: 157946549
    {'aut_label': '8E', 'centralizer': '48.MO', 'counter': 42, 'group_counter': 834, 'group_order': 3072, 'label': '8E', 'order': 8, 'powers': [19, 42], 'representative': 53952291395173687195462, 'size': 48}
  • id: 157946550
    {'aut_label': '8E', 'centralizer': '48.CD', 'counter': 43, 'group_counter': 834, 'group_order': 3072, 'label': '8F', 'order': 8, 'powers': [19, 43], 'representative': 53952291397969706246400, 'size': 48}
  • id: 157946551
    {'aut_label': '8G', 'centralizer': '96.BY', 'counter': 44, 'group_counter': 834, 'group_order': 3072, 'label': '8G', 'order': 8, 'powers': [19, 44], 'representative': 324355644777594682437137, 'size': 96}
  • id: 157946552
    {'aut_label': '8H', 'centralizer': '96.CV', 'counter': 45, 'group_counter': 834, 'group_order': 3072, 'label': '8H', 'order': 8, 'powers': [19, 45], 'representative': 51468701829148437097, 'size': 96}
  • id: 157946553
    {'aut_label': '8I', 'centralizer': '96.QY', 'counter': 46, 'group_counter': 834, 'group_order': 3072, 'label': '8I', 'order': 8, 'powers': [17, 46], 'representative': 108118542991814459976366, 'size': 96}
  • id: 157946554
    {'aut_label': '8J', 'centralizer': '192.KR', 'counter': 47, 'group_counter': 834, 'group_order': 3072, 'label': '8J', 'order': 8, 'powers': [25, 47], 'representative': 404210787742051376872912, 'size': 192}
  • id: 157946555
    {'aut_label': '12A', 'centralizer': '256.G', 'counter': 48, 'group_counter': 834, 'group_order': 3072, 'label': '12A', 'order': 12, 'powers': [35, 18], 'representative': 270189514473156469054096, 'size': 256}
• 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: 15436000
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 15436011
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 15436022
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 15436033
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 15436043
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 15436044
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 15436045
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 15436046
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 15436047
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, -1, 2, 2, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, -1, -1, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, -1], 'schur_index': 1}
  • id: 15436001
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, 0, 0, 0, -2, 2, -2, 2, 0, 0, 0, 2, -2, -2, 0, 2, 0, -2, 2, 0, -2, 2, 0, 0, 0, 2, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15436002
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, 0, 0, 0, 2, -2, -2, 2, 0, 0, 0, 2, -2, -2, 0, 2, 0, -2, -2, 0, 2, 2, 0, 0, 0, -2, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15436003
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, -2, -2, -2, -2, 0, 0, 2, 2, -2, 0, 0, -1, 2, 2, 2, 2, 2, 2, 0, -2, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 1, 1, -2, 0, 0, -2, 0, 0, 0, 0, 2, 0, -1], 'schur_index': 1}
  • id: 15436004
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.2e', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, -2, -2, -2, -2, 0, 0, 2, 2, 2, 0, 0, -1, 2, 2, -2, 2, -2, 2, 0, -2, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 1, -1, 2, 0, 0, 2, 0, 0, 0, 0, -2, 0, 1], 'schur_index': 1}
  • id: 15436005
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, -2, 0, 0, -1, 2, 2, -2, 2, -2, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, -1, 1, -2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 1], 'schur_index': 1}
  • id: 15436006
    {'cdim': 3, 'counter': 15, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.3a', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -1, -1, 3, 1, 1, -1, -1, 3, 1, 1, 0, 3, 3, 3, 3, 3, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 0, 0, 0, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 0], 'schur_index': 1}
  • id: 15436007
    {'cdim': 3, 'counter': 16, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.3b', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -1, -1, 3, -1, -1, -1, -1, 3, -1, -1, 0, 3, 3, 3, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 0], 'schur_index': 1}
  • id: 15436008
    {'cdim': 3, 'counter': 17, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.3c', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, -3, 1, 1, -3, -1, -1, -1, -1, -3, 1, 1, 0, 3, 3, 3, 3, 3, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 0, 0, 0, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 0], 'schur_index': 1}
  • id: 15436009
    {'cdim': 3, 'counter': 18, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.3d', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, -3, 1, 1, -3, -1, -1, -1, -1, 3, -1, 1, 0, 3, 3, -3, 3, -3, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 0, 0, 0, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 0], 'schur_index': 1}
  • id: 15436010
    {'cdim': 3, 'counter': 19, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.3e', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, -3, 1, 1, -3, 1, 1, -1, -1, -3, -1, -1, 0, 3, 3, 3, 3, 3, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 0, 0, 0, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 0], 'schur_index': 1}
  • id: 15436012
    {'cdim': 3, 'counter': 20, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.3f', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, -3, 1, 1, -3, 1, 1, -1, -1, 3, 1, -1, 0, 3, 3, -3, 3, -3, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 0, 0, 0, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 0], 'schur_index': 1}
  • id: 15436013
    {'cdim': 3, 'counter': 21, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.3g', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -1, -1, 3, -1, -1, -1, -1, -3, 1, -1, 0, 3, 3, -3, 3, -3, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 0, 0, 0, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 0], 'schur_index': 1}
  • id: 15436014
    {'cdim': 3, 'counter': 22, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.3h', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -1, -1, 3, 1, 1, -1, -1, -3, -1, 1, 0, 3, 3, -3, 3, -3, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 0, 0, 0, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 0], 'schur_index': 1}
  • id: 15436015
    {'cdim': 4, 'counter': 23, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.4a', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, 4, -4, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, -2, -4, -4, 0, 4, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15436016
    {'cdim': 6, 'counter': 24, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.6a', 'multiplicity': 1, 'nt': [8, 41], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -2, -2, -2, 0, 0, 2, -2, 0, 2, 0, 0, -2, -2, 0, -2, 0, -2, 0, -2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, -2, 0, 0, 0], 'schur_index': 1}
  • id: 15436017
    {'cdim': 6, 'counter': 25, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.6b', 'multiplicity': 1, 'nt': [8, 41], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 2, 2, -2, 2, 2, -2, 2, 0, 0, 2, 0, -2, -2, 0, -2, 0, 2, 2, 2, 2, -2, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15436018
    {'cdim': 6, 'counter': 26, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.6c', 'multiplicity': 1, 'nt': [12, 86], 'qdim': 6, 'qvalues': [6, 6, -6, 0, 0, 0, 0, -2, 2, 2, -2, 0, 0, 0, 0, -6, -6, 0, 6, 0, 2, 2, 0, -2, -2, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15436019
    {'cdim': 6, 'counter': 27, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.6d', 'multiplicity': 1, 'nt': [12, 86], 'qdim': 6, 'qvalues': [6, 6, -6, 0, 0, 0, 0, 2, -2, 2, -2, 0, 0, 0, 0, -6, -6, 0, 6, 0, 2, -2, 0, 2, -2, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15436020
    {'cdim': 6, 'counter': 28, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.6e', 'multiplicity': 1, 'nt': [12, 108], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -2, -2, -2, 0, 0, 2, -2, 0, -2, 0, 0, -2, -2, 0, -2, 0, -2, 0, -2, 0, 2, 0, -2, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0], 'schur_index': 1}
  • id: 15436021
    {'cdim': 6, 'counter': 29, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.6f', 'multiplicity': 1, 'nt': [12, 108], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 2, 2, -2, -2, -2, -2, 2, 0, 0, -2, 0, -2, -2, 0, -2, 0, 2, -2, 2, -2, -2, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15436023
    {'cdim': 6, 'counter': 30, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.6g', 'multiplicity': 1, 'nt': [12, 136], 'qdim': 6, 'qvalues': [6, 6, 6, -6, -2, -2, 2, -2, -2, -2, 2, 0, 0, 2, 0, -2, -2, 0, -2, 0, 2, -2, -2, -2, -2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15436024
    {'cdim': 6, 'counter': 31, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.6h', 'multiplicity': 1, 'nt': [12, 136], 'qdim': 6, 'qvalues': [6, 6, 6, -6, -2, -2, 2, 2, 2, -2, 2, 0, 0, -2, 0, -2, -2, 0, -2, 0, 2, 2, -2, 2, -2, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15436025
    {'cdim': 6, 'counter': 32, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.6i', 'multiplicity': 1, 'nt': [12, 136], 'qdim': 6, 'qvalues': [6, 6, 6, -6, 2, 2, 2, 0, 0, 2, -2, 0, -2, 0, 0, -2, -2, 0, -2, 0, -2, 0, 2, 0, 2, 0, -2, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 2, 0, 0, 0], 'schur_index': 1}
  • id: 15436026
    {'cdim': 6, 'counter': 33, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.6j', 'multiplicity': 1, 'nt': [12, 136], 'qdim': 6, 'qvalues': [6, 6, 6, -6, 2, 2, 2, 0, 0, 2, -2, 0, 2, 0, 0, -2, -2, 0, -2, 0, -2, 0, 2, 0, 2, 0, 2, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, -2, 0, 0, 0], 'schur_index': 1}
  • id: 15436027
    {'cdim': 6, 'counter': 34, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.6k', 'multiplicity': 1, 'nt': [12, 186], 'qdim': 6, 'qvalues': [6, 6, -6, 0, -4, -4, 0, -2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, -2, 0, -2, 2, 4, -2, -2, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15436028
    {'cdim': 6, 'counter': 35, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.6l', 'multiplicity': 1, 'nt': [12, 186], 'qdim': 6, 'qvalues': [6, 6, -6, 0, -4, -4, 0, 2, -2, 2, 2, 0, 0, 0, 0, 2, 2, 0, -2, 0, -2, -2, 4, 2, -2, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15436029
    {'cdim': 6, 'counter': 36, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.6m', 'multiplicity': 1, 'nt': [12, 186], 'qdim': 6, 'qvalues': [6, 6, -6, 0, 4, 4, 0, -2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, -2, 0, -2, 2, -4, -2, -2, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15436030
    {'cdim': 6, 'counter': 37, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.6n', 'multiplicity': 1, 'nt': [12, 186], 'qdim': 6, 'qvalues': [6, 6, -6, 0, 4, 4, 0, 2, -2, 2, 2, 0, 0, 0, 0, 2, 2, 0, -2, 0, -2, -2, -4, 2, -2, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15436031
    {'cdim': 12, 'counter': 38, 'faithful': False, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.12a', 'multiplicity': 1, 'nt': [24, 1557], 'qdim': 12, 'qvalues': [12, 12, -12, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 4, 4, 0, -4, 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, 0], 'schur_index': 1}
  • id: 15436032
    {'cdim': 12, 'counter': 39, 'faithful': True, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.12b', 'multiplicity': 1, 'nt': [24, 7075], 'qdim': 12, 'qvalues': [12, -4, 0, 0, -4, 4, 0, -2, 2, 0, 0, 0, 2, -2, 0, -4, 4, -6, 0, 2, 0, -2, 0, 2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15436034
    {'cdim': 12, 'counter': 40, 'faithful': True, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.12c', 'multiplicity': 1, 'nt': [24, 7075], 'qdim': 12, 'qvalues': [12, -4, 0, 0, 4, -4, 0, 2, -2, 0, 0, 0, 2, -2, 0, -4, 4, -6, 0, 2, 0, 2, 0, -2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15436035
    {'cdim': 12, 'counter': 41, 'faithful': True, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.12d', 'multiplicity': 1, 'nt': [24, 7076], 'qdim': 12, 'qvalues': [12, -4, 0, 0, -4, 4, 0, 2, -2, 0, 0, 0, -2, 2, 0, -4, 4, -6, 0, 2, 0, 2, 0, -2, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15436036
    {'cdim': 12, 'counter': 42, 'faithful': True, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.12e', 'multiplicity': 1, 'nt': [24, 7076], 'qdim': 12, 'qvalues': [12, -4, 0, 0, 4, -4, 0, -2, 2, 0, 0, 0, -2, 2, 0, -4, 4, -6, 0, 2, 0, -2, 0, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15436037
    {'cdim': 12, 'counter': 43, 'faithful': True, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.12f', 'multiplicity': 1, 'nt': [24, 7077], 'qdim': 12, 'qvalues': [12, -4, 0, 0, -4, 4, 0, -2, 2, 0, 0, 0, -2, -2, 0, -4, 4, 6, 0, -2, 0, -2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15436038
    {'cdim': 12, 'counter': 44, 'faithful': True, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.12g', 'multiplicity': 1, 'nt': [24, 7077], 'qdim': 12, 'qvalues': [12, -4, 0, 0, 4, -4, 0, 2, -2, 0, 0, 0, -2, -2, 0, -4, 4, 6, 0, -2, 0, 2, 0, -2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15436039
    {'cdim': 12, 'counter': 45, 'faithful': True, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.12h', 'multiplicity': 1, 'nt': [24, 7085], 'qdim': 12, 'qvalues': [12, -4, 0, 0, -4, 4, 0, 2, -2, 0, 0, 0, 2, 2, 0, -4, 4, 6, 0, -2, 0, 2, 0, -2, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15436040
    {'cdim': 12, 'counter': 46, 'faithful': True, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.12i', 'multiplicity': 1, 'nt': [24, 7085], 'qdim': 12, 'qvalues': [12, -4, 0, 0, 4, -4, 0, -2, 2, 0, 0, 0, 2, 2, 0, -4, 4, 6, 0, -2, 0, -2, 0, 2, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15436041
    {'cdim': 24, 'counter': 47, 'faithful': True, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.24a', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 24, 'qvalues': [24, -8, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15436042
    {'cdim': 24, 'counter': 48, 'faithful': True, 'group': '3072.bgb', 'group_order': 3072, 'image': None, 'label': '3072.bgb.24b', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 24, 'qvalues': [24, -8, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], '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: 35308868
    {'center': None, 'center_index': 1, 'center_order': 3072, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': None, 'kernel_order': 3072, 'label': '3072.bgb.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 35308879
    {'center': None, 'center_index': 1, 'center_order': 3072, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 1536, 'label': '3072.bgb.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 35308890
    {'center': None, 'center_index': 1, 'center_order': 3072, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 1536, 'label': '3072.bgb.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 35308901
    {'center': None, 'center_index': 1, 'center_order': 3072, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 1536, 'label': '3072.bgb.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 35308911
    {'center': None, 'center_index': 1, 'center_order': 3072, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 1536, 'label': '3072.bgb.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 35308912
    {'center': None, 'center_index': 1, 'center_order': 3072, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 1536, 'label': '3072.bgb.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 35308913
    {'center': None, 'center_index': 1, 'center_order': 3072, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 1536, 'label': '3072.bgb.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 35308914
    {'center': None, 'center_index': 1, 'center_order': 3072, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 1536, 'label': '3072.bgb.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 35308915
    {'center': None, 'center_index': 6, 'center_order': 512, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': None, 'kernel_order': 512, 'label': '3072.bgb.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 35308869
    {'center': None, 'center_index': 4, 'center_order': 768, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': None, 'image_order': 8, 'indicator': 1, 'kernel': None, 'kernel_order': 384, 'label': '3072.bgb.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35308870
    {'center': None, 'center_index': 4, 'center_order': 768, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': None, 'image_order': 8, 'indicator': 1, 'kernel': None, 'kernel_order': 384, 'label': '3072.bgb.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35308871
    {'center': None, 'center_index': 6, 'center_order': 512, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': None, 'kernel_order': 256, 'label': '3072.bgb.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 35308872
    {'center': None, 'center_index': 6, 'center_order': 512, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': None, 'kernel_order': 256, 'label': '3072.bgb.2e', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]]]}
  • id: 35308873
    {'center': None, 'center_index': 6, 'center_order': 512, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': None, 'kernel_order': 256, 'label': '3072.bgb.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]]]}
  • id: 35308874
    {'center': None, 'center_index': 24, 'center_order': 128, 'counter': 15, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': None, 'image_order': 24, 'indicator': 1, 'kernel': None, 'kernel_order': 128, 'label': '3072.bgb.3a', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 35308875
    {'center': None, 'center_index': 24, 'center_order': 128, 'counter': 16, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': None, 'image_order': 24, 'indicator': 1, 'kernel': None, 'kernel_order': 128, 'label': '3072.bgb.3b', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]]]}
  • id: 35308876
    {'center': None, 'center_index': 24, 'center_order': 128, 'counter': 17, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 64, 'label': '3072.bgb.3c', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 35308877
    {'center': None, 'center_index': 24, 'center_order': 128, 'counter': 18, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 64, 'label': '3072.bgb.3d', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]]]}
  • id: 35308878
    {'center': None, 'center_index': 24, 'center_order': 128, 'counter': 19, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 64, 'label': '3072.bgb.3e', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]]]}
  • id: 35308880
    {'center': None, 'center_index': 24, 'center_order': 128, 'counter': 20, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 64, 'label': '3072.bgb.3f', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 35308881
    {'center': None, 'center_index': 24, 'center_order': 128, 'counter': 21, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 64, 'label': '3072.bgb.3g', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 35308882
    {'center': None, 'center_index': 24, 'center_order': 128, 'counter': 22, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 64, 'label': '3072.bgb.3h', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]]]}
  • id: 35308883
    {'center': None, 'center_index': 24, 'center_order': 128, 'counter': 23, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 64, 'label': '3072.bgb.4a', 'nt': [12, 28], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]]]}
  • id: 35308884
    {'center': None, 'center_index': 192, 'center_order': 16, 'counter': 24, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '3072.bgb.6a', 'nt': [8, 41], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35308885
    {'center': None, 'center_index': 192, 'center_order': 16, 'counter': 25, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '3072.bgb.6b', 'nt': [8, 41], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35308886
    {'center': None, 'center_index': 96, 'center_order': 32, 'counter': 26, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '3072.bgb.6c', 'nt': [12, 86], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35308887
    {'center': None, 'center_index': 96, 'center_order': 32, 'counter': 27, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '3072.bgb.6d', 'nt': [12, 86], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35308888
    {'center': None, 'center_index': 192, 'center_order': 16, 'counter': 28, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '3072.bgb.6e', 'nt': [12, 108], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35308889
    {'center': None, 'center_index': 192, 'center_order': 16, 'counter': 29, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '3072.bgb.6f', 'nt': [12, 108], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35308891
    {'center': None, 'center_index': 192, 'center_order': 16, 'counter': 30, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': '384.17948', 'image_order': 384, 'indicator': 1, 'kernel': None, 'kernel_order': 8, 'label': '3072.bgb.6g', 'nt': [12, 136], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35308892
    {'center': None, 'center_index': 192, 'center_order': 16, 'counter': 31, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': '384.17948', 'image_order': 384, 'indicator': 1, 'kernel': None, 'kernel_order': 8, 'label': '3072.bgb.6h', 'nt': [12, 136], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35308893
    {'center': None, 'center_index': 192, 'center_order': 16, 'counter': 32, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': '384.17948', 'image_order': 384, 'indicator': 1, 'kernel': None, 'kernel_order': 8, 'label': '3072.bgb.6i', 'nt': [12, 136], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35308894
    {'center': None, 'center_index': 192, 'center_order': 16, 'counter': 33, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': '384.17948', 'image_order': 384, 'indicator': 1, 'kernel': None, 'kernel_order': 8, 'label': '3072.bgb.6j', 'nt': [12, 136], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35308895
    {'center': None, 'center_index': 384, 'center_order': 8, 'counter': 34, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': '768.1087581', 'image_order': 768, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '3072.bgb.6k', 'nt': [12, 186], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35308896
    {'center': None, 'center_index': 384, 'center_order': 8, 'counter': 35, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': '768.1087581', 'image_order': 768, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '3072.bgb.6l', 'nt': [12, 186], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35308897
    {'center': None, 'center_index': 384, 'center_order': 8, 'counter': 36, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': '768.1087581', 'image_order': 768, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '3072.bgb.6m', 'nt': [12, 186], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35308898
    {'center': None, 'center_index': 384, 'center_order': 8, 'counter': 37, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': '768.1087581', 'image_order': 768, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '3072.bgb.6n', 'nt': [12, 186], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35308899
    {'center': None, 'center_index': 384, 'center_order': 8, 'counter': 38, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': '768.1087581', 'image_order': 768, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '3072.bgb.12a', 'nt': [24, 1557], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35308900
    {'center': None, 'center_index': 3072, 'center_order': 1, 'counter': 39, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': '3072.bgb', 'image_order': 3072, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '3072.bgb.12b', 'nt': [24, 7075], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-6, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35308902
    {'center': None, 'center_index': 3072, 'center_order': 1, 'counter': 40, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': '3072.bgb', 'image_order': 3072, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '3072.bgb.12c', 'nt': [24, 7075], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-6, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35308903
    {'center': None, 'center_index': 3072, 'center_order': 1, 'counter': 41, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': '3072.bgb', 'image_order': 3072, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '3072.bgb.12d', 'nt': [24, 7076], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-6, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35308904
    {'center': None, 'center_index': 3072, 'center_order': 1, 'counter': 42, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': '3072.bgb', 'image_order': 3072, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '3072.bgb.12e', 'nt': [24, 7076], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-6, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35308905
    {'center': None, 'center_index': 3072, 'center_order': 1, 'counter': 43, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': '3072.bgb', 'image_order': 3072, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '3072.bgb.12f', 'nt': [24, 7077], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35308906
    {'center': None, 'center_index': 3072, 'center_order': 1, 'counter': 44, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': '3072.bgb', 'image_order': 3072, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '3072.bgb.12g', 'nt': [24, 7077], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35308907
    {'center': None, 'center_index': 3072, 'center_order': 1, 'counter': 45, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': '3072.bgb', 'image_order': 3072, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '3072.bgb.12h', 'nt': [24, 7085], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35308908
    {'center': None, 'center_index': 3072, 'center_order': 1, 'counter': 46, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': '3072.bgb', 'image_order': 3072, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '3072.bgb.12i', 'nt': [24, 7085], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35308909
    {'center': None, 'center_index': 3072, 'center_order': 1, 'counter': 47, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': '3072.bgb', 'image_order': 3072, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '3072.bgb.24a', 'nt': [48, 0], 'q_character': None, 'values': [[[24, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 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, 0]], [[0, 0]], [[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: 35308910
    {'center': None, 'center_index': 3072, 'center_order': 1, 'counter': 48, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '3072.bgb', 'group_counter': 834, 'group_order': 3072, 'image': None, 'image_isoclass': '3072.bgb', 'image_order': 3072, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '3072.bgb.24b', 'nt': [48, 0], 'q_character': None, 'values': [[[24, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 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, 0]], [[0, 0]], [[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: 184760509
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 3072, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '3072.bgb.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3072.bgb', 'subgroup_hash': 7983714371117797868, 'subgroup_order': 3072, 'subgroup_tex': 'C_4^3:(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 184761620
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1536, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.2.A', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1536.408640541', 'subgroup_hash': 8944755179417135467, 'subgroup_order': 1536, 'subgroup_tex': 'C_2^5:(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 184761820
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1536, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.2.B', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1536.408527547', 'subgroup_hash': 3316927255007698598, 'subgroup_order': 1536, 'subgroup_tex': 'C_4^3:(C_2\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 184761931
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1536, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.2.C', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1536.408633532', 'subgroup_hash': 7006179242975571382, 'subgroup_order': 1536, 'subgroup_tex': 'C_4^2.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 184762042
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1536, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.2.D', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1536.408550734', 'subgroup_hash': 7456160622201197021, 'subgroup_order': 1536, 'subgroup_tex': 'C_4^2.(C_2^2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 184762153
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1536, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.2.E', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1536.408544807', 'subgroup_hash': 8450812584686924886, 'subgroup_order': 1536, 'subgroup_tex': 'C_4^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184762264
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1536, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.2.F', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1536.408545563', 'subgroup_hash': 6245505773554357918, 'subgroup_order': 1536, 'subgroup_tex': 'C_4^2.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 184762375
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1536, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.2.G', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1536.408544809', 'subgroup_hash': 631148683583985753, 'subgroup_order': 1536, 'subgroup_tex': 'C_4^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184762486
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 512, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '3072.bgb.3.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1024.dgx', 'subgroup_hash': 7936625845937413593, 'subgroup_order': 1024, 'subgroup_tex': 'C_4^2.D_4^2', 'supersolvable': True, 'sylow': 2}
  • id: 184760510
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 768, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.4.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '768.1085205', 'subgroup_hash': 1085205, 'subgroup_order': 768, 'subgroup_tex': 'C_2^5:(C_2\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 184760621
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 768, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.4.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '768.1090135', 'subgroup_hash': 1090135, 'subgroup_order': 768, 'subgroup_tex': '(C_2\\times C_4^2):S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184760732
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 768, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.4.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '768.1083785', 'subgroup_hash': 1083785, 'subgroup_order': 768, 'subgroup_tex': 'C_4^2.(C_2^2\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 184760843
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 768, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.4.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '768.1090135', 'subgroup_hash': 1090135, 'subgroup_order': 768, 'subgroup_tex': '(C_2\\times C_4^2):S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184760954
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 768, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.4.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '768.1090139', 'subgroup_hash': 1090139, 'subgroup_order': 768, 'subgroup_tex': 'C_4^2.(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 184761065
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 768, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.4.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '768.1083510', 'subgroup_hash': 1083510, 'subgroup_order': 768, 'subgroup_tex': 'C_4^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 184761176
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 768, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.4.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '768.1088659', 'subgroup_hash': 1088659, 'subgroup_order': 768, 'subgroup_tex': '(C_2\\times C_4^2).S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184761287
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 128, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.4.H', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '768.1088009', 'subgroup_hash': 1088009, 'subgroup_order': 768, 'subgroup_tex': 'C_4^3:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 184761398
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 384, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.4.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '768.1090134', 'subgroup_hash': 1090134, 'subgroup_order': 768, 'subgroup_tex': 'C_2^5:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184761509
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 384, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.4.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '768.1086051', 'subgroup_hash': 1086051, 'subgroup_order': 768, 'subgroup_tex': 'C_4^2.(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 184761621
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 512, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.6.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '512.254130', 'subgroup_hash': 8480418368773449077, 'subgroup_order': 512, 'subgroup_tex': 'C_4^2.C_2^4.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761721
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 128, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.6.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.7421336', 'subgroup_hash': 3717343585435044872, 'subgroup_order': 512, 'subgroup_tex': 'C_4^3:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761732
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.6.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.59223', 'subgroup_hash': 2323877150868405465, 'subgroup_order': 512, 'subgroup_tex': 'D_4.C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761743
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 128, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.6.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.59944', 'subgroup_hash': 4494848556309727787, 'subgroup_order': 512, 'subgroup_tex': 'C_4^3:(C_2\\times C_4)', 'supersolvable': True, 'sylow': 0}
  • id: 184761754
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.6.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.59898', 'subgroup_hash': 3974828244099893272, 'subgroup_order': 512, 'subgroup_tex': 'D_4.C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761765
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 256, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.6.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.7530076', 'subgroup_hash': 8222109897935199466, 'subgroup_order': 512, 'subgroup_tex': 'D_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761776
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 256, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.6.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.419015', 'subgroup_hash': 779064748097230029, 'subgroup_order': 512, 'subgroup_tex': 'D_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761787
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.6.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.420060', 'subgroup_hash': 2128154551908325188, 'subgroup_order': 512, 'subgroup_tex': 'D_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761798
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.6.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.59752', 'subgroup_hash': 5260648638953525643, 'subgroup_order': 512, 'subgroup_tex': 'C_4^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761809
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.6.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.60343', 'subgroup_hash': 2006353807606903387, 'subgroup_order': 512, 'subgroup_tex': 'D_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761821
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.6.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.60315', 'subgroup_hash': 4526424194543930778, 'subgroup_order': 512, 'subgroup_tex': 'C_4^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761832
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 256, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.6.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.420081', 'subgroup_hash': 3080942358160601456, 'subgroup_order': 512, 'subgroup_tex': '(C_4\\times \\OD_{16}):D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761843
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 256, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.6.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.59763', 'subgroup_hash': 5861703076455937101, 'subgroup_order': 512, 'subgroup_tex': 'C_4^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761854
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 256, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.6.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.60371', 'subgroup_hash': 4919896935252050934, 'subgroup_order': 512, 'subgroup_tex': '(C_4\\times \\OD_{16}):D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761865
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 256, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.6.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.60329', 'subgroup_hash': 2774682172597644585, 'subgroup_order': 512, 'subgroup_tex': 'C_4^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761876
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 384, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.8.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '384.18236', 'subgroup_hash': 18236, 'subgroup_order': 384, 'subgroup_tex': '(C_2\\times C_4^2):A_4', 'supersolvable': False, 'sylow': 0}
  • id: 184761887
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 384, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.8.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '384.18135', 'subgroup_hash': 18135, 'subgroup_order': 384, 'subgroup_tex': 'C_4^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184761898
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.8.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.17948', 'subgroup_hash': 17948, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184761909
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.8.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.17949', 'subgroup_hash': 17949, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184761920
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 128, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.8.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.5797', 'subgroup_hash': 5797, 'subgroup_order': 384, 'subgroup_tex': 'C_4^3:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 184761932
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.8.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.5660', 'subgroup_hash': 5660, 'subgroup_order': 384, 'subgroup_tex': 'C_2^2.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 184761943
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.8.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.5677', 'subgroup_hash': 5677, 'subgroup_order': 384, 'subgroup_tex': 'C_2^2.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 184761954
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.8.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.17949', 'subgroup_hash': 17949, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184761965
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.8.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.5557', 'subgroup_hash': 5557, 'subgroup_order': 384, 'subgroup_tex': 'C_4\\wr S_3', 'supersolvable': False, 'sylow': 0}
  • id: 184761976
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.8.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.5660', 'subgroup_hash': 5660, 'subgroup_order': 384, 'subgroup_tex': 'C_2^2.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 184761987
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.8.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.5558', 'subgroup_hash': 5558, 'subgroup_order': 384, 'subgroup_tex': 'C_4^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 184761998
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 192, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.8.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18235', 'subgroup_hash': 18235, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 184762009
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 192, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.8.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.591', 'subgroup_hash': 591, 'subgroup_order': 384, 'subgroup_tex': 'C_4^2.(C_2\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 184762020
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 192, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.8.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18135', 'subgroup_hash': 18135, 'subgroup_order': 384, 'subgroup_tex': 'C_4^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184762031
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 192, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.8.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18134', 'subgroup_hash': 18134, 'subgroup_order': 384, 'subgroup_tex': 'C_4^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184762043
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 256, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.12.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '256.55999', 'subgroup_hash': 55999, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762054
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 256, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.12.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '256.12061', 'subgroup_hash': 12061, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184762065
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 256, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.12.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '256.1518', 'subgroup_hash': 1518, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762076
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53376', 'subgroup_hash': 53376, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184762087
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53376', 'subgroup_hash': 53376, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184762098
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26541', 'subgroup_hash': 26541, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762109
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.5743', 'subgroup_hash': 5743, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762120
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.18184', 'subgroup_hash': 18184, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762131
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 128, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.18735', 'subgroup_hash': 18735, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762142
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16860', 'subgroup_hash': 16860, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762154
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.K', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26347', 'subgroup_hash': 26347, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2^2\\times C_4)', 'supersolvable': True, 'sylow': 0}
  • id: 184762165
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.L', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.5706', 'subgroup_hash': 5706, 'subgroup_order': 256, 'subgroup_tex': '(C_2^2\\times D_4).D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762176
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.M', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.1457', 'subgroup_hash': 1457, 'subgroup_order': 256, 'subgroup_tex': '(C_4\\times \\OD_{16}):C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762187
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.N', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53387', 'subgroup_hash': 53387, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762198
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.O', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26336', 'subgroup_hash': 26336, 'subgroup_order': 256, 'subgroup_tex': '(D_4\\times C_2^3):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762209
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.P', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16860', 'subgroup_hash': 16860, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762220
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.18184', 'subgroup_hash': 18184, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762231
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 128, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.R', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.18735', 'subgroup_hash': 18735, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762242
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.S', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.18184', 'subgroup_hash': 18184, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762253
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.T', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.54098', 'subgroup_hash': 54098, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762265
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.U', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.17460', 'subgroup_hash': 17460, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762276
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.V', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.17460', 'subgroup_hash': 17460, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762287
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.W', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.15887', 'subgroup_hash': 15887, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762298
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.X', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26541', 'subgroup_hash': 26541, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762309
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26541', 'subgroup_hash': 26541, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762320
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26534', 'subgroup_hash': 26534, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762331
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16870', 'subgroup_hash': 16870, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762342
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.5699', 'subgroup_hash': 5699, 'subgroup_order': 256, 'subgroup_tex': '(D_4\\times C_2^3):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762353
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.11515', 'subgroup_hash': 11515, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762364
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.BD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26534', 'subgroup_hash': 26534, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762376
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.BE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26534', 'subgroup_hash': 26534, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762387
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.BF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.1428', 'subgroup_hash': 1428, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762398
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.BG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.5753', 'subgroup_hash': 5753, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762409
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.BH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.17460', 'subgroup_hash': 17460, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762420
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.BI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.54098', 'subgroup_hash': 54098, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762431
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.BJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.15887', 'subgroup_hash': 15887, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762442
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.BK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6550', 'subgroup_hash': 6550, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 184762453
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.BL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6552', 'subgroup_hash': 6552, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 184762464
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 128, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.BM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26547', 'subgroup_hash': 26547, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762475
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.BN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.23484', 'subgroup_hash': 23484, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762487
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.BO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.23484', 'subgroup_hash': 23484, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762498
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.BP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6567', 'subgroup_hash': 6567, 'subgroup_order': 256, 'subgroup_tex': '(C_4\\times \\OD_{16}):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762509
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.BQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6573', 'subgroup_hash': 6573, 'subgroup_order': 256, 'subgroup_tex': '(C_4\\times \\OD_{16}):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762520
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.BR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.24064', 'subgroup_hash': 24064, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762531
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.BS', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6556', 'subgroup_hash': 6556, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 184762542
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.BT', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6562', 'subgroup_hash': 6562, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 184762553
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.BU', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6556', 'subgroup_hash': 6556, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 184762564
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.BV', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6550', 'subgroup_hash': 6550, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 184762575
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.BW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.488', 'subgroup_hash': 488, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762586
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.BX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.485', 'subgroup_hash': 485, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760511
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.BY', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.470', 'subgroup_hash': 470, 'subgroup_order': 256, 'subgroup_tex': '(C_2\\times C_4^2).D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760522
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.BZ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.474', 'subgroup_hash': 474, 'subgroup_order': 256, 'subgroup_tex': '(C_2\\times D_4).C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760533
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 128, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.CA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26547', 'subgroup_hash': 26547, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760544
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 128, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.CB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26558', 'subgroup_hash': 26558, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 184760555
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 128, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.CC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.5766', 'subgroup_hash': 5766, 'subgroup_order': 256, 'subgroup_tex': '(C_2\\times C_4^2).D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760566
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.CD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26545', 'subgroup_hash': 26545, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760577
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.CE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26539', 'subgroup_hash': 26539, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760588
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.CF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26539', 'subgroup_hash': 26539, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760599
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.CG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26531', 'subgroup_hash': 26531, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760610
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.CH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6661', 'subgroup_hash': 6661, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760622
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.CI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6663', 'subgroup_hash': 6663, 'subgroup_order': 256, 'subgroup_tex': '(C_4\\times C_8).D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760633
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.CJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6665', 'subgroup_hash': 6665, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 184760644
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.12.CK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6665', 'subgroup_hash': 6665, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 184760655
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 192, 'counter': 113, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.16.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.1023', 'subgroup_hash': 1023, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 184760666
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.16.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1000', 'subgroup_hash': 1000, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 184760677
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.16.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1472', 'subgroup_hash': 1472, 'subgroup_order': 192, 'subgroup_tex': 'D_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184760688
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.16.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1002', 'subgroup_hash': 1002, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 184760699
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.16.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1008', 'subgroup_hash': 1008, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 184760710
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.16.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.955', 'subgroup_hash': 955, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184760721
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.16.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.944', 'subgroup_hash': 944, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 184760733
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.16.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.955', 'subgroup_hash': 955, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184760744
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 8, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.16.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.956', 'subgroup_hash': 956, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 184760755
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 8, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.16.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.185', 'subgroup_hash': 185, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184760766
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.16.K', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1002', 'subgroup_hash': 1002, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 184760777
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.16.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.944', 'subgroup_hash': 944, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 184760788
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.16.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.944', 'subgroup_hash': 944, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 184760799
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.16.N', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.188', 'subgroup_hash': 188, 'subgroup_order': 192, 'subgroup_tex': 'C_4\\wr C_3', 'supersolvable': False, 'sylow': 0}
  • id: 184760810
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.16.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.182', 'subgroup_hash': 182, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184760821
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.16.P', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1538', 'subgroup_hash': 1538, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184760832
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.16.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.956', 'subgroup_hash': 956, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 184760844
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.16.R', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.955', 'subgroup_hash': 955, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184760855
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.16.S', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.956', 'subgroup_hash': 956, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 184760866
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 132, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.24.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1599', 'subgroup_hash': 1599, 'subgroup_order': 128, 'subgroup_tex': 'C_4^3:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760877
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 133, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.24.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.2281', 'subgroup_hash': 2281, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760888
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1753', 'subgroup_hash': 1753, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184760899
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1750', 'subgroup_hash': 1750, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184760910
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1746', 'subgroup_hash': 1746, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184760921
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1751', 'subgroup_hash': 1751, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184760932
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2020', 'subgroup_hash': 2020, 'subgroup_order': 128, 'subgroup_tex': 'D_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760943
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2024', 'subgroup_hash': 2024, 'subgroup_order': 128, 'subgroup_tex': 'D_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760955
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2023', 'subgroup_hash': 2023, 'subgroup_order': 128, 'subgroup_tex': 'D_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760966
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2020', 'subgroup_hash': 2020, 'subgroup_order': 128, 'subgroup_tex': 'D_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760977
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.K', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1758', 'subgroup_hash': 1758, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760988
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.L', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2326', 'subgroup_hash': 2326, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184760999
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.M', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2269', 'subgroup_hash': 2269, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761010
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.N', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1746', 'subgroup_hash': 1746, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761021
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.O', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1751', 'subgroup_hash': 1751, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761032
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.P', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1615', 'subgroup_hash': 1615, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184761043
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1620', 'subgroup_hash': 1620, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761054
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.R', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2230', 'subgroup_hash': 2230, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761066
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.S', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.928', 'subgroup_hash': 928, 'subgroup_order': 128, 'subgroup_tex': 'C_2\\wr D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761077
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.T', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1755', 'subgroup_hash': 1755, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761088
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.U', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2216', 'subgroup_hash': 2216, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761099
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.V', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1751', 'subgroup_hash': 1751, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761110
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.W', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2230', 'subgroup_hash': 2230, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761121
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.X', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1746', 'subgroup_hash': 1746, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761132
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1751', 'subgroup_hash': 1751, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761143
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1620', 'subgroup_hash': 1620, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761154
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1746', 'subgroup_hash': 1746, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761165
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.734', 'subgroup_hash': 734, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761177
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1759', 'subgroup_hash': 1759, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184761188
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.BD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.854', 'subgroup_hash': 854, 'subgroup_order': 128, 'subgroup_tex': '(C_2^2\\times D_4):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761199
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.BE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.646', 'subgroup_hash': 646, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761210
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.BF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.734', 'subgroup_hash': 734, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761221
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.BG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.697', 'subgroup_hash': 697, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761232
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.BH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.646', 'subgroup_hash': 646, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761243
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.BI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.801', 'subgroup_hash': 801, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761254
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.BJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.734', 'subgroup_hash': 734, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761265
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.BK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.697', 'subgroup_hash': 697, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761276
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.BL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.932', 'subgroup_hash': 932, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761288
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.BM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1758', 'subgroup_hash': 1758, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761299
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.BN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2317', 'subgroup_hash': 2317, 'subgroup_order': 128, 'subgroup_tex': 'D_8:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761310
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.BO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2317', 'subgroup_hash': 2317, 'subgroup_order': 128, 'subgroup_tex': 'D_8:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761321
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.BP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1753', 'subgroup_hash': 1753, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761332
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.BQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1750', 'subgroup_hash': 1750, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761343
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.BR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1633', 'subgroup_hash': 1633, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761354
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.BS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1633', 'subgroup_hash': 1633, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761365
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.BT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1757', 'subgroup_hash': 1757, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184761376
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.BU', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.928', 'subgroup_hash': 928, 'subgroup_order': 128, 'subgroup_tex': 'C_2\\wr D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761387
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.BV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2269', 'subgroup_hash': 2269, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761399
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.BW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1746', 'subgroup_hash': 1746, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761410
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.BX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2317', 'subgroup_hash': 2317, 'subgroup_order': 128, 'subgroup_tex': 'D_8:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761421
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.BY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.527', 'subgroup_hash': 527, 'subgroup_order': 128, 'subgroup_tex': '(C_2^2\\times D_4):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761432
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.BZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.527', 'subgroup_hash': 527, 'subgroup_order': 128, 'subgroup_tex': '(C_2^2\\times D_4):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761443
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.CA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1757', 'subgroup_hash': 1757, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184761454
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.CB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.852', 'subgroup_hash': 852, 'subgroup_order': 128, 'subgroup_tex': '(C_2^3\\times C_4):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761465
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.CC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.852', 'subgroup_hash': 852, 'subgroup_order': 128, 'subgroup_tex': '(C_2^3\\times C_4):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761476
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.CD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1757', 'subgroup_hash': 1757, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184761487
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.CE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.852', 'subgroup_hash': 852, 'subgroup_order': 128, 'subgroup_tex': '(C_2^3\\times C_4):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761498
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.CF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.852', 'subgroup_hash': 852, 'subgroup_order': 128, 'subgroup_tex': '(C_2^3\\times C_4):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761510
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.CG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.623', 'subgroup_hash': 623, 'subgroup_order': 128, 'subgroup_tex': '(C_2\\times C_8):D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761521
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.CH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1800', 'subgroup_hash': 1800, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761532
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.CI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.635', 'subgroup_hash': 635, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761543
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.CJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1770', 'subgroup_hash': 1770, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761554
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.CK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1688', 'subgroup_hash': 1688, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761565
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.CL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.638', 'subgroup_hash': 638, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761576
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.CM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.593', 'subgroup_hash': 593, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761587
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.CN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.490', 'subgroup_hash': 490, 'subgroup_order': 128, 'subgroup_tex': 'D_4:C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761598
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.CO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.221', 'subgroup_hash': 221, 'subgroup_order': 128, 'subgroup_tex': 'D_4:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761609
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.CP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1755', 'subgroup_hash': 1755, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761622
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.CQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2216', 'subgroup_hash': 2216, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761633
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.CR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2213', 'subgroup_hash': 2213, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761644
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.CS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1746', 'subgroup_hash': 1746, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761655
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.CT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1770', 'subgroup_hash': 1770, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761666
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.CU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1800', 'subgroup_hash': 1800, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761677
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.CV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.635', 'subgroup_hash': 635, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761688
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.CW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2317', 'subgroup_hash': 2317, 'subgroup_order': 128, 'subgroup_tex': 'D_8:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761699
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.CX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1800', 'subgroup_hash': 1800, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761710
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.CY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.638', 'subgroup_hash': 638, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761720
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.CZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1688', 'subgroup_hash': 1688, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761722
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.DA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.527', 'subgroup_hash': 527, 'subgroup_order': 128, 'subgroup_tex': '(C_2^2\\times D_4):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761723
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.DB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.635', 'subgroup_hash': 635, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761724
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.DC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1746', 'subgroup_hash': 1746, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761725
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.DD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.638', 'subgroup_hash': 638, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761726
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.DE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1688', 'subgroup_hash': 1688, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761727
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.DF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.593', 'subgroup_hash': 593, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761728
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.DG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.490', 'subgroup_hash': 490, 'subgroup_order': 128, 'subgroup_tex': 'D_4:C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761729
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.DH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.593', 'subgroup_hash': 593, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761730
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.DI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1753', 'subgroup_hash': 1753, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761731
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.DJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1750', 'subgroup_hash': 1750, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761733
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.DK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2317', 'subgroup_hash': 2317, 'subgroup_order': 128, 'subgroup_tex': 'D_8:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761734
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.DL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1633', 'subgroup_hash': 1633, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761735
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.DM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1759', 'subgroup_hash': 1759, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184761736
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.DN', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.932', 'subgroup_hash': 932, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761737
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.DO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.734', 'subgroup_hash': 734, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761738
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.DP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1753', 'subgroup_hash': 1753, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761739
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.DQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.740', 'subgroup_hash': 740, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761740
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.DR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.860', 'subgroup_hash': 860, 'subgroup_order': 128, 'subgroup_tex': '(C_2^2\\times D_4):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761741
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.DS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1883', 'subgroup_hash': 1883, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761742
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.DT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.734', 'subgroup_hash': 734, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761744
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.DU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1800', 'subgroup_hash': 1800, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761745
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.DV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.780', 'subgroup_hash': 780, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761746
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.DW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1883', 'subgroup_hash': 1883, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761747
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.DX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1750', 'subgroup_hash': 1750, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761748
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.DY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1750', 'subgroup_hash': 1750, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761749
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.DZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.694', 'subgroup_hash': 694, 'subgroup_order': 128, 'subgroup_tex': 'C_4^3:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761750
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.EA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.616', 'subgroup_hash': 616, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761751
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.EB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.858', 'subgroup_hash': 858, 'subgroup_order': 128, 'subgroup_tex': '(C_2\\times C_4^2):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761752
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.EC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.858', 'subgroup_hash': 858, 'subgroup_order': 128, 'subgroup_tex': '(C_2\\times C_4^2):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761753
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.ED', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.858', 'subgroup_hash': 858, 'subgroup_order': 128, 'subgroup_tex': '(C_2\\times C_4^2):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761755
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.EE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.257', 'subgroup_hash': 257, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761756
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.EF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.292', 'subgroup_hash': 292, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761757
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.EG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.864', 'subgroup_hash': 864, 'subgroup_order': 128, 'subgroup_tex': '(C_2\\times C_4^2).C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761758
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.EH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1753', 'subgroup_hash': 1753, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761759
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.EI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.860', 'subgroup_hash': 860, 'subgroup_order': 128, 'subgroup_tex': '(C_2^2\\times D_4):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761760
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.EJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.642', 'subgroup_hash': 642, 'subgroup_order': 128, 'subgroup_tex': '(C_2\\times C_8):D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761761
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.EK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.866', 'subgroup_hash': 866, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.(C_2\\times C_4)', 'supersolvable': True, 'sylow': 0}
  • id: 184761762
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.EL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1753', 'subgroup_hash': 1753, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761763
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.EM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1800', 'subgroup_hash': 1800, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761764
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.EN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.780', 'subgroup_hash': 780, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761766
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.EO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1750', 'subgroup_hash': 1750, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761767
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.EP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.782', 'subgroup_hash': 782, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761768
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.EQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.664', 'subgroup_hash': 664, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761769
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.ER', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1759', 'subgroup_hash': 1759, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184761770
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.ES', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.854', 'subgroup_hash': 854, 'subgroup_order': 128, 'subgroup_tex': '(C_2^2\\times D_4):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761771
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.ET', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.854', 'subgroup_hash': 854, 'subgroup_order': 128, 'subgroup_tex': '(C_2^2\\times D_4):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761772
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.EU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.740', 'subgroup_hash': 740, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761773
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.EV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1800', 'subgroup_hash': 1800, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761774
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.EW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1750', 'subgroup_hash': 1750, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761775
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.EX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.782', 'subgroup_hash': 782, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761777
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.EY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.740', 'subgroup_hash': 740, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761778
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.EZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.780', 'subgroup_hash': 780, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761779
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.FA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.734', 'subgroup_hash': 734, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761780
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.FB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.616', 'subgroup_hash': 616, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761781
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.FC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.694', 'subgroup_hash': 694, 'subgroup_order': 128, 'subgroup_tex': 'C_4^3:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761782
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.FD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.782', 'subgroup_hash': 782, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761783
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.FE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.664', 'subgroup_hash': 664, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761784
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.FF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.664', 'subgroup_hash': 664, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761785
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.FG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1758', 'subgroup_hash': 1758, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761786
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.FH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1758', 'subgroup_hash': 1758, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761788
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.FI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1746', 'subgroup_hash': 1746, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761789
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.FJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1751', 'subgroup_hash': 1751, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761790
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.FK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1753', 'subgroup_hash': 1753, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761791
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.FL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1750', 'subgroup_hash': 1750, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761792
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.FM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.853', 'subgroup_hash': 853, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761793
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.FN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.853', 'subgroup_hash': 853, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761794
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.FO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.856', 'subgroup_hash': 856, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761795
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.FP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.859', 'subgroup_hash': 859, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761796
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.FQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2275', 'subgroup_hash': 2275, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761797
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.FR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1615', 'subgroup_hash': 1615, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184761799
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.FS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fr2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1757', 'subgroup_hash': 1757, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184761800
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.FT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1755', 'subgroup_hash': 1755, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761801
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.FU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1755', 'subgroup_hash': 1755, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761802
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.FV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.850', 'subgroup_hash': 850, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761803
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.FW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.850', 'subgroup_hash': 850, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761804
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.FX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2251', 'subgroup_hash': 2251, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761805
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.FY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2264', 'subgroup_hash': 2264, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761806
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.FZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2264', 'subgroup_hash': 2264, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761807
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.GA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2216', 'subgroup_hash': 2216, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761808
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.GB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2194', 'subgroup_hash': 2194, 'subgroup_order': 128, 'subgroup_tex': 'C_2\\times D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761810
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.GC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1759', 'subgroup_hash': 1759, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184761811
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.GD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.928', 'subgroup_hash': 928, 'subgroup_order': 128, 'subgroup_tex': 'C_2\\wr D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761812
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.GE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.928', 'subgroup_hash': 928, 'subgroup_order': 128, 'subgroup_tex': 'C_2\\wr D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761813
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.GF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.929', 'subgroup_hash': 929, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761814
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.GG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.928', 'subgroup_hash': 928, 'subgroup_order': 128, 'subgroup_tex': 'C_2\\wr D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761815
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.GH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.928', 'subgroup_hash': 928, 'subgroup_order': 128, 'subgroup_tex': 'C_2\\wr D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761816
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.GI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.742', 'subgroup_hash': 742, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761817
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.GJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gh2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.636', 'subgroup_hash': 636, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761818
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.GK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.929', 'subgroup_hash': 929, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761819
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.GL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.929', 'subgroup_hash': 929, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761822
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.GM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.354', 'subgroup_hash': 354, 'subgroup_order': 128, 'subgroup_tex': 'D_4:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761823
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.GN', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.928', 'subgroup_hash': 928, 'subgroup_order': 128, 'subgroup_tex': 'C_2\\wr D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761824
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.GO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1735', 'subgroup_hash': 1735, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761825
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.GP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.351', 'subgroup_hash': 351, 'subgroup_order': 128, 'subgroup_tex': 'D_4:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761826
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.GQ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.928', 'subgroup_hash': 928, 'subgroup_order': 128, 'subgroup_tex': 'C_2\\wr D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761827
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.GR', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.928', 'subgroup_hash': 928, 'subgroup_order': 128, 'subgroup_tex': 'C_2\\wr D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761828
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.GS', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.932', 'subgroup_hash': 932, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761829
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.GT', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.932', 'subgroup_hash': 932, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761830
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.GU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2024', 'subgroup_hash': 2024, 'subgroup_order': 128, 'subgroup_tex': 'D_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761831
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.GV', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.930', 'subgroup_hash': 930, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761833
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.GW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.134', 'subgroup_hash': 134, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761834
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.GX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.931', 'subgroup_hash': 931, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761835
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.GY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2020', 'subgroup_hash': 2020, 'subgroup_order': 128, 'subgroup_tex': 'D_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761836
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.GZ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.135', 'subgroup_hash': 135, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761837
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.HA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.928', 'subgroup_hash': 928, 'subgroup_order': 128, 'subgroup_tex': 'C_2\\wr D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761838
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.HB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.931', 'subgroup_hash': 931, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761839
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.HC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2020', 'subgroup_hash': 2020, 'subgroup_order': 128, 'subgroup_tex': 'D_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761840
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.HD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2023', 'subgroup_hash': 2023, 'subgroup_order': 128, 'subgroup_tex': 'D_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761841
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.HE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.932', 'subgroup_hash': 932, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761842
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.HF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.740', 'subgroup_hash': 740, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761844
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.HG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.he1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.932', 'subgroup_hash': 932, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761845
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.HH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.352', 'subgroup_hash': 352, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761846
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.HI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.140', 'subgroup_hash': 140, 'subgroup_order': 128, 'subgroup_tex': '(C_4\\times C_8):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761847
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.HJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.930', 'subgroup_hash': 930, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761848
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.HK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.936', 'subgroup_hash': 936, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761849
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.HL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.930', 'subgroup_hash': 930, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761850
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.HM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.134', 'subgroup_hash': 134, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761851
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.HN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.387', 'subgroup_hash': 387, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761852
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.HO', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.931', 'subgroup_hash': 931, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761853
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.HP', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.934', 'subgroup_hash': 934, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761855
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.HQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ho1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.138', 'subgroup_hash': 138, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.(C_2\\times C_4)', 'supersolvable': True, 'sylow': 0}
  • id: 184761856
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.HR', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.136', 'subgroup_hash': 136, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761857
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.HS', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.928', 'subgroup_hash': 928, 'subgroup_order': 128, 'subgroup_tex': 'C_2\\wr D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761858
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.HT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.387', 'subgroup_hash': 387, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761859
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.HU', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.931', 'subgroup_hash': 931, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761860
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.HV', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ht1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.934', 'subgroup_hash': 934, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761861
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.HW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.136', 'subgroup_hash': 136, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761862
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.24.HX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.137', 'subgroup_hash': 137, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761863
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.32.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184761864
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.32.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.197', 'subgroup_hash': 197, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 184761866
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.32.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 184761867
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.32.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184761868
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.32.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.186', 'subgroup_hash': 186, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184761869
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.32.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.70', 'subgroup_hash': 70, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 184761870
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 8, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.32.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.72', 'subgroup_hash': 72, 'subgroup_order': 96, 'subgroup_tex': 'C_4^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 184761871
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.32.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 184761872
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.32.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.187', 'subgroup_hash': 187, 'subgroup_order': 96, 'subgroup_tex': 'C_4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184761873
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.32.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.68', 'subgroup_hash': 68, 'subgroup_order': 96, 'subgroup_tex': 'C_4^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 184761874
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.32.K', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.229', 'subgroup_hash': 229, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 184761875
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.32.L', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.72', 'subgroup_hash': 72, 'subgroup_order': 96, 'subgroup_tex': 'C_4^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 184761877
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.32.M', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.70', 'subgroup_hash': 70, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 184761878
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 4, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.32.N', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.71', 'subgroup_hash': 71, 'subgroup_order': 96, 'subgroup_tex': 'C_4^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 184761879
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.32.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184761880
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.32.P', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.64', 'subgroup_hash': 64, 'subgroup_order': 96, 'subgroup_tex': 'C_4^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 184761881
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.32.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184761882
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.32.R', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.72', 'subgroup_hash': 72, 'subgroup_order': 96, 'subgroup_tex': 'C_4^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 184761883
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.32.S', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.64', 'subgroup_hash': 64, 'subgroup_order': 96, 'subgroup_tex': 'C_4^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 184761884
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.32.T', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.64', 'subgroup_hash': 64, 'subgroup_order': 96, 'subgroup_tex': 'C_4^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 184761885
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 4, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.32.U', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.64', 'subgroup_hash': 64, 'subgroup_order': 96, 'subgroup_tex': 'C_4^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 184761886
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 359, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.48.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.211', 'subgroup_hash': 211, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761888
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 360, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.48.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.211', 'subgroup_hash': 211, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761889
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 64, 'counter': 361, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.48.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.55', 'subgroup_hash': 55, 'subgroup_order': 64, 'subgroup_tex': 'C_4^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761890
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 362, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.48.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.38', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.242', 'subgroup_hash': 242, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761891
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.266', 'subgroup_hash': 266, 'subgroup_order': 64, 'subgroup_tex': 'C_4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184761892
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.266', 'subgroup_hash': 266, 'subgroup_order': 64, 'subgroup_tex': 'C_4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184761893
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.264', 'subgroup_hash': 264, 'subgroup_order': 64, 'subgroup_tex': 'D_4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761894
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.264', 'subgroup_hash': 264, 'subgroup_order': 64, 'subgroup_tex': 'D_4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761895
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761896
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761897
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.K', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761899
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.L', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.136', 'subgroup_hash': 136, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761900
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.M', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761901
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.N', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761902
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.O', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.211', 'subgroup_hash': 211, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761903
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.P', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.216', 'subgroup_hash': 216, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761904
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.216', 'subgroup_hash': 216, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761905
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.R', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.213', 'subgroup_hash': 213, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761906
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.S', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761907
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.T', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.136', 'subgroup_hash': 136, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761908
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.U', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.92', 'subgroup_hash': 92, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761910
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.V', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.94', 'subgroup_hash': 94, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761911
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.W', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761912
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.X', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.231', 'subgroup_hash': 231, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761913
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.257', 'subgroup_hash': 257, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761914
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.258', 'subgroup_hash': 258, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761915
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.254', 'subgroup_hash': 254, 'subgroup_order': 64, 'subgroup_tex': 'C_8:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761916
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.256', 'subgroup_hash': 256, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761917
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.257', 'subgroup_hash': 257, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761918
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.BD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761919
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.BE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.258', 'subgroup_hash': 258, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761921
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.BF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.135', 'subgroup_hash': 135, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761922
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.BG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.101', 'subgroup_hash': 101, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761923
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.BH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.102', 'subgroup_hash': 102, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761924
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.BI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761925
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.BJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.136', 'subgroup_hash': 136, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761926
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.BK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.135', 'subgroup_hash': 135, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761927
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.BL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.137', 'subgroup_hash': 137, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761928
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.BM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.257', 'subgroup_hash': 257, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761929
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.BN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761930
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.BO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761933
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.BP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.258', 'subgroup_hash': 258, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761934
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.BQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.258', 'subgroup_hash': 258, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761935
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.BR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.257', 'subgroup_hash': 257, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761936
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.BS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.153', 'subgroup_hash': 153, 'subgroup_order': 64, 'subgroup_tex': 'C_8.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761937
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.BT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.152', 'subgroup_hash': 152, 'subgroup_order': 64, 'subgroup_tex': 'C_8.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761938
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.BU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.124', 'subgroup_hash': 124, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761939
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.BV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.125', 'subgroup_hash': 125, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761940
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.BW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761941
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.BX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761942
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.BY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.153', 'subgroup_hash': 153, 'subgroup_order': 64, 'subgroup_tex': 'C_8.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761944
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.BZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.152', 'subgroup_hash': 152, 'subgroup_order': 64, 'subgroup_tex': 'C_8.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761945
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.CA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.258', 'subgroup_hash': 258, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761946
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.CB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.258', 'subgroup_hash': 258, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761947
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.CC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.257', 'subgroup_hash': 257, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761948
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.CD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.124', 'subgroup_hash': 124, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761949
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.CE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.125', 'subgroup_hash': 125, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761950
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.CF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.140', 'subgroup_hash': 140, 'subgroup_order': 64, 'subgroup_tex': 'C_4:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761951
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.CG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.254', 'subgroup_hash': 254, 'subgroup_order': 64, 'subgroup_tex': 'C_8:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761952
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.CH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.256', 'subgroup_hash': 256, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761953
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.CI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.101', 'subgroup_hash': 101, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761955
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.CJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.102', 'subgroup_hash': 102, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761956
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.CK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.254', 'subgroup_hash': 254, 'subgroup_order': 64, 'subgroup_tex': 'C_8:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761957
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.CL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.257', 'subgroup_hash': 257, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761958
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.CM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.174', 'subgroup_hash': 174, 'subgroup_order': 64, 'subgroup_tex': 'C_4:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761959
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.CN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.177', 'subgroup_hash': 177, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761960
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.CO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.177', 'subgroup_hash': 177, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761961
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.CP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.173', 'subgroup_hash': 173, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761962
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.CQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.141', 'subgroup_hash': 141, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761963
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.CR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.153', 'subgroup_hash': 153, 'subgroup_order': 64, 'subgroup_tex': 'C_8.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761964
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.CS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.152', 'subgroup_hash': 152, 'subgroup_order': 64, 'subgroup_tex': 'C_8.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761966
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.CT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.135', 'subgroup_hash': 135, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761967
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.CU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761968
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.CV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.135', 'subgroup_hash': 135, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761969
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.CW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.137', 'subgroup_hash': 137, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761970
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.CX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761971
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.CY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.136', 'subgroup_hash': 136, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761972
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.CZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.153', 'subgroup_hash': 153, 'subgroup_order': 64, 'subgroup_tex': 'C_8.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761973
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.DA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.256', 'subgroup_hash': 256, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761974
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.DB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.152', 'subgroup_hash': 152, 'subgroup_order': 64, 'subgroup_tex': 'C_8.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761975
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.DC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.135', 'subgroup_hash': 135, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761977
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.DD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761978
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.DE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.137', 'subgroup_hash': 137, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761979
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.DF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.136', 'subgroup_hash': 136, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761980
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.DG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761981
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.DH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.227', 'subgroup_hash': 227, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761982
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.DI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761983
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.DJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.227', 'subgroup_hash': 227, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761984
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.DK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.128', 'subgroup_hash': 128, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761985
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.DL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.131', 'subgroup_hash': 131, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761986
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.DM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.264', 'subgroup_hash': 264, 'subgroup_order': 64, 'subgroup_tex': 'D_4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761988
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.DN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761989
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.DO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.215', 'subgroup_hash': 215, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761990
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.DP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.90', 'subgroup_hash': 90, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761991
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.DQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.264', 'subgroup_hash': 264, 'subgroup_order': 64, 'subgroup_tex': 'D_4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761992
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.DR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761993
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.DS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761994
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.DT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761995
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.DU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.264', 'subgroup_hash': 264, 'subgroup_order': 64, 'subgroup_tex': 'D_4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761996
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.DV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.216', 'subgroup_hash': 216, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761997
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.DW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.211', 'subgroup_hash': 211, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761999
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.DX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.216', 'subgroup_hash': 216, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762000
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.DY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.92', 'subgroup_hash': 92, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762001
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.DZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.92', 'subgroup_hash': 92, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762002
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.EA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.92', 'subgroup_hash': 92, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762003
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.EB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762004
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.EC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762005
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.ED', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.241', 'subgroup_hash': 241, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762006
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.EE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.264', 'subgroup_hash': 264, 'subgroup_order': 64, 'subgroup_tex': 'D_4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762007
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.EF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.215', 'subgroup_hash': 215, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762008
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.EG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.90', 'subgroup_hash': 90, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762010
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.EH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.215', 'subgroup_hash': 215, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762011
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.EI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762012
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.EJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.234', 'subgroup_hash': 234, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762013
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.EK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762014
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.EL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.266', 'subgroup_hash': 266, 'subgroup_order': 64, 'subgroup_tex': 'C_4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184762015
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.EM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762016
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.EN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762017
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.EO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.264', 'subgroup_hash': 264, 'subgroup_order': 64, 'subgroup_tex': 'D_4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762018
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.EP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762019
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.EQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.206', 'subgroup_hash': 206, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762021
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.ER', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762022
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.ES', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762023
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.ET', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.206', 'subgroup_hash': 206, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762024
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.EU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.254', 'subgroup_hash': 254, 'subgroup_order': 64, 'subgroup_tex': 'C_8:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762025
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.EV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.256', 'subgroup_hash': 256, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762026
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.EW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.101', 'subgroup_hash': 101, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762027
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.EX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.102', 'subgroup_hash': 102, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762028
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.EY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.249', 'subgroup_hash': 249, 'subgroup_order': 64, 'subgroup_tex': 'C_8.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762029
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.EZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.198', 'subgroup_hash': 198, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762030
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.FA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762032
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.FB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.227', 'subgroup_hash': 227, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762033
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.FC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762034
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.FD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.254', 'subgroup_hash': 254, 'subgroup_order': 64, 'subgroup_tex': 'C_8:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762035
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.FE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762036
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.FF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.139', 'subgroup_hash': 139, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762037
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.FG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762038
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.FH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.256', 'subgroup_hash': 256, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762039
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.FI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.264', 'subgroup_hash': 264, 'subgroup_order': 64, 'subgroup_tex': 'D_4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762040
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.FJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.254', 'subgroup_hash': 254, 'subgroup_order': 64, 'subgroup_tex': 'C_8:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762041
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.FK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.256', 'subgroup_hash': 256, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762044
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.FL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.198', 'subgroup_hash': 198, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762045
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.FM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.101', 'subgroup_hash': 101, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762046
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.FN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.102', 'subgroup_hash': 102, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762047
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.FO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.102', 'subgroup_hash': 102, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762048
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.FP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.249', 'subgroup_hash': 249, 'subgroup_order': 64, 'subgroup_tex': 'C_8.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762049
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.FQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.249', 'subgroup_hash': 249, 'subgroup_order': 64, 'subgroup_tex': 'C_8.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762050
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.FR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.101', 'subgroup_hash': 101, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762051
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.FS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.266', 'subgroup_hash': 266, 'subgroup_order': 64, 'subgroup_tex': 'C_4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184762052
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.FT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.241', 'subgroup_hash': 241, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762053
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.FU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762055
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.FV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762056
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.FW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.216', 'subgroup_hash': 216, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762057
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.FX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.211', 'subgroup_hash': 211, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762058
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.FY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.254', 'subgroup_hash': 254, 'subgroup_order': 64, 'subgroup_tex': 'C_8:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762059
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.FZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.254', 'subgroup_hash': 254, 'subgroup_order': 64, 'subgroup_tex': 'C_8:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762060
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.GA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.99', 'subgroup_hash': 99, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762061
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.GB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.92', 'subgroup_hash': 92, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762062
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.GC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762063
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.GD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.139', 'subgroup_hash': 139, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762064
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.GE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762066
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.GF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.34', 'subgroup_hash': 34, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762067
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.GG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.213', 'subgroup_hash': 213, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762068
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.GH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.216', 'subgroup_hash': 216, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762069
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.GI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.254', 'subgroup_hash': 254, 'subgroup_order': 64, 'subgroup_tex': 'C_8:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762070
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.GJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.266', 'subgroup_hash': 266, 'subgroup_order': 64, 'subgroup_tex': 'C_4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184762071
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.GK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.256', 'subgroup_hash': 256, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762072
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.GL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.101', 'subgroup_hash': 101, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762073
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.GM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.102', 'subgroup_hash': 102, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762074
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.GN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.91', 'subgroup_hash': 91, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762075
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.GO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.91', 'subgroup_hash': 91, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762077
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.GP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.94', 'subgroup_hash': 94, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762078
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.GQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.94', 'subgroup_hash': 94, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762079
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.GR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762080
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.GS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.216', 'subgroup_hash': 216, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762081
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.GT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.139', 'subgroup_hash': 139, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762082
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.GU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.33', 'subgroup_hash': 33, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762083
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.GV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.254', 'subgroup_hash': 254, 'subgroup_order': 64, 'subgroup_tex': 'C_8:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762084
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.GW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.256', 'subgroup_hash': 256, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762085
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.GX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.266', 'subgroup_hash': 266, 'subgroup_order': 64, 'subgroup_tex': 'C_4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184762086
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.GY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.101', 'subgroup_hash': 101, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762088
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.GZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.91', 'subgroup_hash': 91, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762089
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.HA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.91', 'subgroup_hash': 91, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762090
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.HB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.249', 'subgroup_hash': 249, 'subgroup_order': 64, 'subgroup_tex': 'C_8.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762091
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.HC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.94', 'subgroup_hash': 94, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762092
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.HD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.94', 'subgroup_hash': 94, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762093
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.HE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.he1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762094
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.HF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.34', 'subgroup_hash': 34, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762095
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.HG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.216', 'subgroup_hash': 216, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762096
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.HH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.254', 'subgroup_hash': 254, 'subgroup_order': 64, 'subgroup_tex': 'C_8:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762097
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.HI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.254', 'subgroup_hash': 254, 'subgroup_order': 64, 'subgroup_tex': 'C_8:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762099
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.HJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.99', 'subgroup_hash': 99, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762100
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.HK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.99', 'subgroup_hash': 99, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762101
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.HL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.92', 'subgroup_hash': 92, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762102
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.HM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.92', 'subgroup_hash': 92, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762103
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.HN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.213', 'subgroup_hash': 213, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762104
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.HO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ho1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.256', 'subgroup_hash': 256, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762105
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.HP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.101', 'subgroup_hash': 101, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762106
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.HQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.102', 'subgroup_hash': 102, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762107
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.HR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.102', 'subgroup_hash': 102, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762108
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.HS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.94', 'subgroup_hash': 94, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762110
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.HT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ht1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.94', 'subgroup_hash': 94, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762111
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.HU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.101', 'subgroup_hash': 101, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762112
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.HV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.101', 'subgroup_hash': 101, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762113
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.HW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.91', 'subgroup_hash': 91, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762114
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.HX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.249', 'subgroup_hash': 249, 'subgroup_order': 64, 'subgroup_tex': 'C_8.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762115
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.HY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.94', 'subgroup_hash': 94, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762116
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.HZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.101', 'subgroup_hash': 101, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762117
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.IA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ia1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.20', 'subgroup_hash': 20, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762118
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.IB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ib1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.20', 'subgroup_hash': 20, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762119
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.IC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ic1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.85', 'subgroup_hash': 85, 'subgroup_order': 64, 'subgroup_tex': 'C_4\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184762121
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.ID', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.id1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.104', 'subgroup_hash': 104, 'subgroup_order': 64, 'subgroup_tex': 'C_4:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184762122
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.IE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ie1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.25', 'subgroup_hash': 25, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762123
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.IF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.if1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.25', 'subgroup_hash': 25, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762124
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.IG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ig1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.25', 'subgroup_hash': 25, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762125
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.IH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ih1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.111', 'subgroup_hash': 111, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184762126
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.II', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ii1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.111', 'subgroup_hash': 111, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184762127
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.IJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ij1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.111', 'subgroup_hash': 111, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184762128
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.IK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ik1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.19', 'subgroup_hash': 19, 'subgroup_order': 64, 'subgroup_tex': 'C_4.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762129
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 578, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.IL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.il1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.20', 'subgroup_hash': 20, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762130
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.IM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.im1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.85', 'subgroup_hash': 85, 'subgroup_order': 64, 'subgroup_tex': 'C_4\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184762132
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.IN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.in1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.104', 'subgroup_hash': 104, 'subgroup_order': 64, 'subgroup_tex': 'C_4:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184762133
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.IO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.io1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.215', 'subgroup_hash': 215, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762134
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.IP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ip1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.90', 'subgroup_hash': 90, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762135
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.IQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.iq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.90', 'subgroup_hash': 90, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762136
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.IR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ir1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.264', 'subgroup_hash': 264, 'subgroup_order': 64, 'subgroup_tex': 'D_4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762137
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.IS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.is1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.266', 'subgroup_hash': 266, 'subgroup_order': 64, 'subgroup_tex': 'C_4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184762138
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.IT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.it1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.227', 'subgroup_hash': 227, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762139
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.IU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.iu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.215', 'subgroup_hash': 215, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762140
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.IV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.iv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762141
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.IW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.iw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.219', 'subgroup_hash': 219, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762143
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.IX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ix1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.90', 'subgroup_hash': 90, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762144
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.IY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ix2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.90', 'subgroup_hash': 90, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762145
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.IZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.iy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.92', 'subgroup_hash': 92, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762146
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.JA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.iz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.215', 'subgroup_hash': 215, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762147
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.JB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ja1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.234', 'subgroup_hash': 234, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762148
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.JC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.jb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.219', 'subgroup_hash': 219, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762149
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.JD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.jc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.94', 'subgroup_hash': 94, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762150
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.JE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.jd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.211', 'subgroup_hash': 211, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762151
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.JF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.je1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.216', 'subgroup_hash': 216, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762152
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.JG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.jf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.216', 'subgroup_hash': 216, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762155
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.JH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.jg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.213', 'subgroup_hash': 213, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762156
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.JI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.jh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762157
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.JJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ji1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.264', 'subgroup_hash': 264, 'subgroup_order': 64, 'subgroup_tex': 'D_4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762158
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.JK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.jj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.227', 'subgroup_hash': 227, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762159
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.JL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.jj2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.227', 'subgroup_hash': 227, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762160
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.JM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.jk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.203', 'subgroup_hash': 203, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762161
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 606, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.JN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.jl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762162
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 607, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.JO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.jm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.199', 'subgroup_hash': 199, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762163
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.JP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.jm2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.206', 'subgroup_hash': 206, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762164
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.JQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.jn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.199', 'subgroup_hash': 199, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762166
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 610, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.JR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.jo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762167
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 611, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.JS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.jp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762168
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 612, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.JT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.jq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762169
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 613, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.JU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.jr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762170
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 614, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.JV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.js1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762171
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.JW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.jt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.261', 'subgroup_hash': 261, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762172
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 616, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.JX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ju1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762173
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 617, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.JY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.jv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.136', 'subgroup_hash': 136, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762174
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 618, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.JZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.jw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762175
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 619, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.KA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.jx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762177
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 620, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.KB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.jy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762178
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 621, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.KC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.jz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.139', 'subgroup_hash': 139, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762179
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 622, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.KD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ka1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762180
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 623, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.KE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.kb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.266', 'subgroup_hash': 266, 'subgroup_order': 64, 'subgroup_tex': 'C_4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184762181
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 624, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.KF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.kc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.221', 'subgroup_hash': 221, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762182
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 625, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.KG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.kd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.241', 'subgroup_hash': 241, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762183
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 626, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.KH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ke1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.91', 'subgroup_hash': 91, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762184
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 627, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.KI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.kf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.216', 'subgroup_hash': 216, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762185
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 628, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.KJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.kg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.231', 'subgroup_hash': 231, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762186
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 629, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.KK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.kh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.90', 'subgroup_hash': 90, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762188
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 630, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.KL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ki1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.90', 'subgroup_hash': 90, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762189
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 631, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.KM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.kj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.215', 'subgroup_hash': 215, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762190
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 632, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.KN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.kk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.254', 'subgroup_hash': 254, 'subgroup_order': 64, 'subgroup_tex': 'C_8:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762191
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 633, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.KO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.kl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.256', 'subgroup_hash': 256, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762192
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 634, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.KP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.km1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.101', 'subgroup_hash': 101, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762193
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 635, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.KQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.kn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.102', 'subgroup_hash': 102, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762194
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 636, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.KR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ko1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.219', 'subgroup_hash': 219, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762195
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.KS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ko2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.219', 'subgroup_hash': 219, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762196
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 638, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.KT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.kp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.227', 'subgroup_hash': 227, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762197
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 639, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.KU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.kq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.215', 'subgroup_hash': 215, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762199
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.KV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.kr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.234', 'subgroup_hash': 234, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762200
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 641, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.KW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ks1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762201
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 642, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.KX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.kt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.210', 'subgroup_hash': 210, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762202
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 643, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.KY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ku1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762203
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 644, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.KZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.kv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.257', 'subgroup_hash': 257, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762204
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 645, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.LA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.kw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.206', 'subgroup_hash': 206, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762205
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.LB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.kx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762206
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 647, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.LC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ky1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.203', 'subgroup_hash': 203, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762207
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 648, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.LD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.kz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762208
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.LE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.la1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.227', 'subgroup_hash': 227, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762210
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 650, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.LF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.lb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762211
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 651, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.LG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.lc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.254', 'subgroup_hash': 254, 'subgroup_order': 64, 'subgroup_tex': 'C_8:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762212
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 652, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.LH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ld1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.99', 'subgroup_hash': 99, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762213
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.LI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.le1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.206', 'subgroup_hash': 206, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762214
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 654, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.LJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.le2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.199', 'subgroup_hash': 199, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762215
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 655, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.LK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.lf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.227', 'subgroup_hash': 227, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762216
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 656, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.LL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.lg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.206', 'subgroup_hash': 206, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762217
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 657, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.LM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.lh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762218
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 658, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.LN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.li1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762219
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 659, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.LO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.lj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762221
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 660, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.LP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.lk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.232', 'subgroup_hash': 232, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762222
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 661, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.LQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ll1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.206', 'subgroup_hash': 206, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762223
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 662, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.LR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.lm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.88', 'subgroup_hash': 88, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184762224
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 663, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.LS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ln1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762225
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 664, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.LT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.lo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762226
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 665, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.LU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.lp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.232', 'subgroup_hash': 232, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762227
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 666, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.LV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.lq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.140', 'subgroup_hash': 140, 'subgroup_order': 64, 'subgroup_tex': 'C_4:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184762228
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 667, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.LW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.lr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.235', 'subgroup_hash': 235, 'subgroup_order': 64, 'subgroup_tex': 'D_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184762229
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 668, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.LX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ls1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.6', 'subgroup_hash': 6, 'subgroup_order': 64, 'subgroup_tex': 'D_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 184762230
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 669, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.LY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.lt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762232
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 670, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.LZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.lu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762233
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 671, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.MA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.lv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762234
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 672, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.MB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.lw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.196', 'subgroup_hash': 196, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762235
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 673, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.MC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.lx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.261', 'subgroup_hash': 261, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762236
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 674, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.MD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ly1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762237
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 675, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.ME', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.lz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762238
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 676, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.MF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ma1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.139', 'subgroup_hash': 139, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762239
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 677, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.MG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.mb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762240
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 678, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.MH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.mc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.257', 'subgroup_hash': 257, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762241
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 679, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.MI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.md1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.153', 'subgroup_hash': 153, 'subgroup_order': 64, 'subgroup_tex': 'C_8.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762243
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 680, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.MJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.me1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.258', 'subgroup_hash': 258, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762244
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 681, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.MK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.mf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.258', 'subgroup_hash': 258, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762245
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 682, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.ML', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.mg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.152', 'subgroup_hash': 152, 'subgroup_order': 64, 'subgroup_tex': 'C_8.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762246
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 683, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.MM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.mh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762247
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 684, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.MN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.mi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762248
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 685, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.MO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.mj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.124', 'subgroup_hash': 124, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762249
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 686, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.MP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.mk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.125', 'subgroup_hash': 125, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762250
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 687, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.MQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ml1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762251
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 688, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.MR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.mm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.135', 'subgroup_hash': 135, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762252
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 689, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.MS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.mn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.91', 'subgroup_hash': 91, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762254
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 690, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.MT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.mo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.91', 'subgroup_hash': 91, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762255
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 691, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.MU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.mp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762256
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 692, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.MV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.mq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762257
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 693, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.MW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.mr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.257', 'subgroup_hash': 257, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762258
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 694, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.MX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ms1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.139', 'subgroup_hash': 139, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762259
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 695, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.MY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.mt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.136', 'subgroup_hash': 136, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762260
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 696, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.MZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.mu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.216', 'subgroup_hash': 216, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762261
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 697, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.NA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.mv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762262
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 698, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.NB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.mw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.135', 'subgroup_hash': 135, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762263
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 699, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.NC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.mx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.258', 'subgroup_hash': 258, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762266
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 700, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.ND', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.my1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.137', 'subgroup_hash': 137, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762267
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 701, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.NE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.mz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.221', 'subgroup_hash': 221, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762268
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 702, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.NF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.na1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.241', 'subgroup_hash': 241, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762269
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 703, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.NG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.nb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.216', 'subgroup_hash': 216, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762270
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 704, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.NH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.nc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762271
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 705, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.NI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.nd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.34', 'subgroup_hash': 34, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762272
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 706, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.NJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.nd2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.34', 'subgroup_hash': 34, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762273
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 707, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.NK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ne1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.241', 'subgroup_hash': 241, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762274
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 708, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.NL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.nf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.256', 'subgroup_hash': 256, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762275
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 709, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.NM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ng1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.102', 'subgroup_hash': 102, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762277
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 710, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.NN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.nh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.135', 'subgroup_hash': 135, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762278
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 711, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.NO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ni1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.91', 'subgroup_hash': 91, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762279
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 712, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.NP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.nj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.91', 'subgroup_hash': 91, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762280
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 713, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.NQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.nk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.174', 'subgroup_hash': 174, 'subgroup_order': 64, 'subgroup_tex': 'C_4:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184762281
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 714, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.NR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.nl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762282
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 715, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.NS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.nm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762283
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 716, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.NT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.nn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762284
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 717, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.NU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.no1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.236', 'subgroup_hash': 236, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762285
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 718, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.NV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.np1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.240', 'subgroup_hash': 240, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762286
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 719, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.NW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.nq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.34', 'subgroup_hash': 34, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762288
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 720, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.NX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.nr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.34', 'subgroup_hash': 34, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762289
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 721, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.NY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ns1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.34', 'subgroup_hash': 34, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762290
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 722, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.NZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.nt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.12', 'subgroup_hash': 12, 'subgroup_order': 64, 'subgroup_tex': 'C_4.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184762291
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 723, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.OA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.nu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762292
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 724, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.OB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.nv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762293
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 725, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.OC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.nw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.254', 'subgroup_hash': 254, 'subgroup_order': 64, 'subgroup_tex': 'C_8:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762294
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 726, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.OD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.nx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.99', 'subgroup_hash': 99, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762295
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 727, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.OE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ny1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.242', 'subgroup_hash': 242, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762296
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 728, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.OF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.nz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.153', 'subgroup_hash': 153, 'subgroup_order': 64, 'subgroup_tex': 'C_8.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762297
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 729, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.OG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.oa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.177', 'subgroup_hash': 177, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762299
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 730, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.OH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ob1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.139', 'subgroup_hash': 139, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762300
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 731, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.OI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.oc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.136', 'subgroup_hash': 136, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762301
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 732, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.OJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.od1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.135', 'subgroup_hash': 135, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762302
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 733, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.OK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.oe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.135', 'subgroup_hash': 135, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762303
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 734, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.OL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.of1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.36', 'subgroup_hash': 36, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762304
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 735, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.OM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.og1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.33', 'subgroup_hash': 33, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762305
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 736, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.ON', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.oh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.33', 'subgroup_hash': 33, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762306
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 737, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.OO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.oi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.35', 'subgroup_hash': 35, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762307
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 738, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.OP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.oj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.35', 'subgroup_hash': 35, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762308
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 739, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.OQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ok1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.10', 'subgroup_hash': 10, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762310
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 740, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.OR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ol1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.36', 'subgroup_hash': 36, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762311
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 741, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.OS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.om1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.216', 'subgroup_hash': 216, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762312
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 742, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.OT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.on1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762313
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 743, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.OU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.oo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762314
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 744, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.OV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.op1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762315
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 745, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.OW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.oq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762316
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 746, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.OX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.or1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.91', 'subgroup_hash': 91, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762317
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 747, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.OY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.os1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.102', 'subgroup_hash': 102, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762318
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 748, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.OZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ot1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.25', 'subgroup_hash': 25, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762319
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 749, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.PA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ou1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.18', 'subgroup_hash': 18, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762321
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 750, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.PB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ov1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.177', 'subgroup_hash': 177, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762322
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 751, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.PC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ow1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.135', 'subgroup_hash': 135, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762323
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 752, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.PD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ox1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.135', 'subgroup_hash': 135, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762324
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 753, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.PE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.oy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.139', 'subgroup_hash': 139, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762325
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 754, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.PF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.oz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.136', 'subgroup_hash': 136, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762326
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 755, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.PG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.pa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.36', 'subgroup_hash': 36, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762327
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 756, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.PH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.pb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.33', 'subgroup_hash': 33, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762328
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 757, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.PI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.pc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.35', 'subgroup_hash': 35, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762329
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 758, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.PJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.pd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.10', 'subgroup_hash': 10, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762330
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 759, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.PK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.pe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.152', 'subgroup_hash': 152, 'subgroup_order': 64, 'subgroup_tex': 'C_8.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762332
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 760, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.PL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.pf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.173', 'subgroup_hash': 173, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762333
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 761, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.PM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.pg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.141', 'subgroup_hash': 141, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762334
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 762, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.PN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ph1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.137', 'subgroup_hash': 137, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762335
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 763, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.PO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.pi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.137', 'subgroup_hash': 137, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762336
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 764, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.PP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.pj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.14', 'subgroup_hash': 14, 'subgroup_order': 64, 'subgroup_tex': 'C_4.Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184762337
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 765, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.PQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.pk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.37', 'subgroup_hash': 37, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762338
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 766, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.48.PR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.pl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.7', 'subgroup_hash': 7, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 184762339
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 767, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.64.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 184762340
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 768, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.64.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184762341
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 769, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.64.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 184762343
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 770, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.64.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184762344
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 771, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.64.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184762345
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 772, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.64.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 184762346
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 773, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.64.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 184762347
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 774, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.64.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184762348
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 775, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.64.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184762349
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 776, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.64.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.50', 'subgroup_hash': 50, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 184762350
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 777, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.64.K', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.3', 'subgroup_hash': 3, 'subgroup_order': 48, 'subgroup_tex': 'C_4^2:C_3', 'supersolvable': False, 'sylow': 0}
  • id: 184762351
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 4, 'counter': 778, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.64.L', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.3', 'subgroup_hash': 3, 'subgroup_order': 48, 'subgroup_tex': 'C_4^2:C_3', 'supersolvable': False, 'sylow': 0}
  • id: 184762352
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 779, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.64.M', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762354
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 780, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.64.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184762355
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 32, 'counter': 781, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.96.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '96.226', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 226, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': ['Phi'], '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: 184762356
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 782, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762357
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 783, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762358
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 784, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762359
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 785, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762360
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 786, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762361
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 787, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762362
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 788, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762363
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 789, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762365
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 790, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762366
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 791, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.K', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762367
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 792, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.L', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762368
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 793, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.M', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762369
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 794, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.N', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762370
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 795, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.O', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762371
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 796, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.P', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762372
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 797, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762373
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 798, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.R', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762374
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 799, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.S', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762377
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 800, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.T', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762378
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 801, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.U', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762379
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 802, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.V', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762380
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 803, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.W', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762381
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 804, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.X', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762382
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 805, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762383
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 806, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762384
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 807, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762385
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 808, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762386
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 809, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762388
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 810, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.BD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762389
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 811, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.BE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762390
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 812, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.BF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762391
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 813, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.BG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762392
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 814, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.BH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762393
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 815, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.BI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762394
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 816, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.BJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762395
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 817, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.BK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.50', 'subgroup_hash': 50, 'subgroup_order': 32, 'subgroup_tex': 'C_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762396
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 818, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.BL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762397
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 819, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.BM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762399
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 820, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.BN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762400
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 821, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.BO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762401
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 822, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.BP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bo2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762402
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 823, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.BQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.50', 'subgroup_hash': 50, 'subgroup_order': 32, 'subgroup_tex': 'C_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762403
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 824, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.BR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762404
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 825, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.BS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762405
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 826, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.BT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762406
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 827, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.BU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762407
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 828, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.BV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762408
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 829, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.BW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762410
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 830, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.BX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.38', 'subgroup_hash': 38, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762411
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 831, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.BY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.38', 'subgroup_hash': 38, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762412
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 832, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.BZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762413
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 833, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.CA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762414
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 834, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.CB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762415
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 835, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.CC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762416
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 836, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.CD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762417
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 837, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.CE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.50', 'subgroup_hash': 50, 'subgroup_order': 32, 'subgroup_tex': 'C_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762418
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 838, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.CF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762419
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 839, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.CG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762421
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 840, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.CH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762422
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 841, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.CI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762423
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 842, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.CJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762424
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 843, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.CK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762425
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 844, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.CL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762426
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 845, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.CM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762427
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 846, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.CN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762428
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 847, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.CO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762429
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 848, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.CP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762430
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 849, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.CQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762432
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 850, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.CR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762433
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 851, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.CS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184762434
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 852, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.CT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184762435
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 853, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.CU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cs2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.38', 'subgroup_hash': 38, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762436
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 854, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.CV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.38', 'subgroup_hash': 38, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762437
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 855, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.CW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184762438
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 856, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.CX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762439
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 857, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.CY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762440
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 858, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.CZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762441
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 859, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.DA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184762443
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 860, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.DB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762444
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 861, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.DC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762445
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 862, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.DD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762446
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 863, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.DE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762447
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 864, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.DF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762448
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 865, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.DG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762449
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 866, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.DH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762450
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 867, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.DI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762451
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 868, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.DJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762452
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 869, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.DK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762454
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 870, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.DL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762455
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 871, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.DM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184762456
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 872, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.DN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762457
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 873, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.DO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184762458
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 874, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.DP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184762459
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 875, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.DQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184762460
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 876, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.DR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762461
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 877, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.DS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184762462
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 878, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.DT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762463
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 879, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.DU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762465
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 880, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.DV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762466
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 881, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.DW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.50', 'subgroup_hash': 50, 'subgroup_order': 32, 'subgroup_tex': 'C_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762467
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 882, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.DX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762468
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 883, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.DY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762469
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 884, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.DZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762470
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 885, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.EA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762471
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 886, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.EB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762472
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 887, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.EC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762473
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 888, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.ED', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762474
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 889, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.EE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762476
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 890, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.EF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762477
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 891, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.EG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762478
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 892, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.EH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762479
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 893, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.EI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762480
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 894, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.EJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.50', 'subgroup_hash': 50, 'subgroup_order': 32, 'subgroup_tex': 'C_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762481
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 895, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.EK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762482
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 896, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.EL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762483
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 897, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.EM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762484
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 898, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.EN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762485
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 899, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.EO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762488
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 900, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.EP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.38', 'subgroup_hash': 38, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762489
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 901, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.EQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762490
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 902, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.ER', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762491
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 903, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.ES', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762492
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 904, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.ET', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762493
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 905, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.EU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184762494
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 906, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.EV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762495
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 907, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.EW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762496
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 908, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.EX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184762497
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 909, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.EY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184762499
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 910, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.EZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762500
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 911, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.FA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184762501
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 912, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.FB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762502
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 913, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.FC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184762503
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 914, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.FD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762504
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 915, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.FE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762505
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 916, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.FF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762506
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 917, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.FG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762507
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 918, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.FH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762508
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 919, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.FI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762510
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 920, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.FJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762511
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 921, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.FK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762512
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 922, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.FL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762513
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 923, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.FM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762514
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 924, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.FN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762515
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 925, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.FO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762516
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 926, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.FP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762517
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 927, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.FQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762518
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 928, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.FR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762519
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 929, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.FS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.38', 'subgroup_hash': 38, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762521
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 930, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.FT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762522
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 931, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.FU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184762523
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 932, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.FV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762524
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 933, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.FW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762525
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 934, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.FX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184762526
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 935, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.FY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 184762527
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 936, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.FZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.4', 'subgroup_hash': 4, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762528
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 937, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.GA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.8', 'subgroup_hash': 8, 'subgroup_order': 32, 'subgroup_tex': 'C_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762529
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 938, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.GB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.8', 'subgroup_hash': 8, 'subgroup_order': 32, 'subgroup_tex': 'C_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762530
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 939, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.GC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.8', 'subgroup_hash': 8, 'subgroup_order': 32, 'subgroup_tex': 'C_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762532
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 940, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.GD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.15', 'subgroup_hash': 15, 'subgroup_order': 32, 'subgroup_tex': 'C_8.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762533
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 941, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.GE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.15', 'subgroup_hash': 15, 'subgroup_order': 32, 'subgroup_tex': 'C_8.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762534
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 942, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.GF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184762535
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 943, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.GG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 184762536
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 944, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.GH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762537
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 945, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.GI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762538
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 946, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.GJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.50', 'subgroup_hash': 50, 'subgroup_order': 32, 'subgroup_tex': 'C_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762539
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 947, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.GK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762540
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 948, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.GL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762541
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 949, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.GM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762543
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 950, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.GN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762544
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 951, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.GO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762545
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 952, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.GP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762546
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 953, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.GQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762547
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 954, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.GR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762548
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 955, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.GS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762549
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 956, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.GT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762550
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 957, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.GU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762551
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 958, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.GV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762552
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 959, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.GW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762554
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 960, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.GX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762555
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 961, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.GY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762556
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 962, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.GZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762557
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 963, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.HA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762558
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 964, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.HB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762559
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 965, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.HC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762560
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 966, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.HD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.hb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762561
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 967, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.HE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.hc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762562
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 968, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.HF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.hd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762563
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 969, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.HG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.he1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762565
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 970, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.HH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.hf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762566
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 971, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.HI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.hg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762567
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 972, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.HJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.hh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762568
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 973, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.HK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.hi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.50', 'subgroup_hash': 50, 'subgroup_order': 32, 'subgroup_tex': 'C_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762569
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 974, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.HL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.hj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184762570
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 975, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.HM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.hk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.50', 'subgroup_hash': 50, 'subgroup_order': 32, 'subgroup_tex': 'C_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184762571
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 976, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.HN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.hl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762572
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 977, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.HO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.hm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762573
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 978, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.HP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.hn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184762574
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 979, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.HQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ho1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762576
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 980, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.HR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.hp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762577
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 981, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.HS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.hq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762578
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 982, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.HT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.hr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762579
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 983, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.HU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.hs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762580
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 984, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.HV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ht1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762581
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 985, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.HW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.hu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184762582
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 986, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.HX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.hv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762583
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 987, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.HY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.hw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762584
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 988, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.HZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.hx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184762585
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 989, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.IA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.hy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762587
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 990, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.IB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.hz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762588
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 991, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.IC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ia1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762589
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 992, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.ID', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ib1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762590
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 993, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.IE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ic1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762591
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 994, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.IF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.id1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184762592
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 995, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.IG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ie1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184762593
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 996, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.IH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.if1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184762594
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 997, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.II', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ig1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762595
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 998, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.IJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ih1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184762596
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 999, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.IK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ii1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760512
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1000, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.IL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ij1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184760513
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1001, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.IM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ik1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184760514
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1002, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.IN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.il1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760515
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1003, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.IO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.im1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760516
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1004, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.IP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.in1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184760517
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1005, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.IQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.io1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 184760518
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1006, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.IR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ip1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760519
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1007, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.IS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.iq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760520
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1008, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.IT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ir1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760521
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1009, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.IU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.is1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760523
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1010, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.IV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.it1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760524
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1011, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.IW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.iu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760525
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1012, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.IX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.iv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760526
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1013, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.IY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.iw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760527
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1014, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.IZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ix1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760528
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1015, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.JA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.iy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760529
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1016, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.JB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.iz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184760530
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1017, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.JC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ja1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184760531
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1018, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.JD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.jb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760532
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1019, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.JE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.jc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760534
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1020, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.JF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.jd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760535
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1021, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.JG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.je1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760536
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1022, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.JH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.jf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184760537
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1023, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.JI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.jg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184760538
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1024, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.JJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.jh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760539
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1025, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.JK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ji1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184760540
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1026, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.JL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.jj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760541
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1027, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.JM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.jk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760542
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1028, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.JN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.jl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760543
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1029, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.JO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.jm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760545
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1030, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.JP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.jn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760546
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1031, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.JQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.jo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760547
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1032, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.JR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.jp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760548
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1033, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.JS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.jq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760549
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1034, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.JT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.jr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760550
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1035, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.JU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.js1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184760551
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1036, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.JV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.jt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184760552
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1037, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.JW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ju1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760553
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1038, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.JX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.jv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760554
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1039, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.JY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.jw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760556
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1040, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.JZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.jx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760557
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1041, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.KA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.jy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760558
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1042, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.KB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.jz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760559
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1043, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.KC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ka1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760560
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1044, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.KD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.kb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760561
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1045, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.KE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.kc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760562
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 1046, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.KF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.kd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760563
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 1047, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.KG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ke1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760564
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 1048, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.KH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.kf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760565
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 1049, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.KI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.kg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760567
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 1050, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.KJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.kh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760568
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 1051, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.KK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ki1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760569
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1052, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.KL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.kj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760570
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1053, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.KM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.kk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760571
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1054, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.KN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.kl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760572
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1055, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.KO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.km1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760573
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1056, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.KP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.kn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760574
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1057, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.KQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ko1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760575
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1058, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.KR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.kp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760576
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1059, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.KS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.kq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760578
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1060, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.KT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.kr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760579
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1061, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.KU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ks1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760580
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1062, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.KV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.kt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760581
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1063, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.KW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ku1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760582
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1064, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.KX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.kv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760583
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1065, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.KY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.kw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760584
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 1066, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.KZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.kx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760585
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 1067, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.LA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ky1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760586
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1068, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.LB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.kz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760587
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 1069, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.LC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.la1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760589
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1070, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.LD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.lb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760590
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1071, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.LE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.lc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760591
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1072, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.LF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ld1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760592
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1073, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.LG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.le1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760593
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1074, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.LH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.lf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760594
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1075, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.LI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.lg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760595
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1076, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.LJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.lh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760596
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 1077, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.LK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.li1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760597
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1078, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.LL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.lj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760598
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1079, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.LM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.lk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760600
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 1080, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.LN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ll1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760601
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1081, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.LO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.lm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760602
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 1082, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.LP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ln1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760603
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 1083, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.LQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.lo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760604
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 1084, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.LR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.lp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760605
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1085, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.LS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.lq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760606
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 1086, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.LT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.lr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760607
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 1087, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.LU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ls1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760608
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1088, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.LV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.lt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760609
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1089, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.LW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.lu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760611
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1090, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.LX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.lv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760612
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 1091, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.LY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.lw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760613
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1092, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.LZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.lx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760614
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 1093, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.MA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ly1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760615
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1094, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.MB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.lz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760616
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1095, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.MC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ma1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760617
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1096, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.MD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.mb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184760618
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1097, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.ME', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.mc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184760619
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1098, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.MF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.md1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184760620
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1099, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.MG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.me1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184760623
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.MH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.mf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184760624
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.MI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.mg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184760625
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.MJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.mh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760626
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.MK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.mi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760627
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.ML', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.mj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760628
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.MM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.mk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760629
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.MN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ml1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760630
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.MO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.mm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760631
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.MP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.mn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760632
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.MQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.mo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760634
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.MR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.mp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760635
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.MS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.mq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760636
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.MT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.mr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760637
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.MU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ms1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760638
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.MV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.mt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760639
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.MW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.mu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760640
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.MX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.mv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760641
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.MY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.mw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760642
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.MZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.mx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760643
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.NA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.my1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760645
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.NB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.mz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 184760646
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.NC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.na1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760647
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.ND', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.nb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760648
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.NE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.nc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760649
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.NF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.nd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760650
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.NG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ne1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760651
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.NH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.nf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760652
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.NI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ng1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760653
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.NJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.nh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760654
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.NK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ni1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760656
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.NL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.nj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760657
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.NM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.nk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760658
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.NN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.nl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760659
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.NO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.nm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760660
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.NP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.nn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760661
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 1135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.NQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.no1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760662
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.NR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.np1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760663
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.NS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.nq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760664
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.NT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.nr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760665
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.NU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ns1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760667
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.NV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.nt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760668
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.NW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.nu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760669
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.NX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.nv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760670
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.NY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.nw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.33', 'subgroup_hash': 33, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760671
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.NZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.nx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760672
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.OA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ny1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760673
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.OB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.nz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760674
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.OC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.oa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760675
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.OD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.oa2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760676
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.OE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ob1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760678
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.OF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.oc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760679
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.OG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.od1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760680
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.OH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.oe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760681
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.OI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.oe2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760682
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.OJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.of1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760683
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.OK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.og1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760684
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.OL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.oh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760685
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.OM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.oi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760686
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.ON', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.oi2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760687
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.OO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.oj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760689
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.OP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ok1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760690
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.OQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ok2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760691
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.OR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ol1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760692
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.OS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.om1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760693
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.OT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.on1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760694
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.OU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.oo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760695
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.OV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.op1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760696
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.OW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.oq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760697
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.OX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.or1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760698
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.OY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.os1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760700
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.OZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ot1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760701
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.PA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ou1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760702
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.PB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ov1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760703
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.PC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ow1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760704
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.PD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ox1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760705
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.PE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.oy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760706
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.PF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.oz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184760707
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.PG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.pa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760708
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.PH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.pb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760709
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.PI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.pc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184760711
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.PJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.pd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184760712
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.PK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.pe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184760713
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 1182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.PL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.pf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760714
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.PM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.pg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760715
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.PN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ph1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760716
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.PO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.pi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760717
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.PP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.pj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760718
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.PQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.pk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760719
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.PR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.pl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760720
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.PS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.pm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760722
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.PT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.pn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760723
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.PU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.po1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760724
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.PV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.pp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760725
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.PW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.pq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760726
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.PX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.pr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760727
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.PY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ps1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760728
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.PZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.pt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760729
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.QA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.pu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760730
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.QB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.pv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760731
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.QC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.pw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184760734
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.QD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.px1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760735
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.QE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.py1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760736
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.QF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.pz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760737
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.QG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.qa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 184760738
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.QH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.qb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760739
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.QI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.qc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760740
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.QJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.qd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760741
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.QK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.qe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760742
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.QL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.qf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760743
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.QM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.qg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760745
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.QN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.qh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760746
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.QO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.qi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760747
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.QP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.qj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760748
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.QQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.qj2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760749
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.QR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.qk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760750
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.QS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ql1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760751
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.QT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.qm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760752
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.QU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.qn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760753
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.QV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.qo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760754
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.QW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.qp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.50', 'subgroup_hash': 50, 'subgroup_order': 32, 'subgroup_tex': 'C_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184760756
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.QX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.qq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760757
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.QY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.qr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.38', 'subgroup_hash': 38, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760758
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.QZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.qs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760759
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.RA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.qt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760760
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.RB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.qu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760761
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.RC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.qv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.38', 'subgroup_hash': 38, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760762
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 1226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.RD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.qw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760763
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.RE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.qx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760764
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.RF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.qy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760765
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.RG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.qz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.50', 'subgroup_hash': 50, 'subgroup_order': 32, 'subgroup_tex': 'C_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184760767
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.RH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ra1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760768
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.RI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.rb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760769
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.RJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.rb2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760770
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.RK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.rc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760771
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.RL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.rd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760772
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.RM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.re1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760773
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.RN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.rf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760774
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.RO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.rf2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760775
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.RP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.rg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760776
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.RQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.rh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760778
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.RR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ri1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760779
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.RS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.rj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760780
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.RT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.rk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760781
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.RU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.rk2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760782
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.RV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.rl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760783
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.RW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.rm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.33', 'subgroup_hash': 33, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760784
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.RX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.rn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760785
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.RY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ro1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760786
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.RZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.rp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760787
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.SA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.rq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760789
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.SB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.rr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760790
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.SC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.rs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760791
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.SD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.rt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760792
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.SE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ru1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760793
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.SF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.rv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760794
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.SG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.rw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760795
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.SH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.rx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760796
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.SI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ry1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760797
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.SJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.rz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760798
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.SK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.sa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760800
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.SL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.sb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760801
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.SM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.sc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760802
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.SN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.sd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760803
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.SO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.se1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760804
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.SP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.sf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760805
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.SQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.sg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760806
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.SR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.sh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760807
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.SS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.sh2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760808
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.ST', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.si1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760809
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.SU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.sj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760811
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.SV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.sk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760812
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.SW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.sl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760813
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.SX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.sm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760814
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.SY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.sn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.33', 'subgroup_hash': 33, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760815
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.SZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.so1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760816
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.TA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.sp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760817
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.TB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.sq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760818
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.TC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.sr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760819
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.TD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ss1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184760820
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.TE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.st1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760822
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.TF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.su1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760823
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.TG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.sv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760824
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.TH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.sw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760825
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.TI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.sx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760826
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.TJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.sy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760827
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.TK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.sz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760828
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.TL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ta1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760829
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.TM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.tb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760830
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 1288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.TN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.tc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760831
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.TO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.td1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760833
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.TP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.te1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760834
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.TQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.tf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760835
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.TR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.tg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760836
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.TS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.th1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760837
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.TT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.th2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760838
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.TU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ti1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760839
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.TV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.tj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760840
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.TW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.tk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760841
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.TX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.tl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184760842
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.TY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.tm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184760845
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.TZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.tn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760846
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.UA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.to1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.33', 'subgroup_hash': 33, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760847
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.UB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.tp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184760848
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.UC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.tq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760849
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.UD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.tr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760850
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.UE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ts1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760851
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.UF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.tt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760852
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.UG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.tu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760853
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.UH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.tv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760854
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.UI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.tw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760856
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 1310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.UJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.tx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760857
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.UK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ty1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760858
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.UL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.tz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760859
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.UM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ua1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184760860
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.UN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ub1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760861
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.UO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.uc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184760862
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.UP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ud1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184760863
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.UQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ue1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760864
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.UR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.uf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760865
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 1319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.US', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ug1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760867
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.UT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.uh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760868
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.UU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ui1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760869
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.UV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.uj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760870
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.UW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.uk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760871
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 1324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.UX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ul1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760872
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.UY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.um1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.50', 'subgroup_hash': 50, 'subgroup_order': 32, 'subgroup_tex': 'C_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184760873
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.UZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.un1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760874
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.VA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.uo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760875
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.VB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.up1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760876
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.VC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.uq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.38', 'subgroup_hash': 38, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760878
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 1330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.VD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ur1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760879
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.VE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.us1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760880
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.VF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ut1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760881
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.VG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.uu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.50', 'subgroup_hash': 50, 'subgroup_order': 32, 'subgroup_tex': 'C_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184760882
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.VH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.uv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.32', 'subgroup_hash': 32, 'subgroup_order': 32, 'subgroup_tex': 'C_4.Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184760883
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.VI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.uw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184760884
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.VJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ux1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184760885
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.VK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.uy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 184760886
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.VL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.uz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 184760887
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.VM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.va1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.8', 'subgroup_hash': 8, 'subgroup_order': 32, 'subgroup_tex': 'C_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760889
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.VN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.vb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.8', 'subgroup_hash': 8, 'subgroup_order': 32, 'subgroup_tex': 'C_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760890
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.VO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.vc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.8', 'subgroup_hash': 8, 'subgroup_order': 32, 'subgroup_tex': 'C_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760891
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.VP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.vd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.8', 'subgroup_hash': 8, 'subgroup_order': 32, 'subgroup_tex': 'C_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760892
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.VQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ve1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.15', 'subgroup_hash': 15, 'subgroup_order': 32, 'subgroup_tex': 'C_8.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760893
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 1344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.96.VR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.vf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.4', 'subgroup_hash': 4, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760894
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 1345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.128.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 184760895
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.128.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 184760896
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.128.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184760897
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.128.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 184760898
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.128.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184760900
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 1350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.128.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184760901
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.128.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 184760902
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.128.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760903
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.128.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760904
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.128.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 184760905
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.128.K', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 184760906
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.128.L', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760907
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.128.M', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 184760908
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.128.N', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 184760909
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.128.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184760911
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.128.P', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 184760912
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 1361, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.192.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '192.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '192.955', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 955, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^3:S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184760913
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 1362, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.192.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '192.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '192.1472', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1472, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'D_4\\times S_4', 'simple': False, 'solvable': True, 'special_labels': ['C6'], '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: 184760914
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760915
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760916
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184760917
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760918
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760919
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760920
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760922
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760923
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.K', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760924
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.L', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760925
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.M', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760926
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.N', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760927
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.O', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760928
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.P', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760929
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760930
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.R', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760931
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.S', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760933
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.T', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760934
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.U', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760935
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.V', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760936
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.W', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760937
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.X', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760938
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760939
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184760940
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760941
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184760942
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760944
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.BD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760945
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.BE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bd2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760946
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.BF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760947
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.BG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760948
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.BH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760949
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.BI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760950
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.BJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760951
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.BK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760952
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.BL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bj2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760953
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.BM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760956
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.BN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bk2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760957
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.BO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760958
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.BP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760959
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.BQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760960
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.BR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760961
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.BS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760962
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.BT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760963
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.BU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760964
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.BV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760965
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.BW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760967
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.BX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760968
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.BY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760969
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.BZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760970
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.CA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760971
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.CB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760972
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.CC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760973
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.CD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bz2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760974
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.CE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760975
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.CF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760976
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.CG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760978
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.CH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cc2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760979
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.CI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760980
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.CJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cd2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760981
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.CK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760982
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.CL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ce2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760983
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.CM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760984
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.CN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760985
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.CO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760986
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.CP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ch2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760987
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.CQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760989
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.CR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760990
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.CS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760991
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.CT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760992
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.CU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cl2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184760993
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.CV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760994
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.CW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184760995
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 1436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.CX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760996
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.CY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184760997
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.CZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184760998
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.DA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761000
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.DB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761001
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.DC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761002
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.DD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761003
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.DE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761004
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.DF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cv2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761005
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.DG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761006
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.DH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761007
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.DI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761008
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.DJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cy2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761009
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.DK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761011
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.DL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761012
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.DM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761013
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.DN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761014
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.DO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761015
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.DP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761016
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.DQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761017
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.DR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761018
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.DS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761019
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.DT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761020
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.DU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761022
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.DV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.dj2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761023
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.DW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761024
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.DX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761025
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.DY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184761026
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.DZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761027
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.EA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761028
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.EB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761029
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.EC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761030
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.ED', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761031
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.EE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761033
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.EF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761034
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.EG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761035
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.EH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761036
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.EI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761037
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.EJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.dw2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761038
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.EK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761039
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.EL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761040
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.EM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761041
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.EN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761042
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.EO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184761044
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.EP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761045
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.EQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761046
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.ER', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761047
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.ES', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761048
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.ET', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761049
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.EU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761050
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.EV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761051
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.EW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ei2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761052
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.EX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761053
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.EY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761055
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.EZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761056
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.FA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761057
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.FB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761058
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.FC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761059
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.FD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761060
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.FE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761061
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.FF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761062
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.FG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761063
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.FH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761064
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.FI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761067
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.FJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761068
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.FK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ev2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761069
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.FL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761070
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.FM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761071
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.FN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761072
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.FO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ey2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761073
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.FP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184761074
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.FQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761075
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.FR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761076
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.FS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761078
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.FT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761079
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.FU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761080
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.FV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761081
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.FW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761082
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.FX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761083
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.FY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.fh2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761084
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.FZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761085
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.GA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761086
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.GB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761087
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.GC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761089
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.GD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761090
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.GE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761091
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.GF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761092
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.GG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761093
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.GH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761094
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.GI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.fq2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761095
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.GJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761096
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.GK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761097
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.GL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761098
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.GM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761100
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.GN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761101
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.GO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761102
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.GP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761103
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.GQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761104
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.GR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761105
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.GS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761106
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.GT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761107
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.GU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761108
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.GV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761109
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.GW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761111
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.GX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761112
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.GY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761113
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.GZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761114
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.HA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761115
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.HB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761116
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.HC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761117
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.HD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761118
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.HE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761119
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.HF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184761120
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.HG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.gn2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184761122
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.HH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761123
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.HI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761124
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.HJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761125
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.HK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761126
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.HL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761127
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.HM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.gs2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761128
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.HN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761129
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.HO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761130
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.HP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761131
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.HQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761133
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.HR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761134
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.HS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761135
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.HT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761136
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.HU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761137
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.HV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ha2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761138
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.HW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.hb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761139
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.HX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.hb2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761140
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.HY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.hc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761141
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.HZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.hd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761142
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.IA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.he1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761144
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.IB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.hf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761145
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.IC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.hg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761146
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.ID', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.hh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761147
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.IE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.hi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761148
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.IF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.hi2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761149
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.IG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.hj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761150
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.IH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.hk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761151
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.II', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.hl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761152
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1578, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.IJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.hm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761153
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.IK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.hn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761155
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.IL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ho1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761156
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.IM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.hp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761157
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.IN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.hq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761158
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.IO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.hr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761159
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.IP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.hs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761160
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.IQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ht1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761161
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.IR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.hu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761162
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.IS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.hv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761163
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.IT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.hw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761164
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.IU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.hx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761166
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.IV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.hy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761167
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.IW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.hz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761168
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.IX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ia1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761169
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.IY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ib1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761170
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.IZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ic1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761171
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.JA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.id1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761172
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.JB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ie1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761173
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.JC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.if1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761174
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.JD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ig1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761175
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.JE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ih1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761178
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.JF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ii1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761179
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.JG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ij1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761180
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.JH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ik1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761181
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.JI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.il1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761182
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.JJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.il2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761183
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.JK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.im1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761184
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1606, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.JL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.in1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761185
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1607, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.JM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.io1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761186
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.JN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ip1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761187
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.JO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.iq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761189
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1610, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.JP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ir1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761190
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1611, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.JQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.is1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761191
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1612, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.JR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.it1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761192
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1613, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.JS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.iu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761193
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1614, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.JT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.iv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761194
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.JU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.iw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761195
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1616, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.JV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ix1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761196
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1617, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.JW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.iy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761197
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1618, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.JX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.iz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761198
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1619, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.JY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ja1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761200
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1620, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.JZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.jb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761201
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1621, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.KA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.jc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761202
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1622, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.KB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.jd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761203
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1623, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.KC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.je1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761204
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1624, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.KD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.jf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761205
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1625, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.KE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.jg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761206
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1626, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.KF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.jh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761207
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1627, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.KG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ji1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761208
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1628, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.KH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.jj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761209
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1629, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.KI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.jk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761211
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1630, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.KJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.jl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761212
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1631, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.KK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.jl2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761213
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1632, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.KL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.jm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761214
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1633, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.KM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.jn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761215
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1634, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.KN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.jo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761216
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1635, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.KO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.jp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761217
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1636, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.KP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.jq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761218
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.KQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.jq2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761219
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1638, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.KR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.jr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761220
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1639, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.KS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.js1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761222
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.KT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.jt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761223
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1641, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.KU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ju1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761224
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1642, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.KV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.jv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761225
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1643, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.KW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.jw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761226
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1644, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.KX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.jx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761227
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1645, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.KY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.jy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761228
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.KZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.jz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761229
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1647, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.LA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ka1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761230
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1648, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.LB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.kb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761231
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.LC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.kc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761233
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1650, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.LD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.kd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761234
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1651, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.LE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ke1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761235
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1652, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.LF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.kf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761236
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.LG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.kg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761237
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1654, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.LH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.kh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761238
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1655, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.LI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ki1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761239
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1656, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.LJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.kj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761240
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1657, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.LK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.kk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761241
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1658, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.LL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.kl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761242
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1659, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.LM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.km1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761244
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1660, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.LN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.kn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761245
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1661, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.LO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ko1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761246
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1662, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.LP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.kp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761247
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1663, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.LQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.kq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761248
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1664, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.LR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.kr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761249
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1665, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.LS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ks1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761250
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1666, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.LT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.kt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761251
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1667, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.LU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ku1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761252
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1668, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.LV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ku2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761253
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1669, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.LW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.kv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761255
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1670, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.LX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.kw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761256
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1671, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.LY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.kx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761257
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1672, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.LZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ky1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761258
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1673, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.MA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.kz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761259
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1674, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.MB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.la1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761260
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1675, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.MC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.lb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761261
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1676, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.MD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.lc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761262
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1677, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.ME', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ld1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761263
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1678, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.MF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.le1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761264
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1679, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.MG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.lf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761266
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 1680, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.MH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.lg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761267
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 1681, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.MI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.lh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761268
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1682, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.MJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.li1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184761269
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1683, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.MK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.lj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761270
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1684, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.ML', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.lk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761271
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1685, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.MM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ll1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184761272
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1686, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.MN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.lm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761273
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1687, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.MO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ln1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761274
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 1688, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.MP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.lo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761275
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 1689, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.MQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.lp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761277
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1690, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.MR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.lq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761278
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 1691, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.MS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.lr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761279
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1692, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.MT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ls1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184761280
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1693, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.MU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.lt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761281
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1694, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.MV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.lu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761282
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1695, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.MW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.lv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761283
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1696, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.MX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.lw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761284
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1697, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.MY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.lx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761285
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1698, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.MZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ly1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761286
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1699, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.NA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.lz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761289
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1700, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.NB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ma1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761290
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1701, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.NC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.mb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761291
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1702, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.ND', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.mc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184761292
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1703, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.NE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.md1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184761293
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1704, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.NF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.me1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761294
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1705, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.NG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.mf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761295
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1706, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.NH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.mg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761296
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1707, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.NI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.mh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761297
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1708, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.NJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.mi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761298
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1709, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.NK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.mj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761300
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1710, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.NL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.mk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761301
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1711, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.NM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ml1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761302
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1712, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.NN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.mm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761303
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1713, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.NO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.mn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761304
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1714, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.NP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.mo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761305
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1715, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.NQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.mp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184761306
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1716, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.NR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.mq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184761307
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1717, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.NS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.mr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761308
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1718, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.NT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ms1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761309
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1719, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.NU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.mt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761311
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1720, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.NV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.mu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761312
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1721, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.NW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.mv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761313
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1722, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.NX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.mw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761314
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1723, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.NY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.mx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761315
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1724, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.NZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.my1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761316
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1725, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.OA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.mz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761317
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1726, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.OB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.na1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761318
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1727, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.OC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.na2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761319
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1728, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.OD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.nb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761320
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1729, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.OE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.nc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761322
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1730, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.OF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.nd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761323
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1731, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.OG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ne1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761324
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1732, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.OH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.nf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761325
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1733, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.OI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ng1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761326
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1734, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.OJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ng2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761327
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1735, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.OK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.nh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761328
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1736, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.OL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ni1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761329
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1737, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.OM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.nj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761330
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1738, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.ON', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.nk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761331
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1739, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.OO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.nl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184761333
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1740, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.OP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.nm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761334
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1741, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.OQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.nn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761335
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1742, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.OR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.no1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761336
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1743, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.OS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.np1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761337
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1744, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.OT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.nq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761338
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1745, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.OU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.nr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761339
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1746, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.OV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ns1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761340
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1747, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.OW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.nt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761341
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1748, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.OX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.nt2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761342
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1749, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.OY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.nu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761344
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1750, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.OZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.nv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761345
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1751, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.PA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.nw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761346
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1752, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.PB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.nx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761347
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1753, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.PC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ny1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 184761348
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1754, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.PD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.nz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761349
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1755, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.PE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.oa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761350
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1756, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.PF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ob1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761351
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1757, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.PG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.oc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761352
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1758, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.PH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.od1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761353
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1759, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.PI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.oe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761355
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1760, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.PJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.of1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761356
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1761, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.PK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.of2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761357
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1762, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.PL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.og1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761358
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1763, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.PM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.oh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761359
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1764, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.PN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.oi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761360
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1765, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.PO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.oj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761361
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1766, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.PP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ok1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761362
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1767, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.PQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ol1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761363
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1768, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.PR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.om1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761364
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1769, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.PS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.on1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761366
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1770, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.PT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.oo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761367
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1771, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.PU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.op1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761368
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1772, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.PV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.oq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 184761369
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1773, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.PW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.or1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761370
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1774, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.PX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.os1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761371
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1775, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.PY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ot1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761372
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1776, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.PZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ou1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761373
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1777, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.QA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ov1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761374
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1778, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.QB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ow1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761375
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 1779, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.QC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ox1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761377
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1780, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.QD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.oy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761378
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1781, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.QE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.oz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761379
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1782, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.QF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.pa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761380
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1783, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.QG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.pb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761381
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1784, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.QH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.pc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761382
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1785, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.QI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.pd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761383
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1786, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.QJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.pe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761384
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1787, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.QK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.pf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761385
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1788, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.QL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.pg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761386
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1789, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.QM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ph1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761388
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1790, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.QN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.pi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761389
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1791, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.QO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.pj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 184761390
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1792, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.QP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.pk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 184761391
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1793, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.QQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.pl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761392
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1794, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.QR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.pm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761393
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1795, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.QS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.pn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761394
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1796, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.QT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.po1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761395
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1797, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.QU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.pp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761396
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1798, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.QV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.pq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761397
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1799, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.QW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.pr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761400
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1800, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.QX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.pr2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761401
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1801, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.QY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ps1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761402
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1802, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.192.QZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ps2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761403
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 1803, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.256.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '256.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 184761404
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1804, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.256.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '256.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 184761405
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1805, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.256.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '256.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 184761406
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1806, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.256.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '256.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 184761407
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1807, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.256.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '256.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 184761408
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1808, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.256.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '256.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 184761409
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1809, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.256.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '256.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 184761411
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1810, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.256.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '256.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761412
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1811, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.256.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '256.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 184761413
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1812, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.256.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '256.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 184761414
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1813, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.256.K', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '256.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 184761415
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 8, 'counter': 1814, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.384.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '384.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '384.17948', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 17948, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 384, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^4:S_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: 184761416
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1815, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761417
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1816, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761418
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1817, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761419
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1818, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761420
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1819, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761422
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1820, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.f2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761423
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1821, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761424
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1822, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761425
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1823, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761426
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1824, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.K', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.i2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761427
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1825, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.L', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761428
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1826, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.M', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761429
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1827, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.N', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761430
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1828, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.O', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761431
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 1829, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.P', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761433
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 1830, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761434
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 1831, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.R', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761435
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1832, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.S', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761436
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1833, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.T', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761437
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1834, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.U', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761438
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1835, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.V', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761439
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1836, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.W', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761440
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1837, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.X', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761441
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1838, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.v2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761442
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1839, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761444
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1840, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761445
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1841, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761446
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1842, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761447
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1843, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.BD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761448
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1844, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.BE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761449
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1845, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.BF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761450
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1846, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.BG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761451
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1847, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.BH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761452
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1848, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.BI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761453
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1849, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.BJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761455
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1850, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.BK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761456
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1851, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.BL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761457
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1852, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.BM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761458
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1853, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.BN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.bj2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761459
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1854, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.BO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761460
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1855, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.BP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.bk2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761461
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1856, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.BQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.bk3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761462
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1857, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.BR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761463
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1858, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.BS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761464
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1859, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.BT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761466
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1860, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.BU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761467
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1861, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.BV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761468
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1862, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.BW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761469
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1863, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.BX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761470
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1864, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.BY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761471
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1865, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.BZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761472
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1866, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.CA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761473
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1867, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.CB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761474
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1868, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.CC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761475
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1869, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.CD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.bw2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761477
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1870, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.CE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761478
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1871, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.CF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.bx2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761479
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 1872, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.CG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761480
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 1873, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.CH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761481
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1874, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.CI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761482
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1875, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.CJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761483
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1876, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.CK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761484
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1877, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.CL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761485
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1878, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.CM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761486
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1879, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.CN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761488
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1880, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.CO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761489
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1881, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.CP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761490
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1882, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.CQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761491
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1883, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.CR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761492
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1884, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.CS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761493
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1885, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.CT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761494
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1886, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.CU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761495
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1887, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.CV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761496
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1888, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.CW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761497
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1889, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.CX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761499
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1890, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.CY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.cp2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761500
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1891, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.CZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761501
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1892, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.DA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761502
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1893, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.DB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761503
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1894, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.DC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761504
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1895, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.DD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761505
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1896, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.DE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761506
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1897, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.DF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761507
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1898, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.DG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761508
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1899, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.DH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761511
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1900, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.DI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761512
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1901, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.DJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761513
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1902, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.DK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761514
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1903, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.DL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761515
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1904, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.DM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.dc2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761516
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1905, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.DN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761517
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1906, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.DO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761518
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1907, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.DP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761519
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1908, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.DQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761520
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1909, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.DR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761522
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1910, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.DS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761523
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1911, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.DT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761524
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1912, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.DU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761525
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1913, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.DV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761526
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1914, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.DW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761527
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1915, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.DX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761528
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1916, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.DY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761529
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1917, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.DZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761530
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1918, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.EA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761531
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1919, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.EB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761533
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1920, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.EC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761534
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1921, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.ED', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761535
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1922, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.EE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761536
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1923, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.EF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761537
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1924, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.EG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761538
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1925, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.EH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761539
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1926, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.EI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761540
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1927, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.EJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761541
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1928, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.EK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761542
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1929, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.EL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761544
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1930, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.EM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761545
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1931, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.EN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.ec2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761546
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1932, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.EO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761547
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1933, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.EP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761548
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1934, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.EQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761549
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1935, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.ER', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761550
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1936, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.ES', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761551
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1937, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.ET', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761552
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1938, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.EU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761553
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1939, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.EV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761555
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1940, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.EW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761556
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1941, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.EX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761557
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1942, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.EY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761558
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1943, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.EZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761559
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1944, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.FA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761560
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1945, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.FB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761561
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1946, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.FC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761562
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1947, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.FD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761563
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1948, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.FE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761564
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1949, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.FF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761566
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1950, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.FG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761567
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1951, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.FH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761568
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1952, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.FI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761569
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1953, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.FJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761570
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1954, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.FK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761571
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1955, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.FL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761572
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1956, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.FM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761573
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1957, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.FN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761574
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1958, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.FO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761575
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1959, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.FP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761577
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1960, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.FQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761578
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1961, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.FR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761579
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1962, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.FS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761580
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1963, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.FT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761581
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1964, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.FU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761582
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1965, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.FV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 184761583
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1966, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.FW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761584
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 1967, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.FX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761585
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1968, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.FY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761586
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1969, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.FZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761588
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1970, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.GA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761589
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1971, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.GB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761590
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1972, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.GC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761591
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1973, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.GD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761592
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1974, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.GE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761593
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 4, 'counter': 1975, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.GF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761594
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 1976, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.GG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761595
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1977, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.GH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761596
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1978, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.GI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761597
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1979, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.GJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761599
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1980, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.GK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761600
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1981, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.GL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761601
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1982, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.GM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761602
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1983, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.GN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761603
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1984, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.GO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761604
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1985, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.GP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761605
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1986, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.GQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761606
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1987, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.GR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.gf2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761607
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1988, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.GS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761608
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1989, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.GT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761610
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1990, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.GU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761611
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1991, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.GV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761612
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1992, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.GW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.gj2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761613
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1993, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.GX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761614
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1994, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.GY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761615
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1995, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.GZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.gl2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761616
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1996, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.HA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761617
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1997, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.HB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761618
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1998, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.HC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761619
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1999, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.HD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761623
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2000, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.HE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761624
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2001, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.HF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.gq2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761625
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2002, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.HG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761626
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2003, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.HH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 184761627
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2004, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.HI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761628
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2005, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.HJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.gt2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761629
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2006, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.HK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761630
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2007, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.HL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.gu2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761631
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2008, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.HM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761632
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2009, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.HN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761634
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2010, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.HO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.gw2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761635
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2011, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.HP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.gw3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 184761636
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2012, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.HQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761637
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2013, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.HR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761638
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2014, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.HS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761639
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2015, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.384.HT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 184761640
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2016, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.512.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '512.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 184761641
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2017, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.512.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '512.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 184761642
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2018, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.512.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '512.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 184761643
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2019, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.512.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '512.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 184761645
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2020, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.512.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '512.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 184761646
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2021, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.512.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '512.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 184761647
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 512, 'characteristic': True, 'core_order': 4, 'counter': 2022, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.bgb.768.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '768.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '768.1087581', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1087581, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 768, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\wr D_6', 'simple': False, 'solvable': True, 'special_labels': ['S', 'D3', 'C7'], '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: 184761648
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 2023, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761649
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 2024, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761650
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 2025, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761651
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 2026, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.d2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761652
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 2027, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761653
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 2028, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761654
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 2029, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.f2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761656
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 2030, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761657
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 2031, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.g2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761658
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 2032, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.K', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761659
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 2033, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.L', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.h2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761660
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2034, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.M', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761661
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 2035, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.N', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761662
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 2036, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.O', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761663
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 512, 'characteristic': False, 'core_order': 1, 'counter': 2037, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.P', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761664
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 512, 'characteristic': False, 'core_order': 1, 'counter': 2038, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761665
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 2039, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.R', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761667
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 2040, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.S', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761668
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 2041, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.T', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761669
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 2042, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.U', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761670
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 2043, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.V', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761671
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 2044, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.W', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761672
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 2045, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.X', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761673
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 2046, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761674
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2047, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761675
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 2048, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761676
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2049, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761678
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2050, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761679
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2051, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.BD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.y2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761680
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2052, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.BE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761681
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2053, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.BF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761682
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 2054, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.BG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761683
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 2055, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.BH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761684
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2056, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.BI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761685
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 2057, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.BJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761686
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2058, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.BK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761687
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2059, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.BL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761689
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 2060, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.BM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761690
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2061, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.BN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761691
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 2062, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.BO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761692
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 2063, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.BP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.bj2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761693
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 2064, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.BQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761694
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 2065, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.BR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.bk2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761695
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2066, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.BS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761696
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2067, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.BT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761697
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2068, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.BU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761698
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2069, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.BV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761700
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2070, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.BW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761701
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2071, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.BX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761702
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2072, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.BY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761703
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2073, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.BZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761704
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2074, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.CA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761705
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2075, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.768.CB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 184761706
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2076, 'cyclic': True, 'direct': None, 'hall': 3, 'label': '3072.bgb.1024.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1024.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1024, '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': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
  • id: 184761707
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1024, 'characteristic': False, 'core_order': 1, 'counter': 2077, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.1536.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, '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: 184761708
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 768, 'characteristic': False, 'core_order': 1, 'counter': 2078, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.1536.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, '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: 184761709
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 2079, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.1536.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, '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: 184761711
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 2080, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.1536.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, '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: 184761712
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 2081, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.1536.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, '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: 184761713
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 2082, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.1536.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, '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: 184761714
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 2083, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.1536.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, '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: 184761715
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 2084, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.1536.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, '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: 184761716
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 2085, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.1536.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, '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: 184761717
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 2086, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.1536.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, '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: 184761718
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 2087, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3072.bgb.1536.K', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, '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: 184761719
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3072.bgb', 'ambient_counter': 834, 'ambient_order': 3072, 'ambient_tex': 'C_4^3:(C_2\\times S_4)', 'central': True, 'central_factor': False, 'centralizer_order': 3072, 'characteristic': True, 'core_order': 1, 'counter': 2088, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '3072.bgb.3072.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '3072.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '3072.bgb', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7983714371117797868, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 3072, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_4^3:(C_2\\times S_4)', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'PC', 'U0', 'D4', 'C8'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 184760509
    {'ambient': '3072.bgb', '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': '3072.a1', 'complements': ['3072.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.A', '2.B', '2.C', '2.D', '2.E', '2.F', '2.G', '3.a1', '4.H'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [25903229681844523013167, 134021529040297499210286, 1313941673647, 187922473375925652905521, 404159831259638948150382, 133970303627361494479417, 108118421696801471190456, 566444897749485959875336, 108118165248982343710201, 162070456272950954131199, 378358649363678452761737], 'label': '3072.bgb.1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.A', '2.B', '2.C', '2.D', '2.E', '2.F', '2.G'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '3072.bgb'}
  • id: 184760510
    {'ambient': '3072.bgb', 'aut_centralizer_order': 1, 'aut_label': '4.A', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '3072.a1', 'complements': ['768.BT'], 'conjugacy_class_count': 1, 'contained_in': ['2.A', '2.B', '2.C'], 'contains': ['8.A', '8.L', '12.A', '16.B', '16.D', '16.E'], 'core': '4.A', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [25903229681844523013167, 108118165248982343710201, 187922473375925652905521, 566444897749485959875336, 133970303627361494479417, 404159831259638948150382, 1313941673647, 486427128433516595381056, 162070456272950954131199], 'label': '3072.bgb.4.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': ['2.A', '2.B', '2.C'], 'normal_contains': ['8.A', '12.A'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '3072.bgb', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.A', 'subgroup_fusion': None, 'weyl_group': '3072.bgb'}
  • id: 184760511
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.BY', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.E', '6.J', '6.M'], 'contains': ['24.EA', '24.EB', '24.EF'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 79804429413572684637382, 378358905093235639407953, 296041409911409376977422], 'label': '3072.bgb.12.BY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.by1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BY', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184760512
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.IL', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.DQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DH', '48.LL'], 'contains': ['192.GT', '192.GW', '192.JM', '192.JN', '192.JT'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [368207923870206, 1313941673647, 25852017101492540879976, 25852017102974698844878, 162070456280045573438767], 'label': '3072.bgb.96.IL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.ij1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.IL', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760513
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.IM', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.DP', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DJ', '48.LA'], 'contains': ['192.GU', '192.GV', '192.JP', '192.JR', '192.JS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922473021741077083393, 51212594192254410823, 187973685961890096441600, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.IM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.ik1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.IM', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761605
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '384.GQ', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.BB', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.J', '192.BB', '192.QS', '192.QT'], 'contains': ['768.BA', '768.BC', '768.BF', '768.BT'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [378358770650295628183080, 25852272837936812846761, 122002101738321960], 'label': '3072.bgb.384.GQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.L', 'old_label': '384.gf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.GQ', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184760514
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.IN', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.EC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.LQ'], 'contains': ['192.GX', '192.GZ', '192.HA', '192.KJ', '192.KL', '192.KS', '192.KU'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [54003382330230002441647, 404159575154785525538638, 25903229683158464676480, 134021272934136496216343, 216288705272228144236816], 'label': '3072.bgb.96.IN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.LQ', 'old_label': '96.il1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.IN', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760515
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.IO', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.EC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DK', '48.LQ'], 'contains': ['192.GX', '192.GY', '192.KL', '192.KM', '192.KO'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804429416356250372480, 108118287253867647069496, 404159575153471583875073, 25903229683158464676480, 216288705272228144236816], 'label': '3072.bgb.96.IO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GO', 'old_label': '96.im1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.IO', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760516
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.IP', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.EC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DL', '48.LQ'], 'contains': ['192.GY', '192.HA', '192.KN', '192.KO', '192.KU'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804429416356250372480, 108118287253867647069496, 216288705273529552035263, 404159575153471583875073, 25903229683158464676480], 'label': '3072.bgb.96.IP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GO', 'old_label': '96.in1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.IP', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760517
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.IQ', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.EB', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DK', '48.DL', '48.LR'], 'contains': ['192.GY', '192.KQ', '192.KR'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79804429416356250372480, 108118287253867647069496, 242140721662339602266753, 378307558065813088567696, 25903229683158464676480], 'label': '3072.bgb.96.IQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GO', 'old_label': '96.io1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.IQ', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760518
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.IR', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.BM', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DG', '48.DI', '48.LY'], 'contains': ['192.FP', '192.FY', '192.GL', '192.GS', '192.HF', '192.ID', '192.JE', '192.QY', '192.QZ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [162121669227129588479873, 187973685961890096441600, 1313941673647, 162070456274433112077942, 25852017102974698844878], 'label': '3072.bgb.96.IR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.ip1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.IR', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760519
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.IS', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.BM', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DH', '48.DI', '48.LY'], 'contains': ['192.FQ', '192.FX', '192.GL', '192.GW', '192.HF', '192.ID', '192.JG'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922473021741077083393, 1313941673647, 162070456274433112077942, 25852017102974698844878, 162070456280045573438767], 'label': '3072.bgb.96.IS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.iq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.IS', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760520
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.IT', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.BM', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DG', '48.DJ', '48.LY'], 'contains': ['192.FV', '192.FX', '192.GS', '192.GV', '192.HF', '192.JE', '192.JF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [162121669227129588479873, 1313941673647, 162070456274433112077942, 25852017102974698844878, 162070456280045573438767], 'label': '3072.bgb.96.IT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.ir1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.IT', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760521
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.IU', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.BM', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DH', '48.DJ', '48.LY'], 'contains': ['192.FW', '192.FY', '192.GV', '192.GW', '192.HF', '192.JF', '192.JG'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922473021741077083393, 187973685961890096441600, 1313941673647, 162070456274433112077942, 25852017102974698844878], 'label': '3072.bgb.96.IU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.is1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.IU', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760522
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '12.BZ', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 12, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.E', '6.I', '6.N'], 'contains': ['24.EA', '24.EC', '24.EE'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118421696801471190456, 53952291033879672806278, 25903229681844523013167, 79804052047512561508433, 122002101738321960, 1313941673647, 79804429413572684637382, 25852017102974698844878], 'label': '3072.bgb.12.BZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BZ', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 184760523
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.IV', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '192.NR', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DK', '48.DL', '48.MC'], 'contains': ['192.FU', '192.GB', '192.GO', '192.GP', '192.GQ', '192.GY', '192.HG', '192.HH', '192.JU'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79804308122845802507662, 108118165248982343710201, 25903229681844523013167, 187973685961890096441600, 25852017102974698844878], 'label': '3072.bgb.96.IV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GO', 'old_label': '96.it1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.IV', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184760524
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.IW', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '192.NR', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.MC'], 'contains': ['192.FU', '192.GC', '192.GO', '192.GP', '192.GR', '192.GZ', '192.HG', '192.HI', '192.JV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187973685961890096441600, 79804308124159744181057, 25852017102974698844878], 'label': '3072.bgb.96.IW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.MC', 'old_label': '96.iu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.IW', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184760525
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.IX', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.F', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.CA', '48.CG', '48.MW'], 'contains': ['192.HN', '192.HP', '192.HW', '192.JW', '192.JZ', '192.LJ', '192.LY'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922473375925652905521, 134021394930826866723126, 25903229683158464676480, 378358649362364591657542, 79855264262271969233416], 'label': '3072.bgb.96.IX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.DK', 'old_label': '96.iv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.IX', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760526
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.IY', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.S', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.CA', '48.CH', '48.MW'], 'contains': ['192.HN', '192.HR', '192.HX', '192.JW', '192.KB', '192.LJ', '192.ME'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922473375925652905521, 134021394930826866723126, 25903229683158464676480, 53952035291802302422343, 378358649363678452761737], 'label': '3072.bgb.96.IY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.DK', 'old_label': '96.iw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.IY', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760527
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.IZ', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.F', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BA', '48.BC', '48.MJ'], 'contains': ['192.HO', '192.HS', '192.HV', '192.LD', '192.LH', '192.LP', '192.LW'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [51469042011382569606, 79804429416356250372480, 378358770650295628183080, 270240484111912758504367, 25903229683158464676480], 'label': '3072.bgb.96.IZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BO', 'old_label': '96.ix1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.IZ', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760528
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.JA', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.S', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BB', '48.BC', '48.MJ'], 'contains': ['192.HQ', '192.HS', '192.HU', '192.LD', '192.LH', '192.LQ', '192.MB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [51469042011382569606, 79804429416356250372480, 378358770648994141276807, 270240484111912758504367, 25903229683158464676480], 'label': '3072.bgb.96.JA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BO', 'old_label': '96.iy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.JA', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760529
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.JB', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.F', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BA', '48.BE', '48.MJ'], 'contains': ['192.HO', '192.HT', '192.HU', '192.LH', '192.LI', '192.LW', '192.LX'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79804429416356250372480, 378358770650295628183080, 270240484111912758504367, 25852272837936812846761, 25903229683158464676480], 'label': '3072.bgb.96.JB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BO', 'old_label': '96.iz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.JB', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760530
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.JC', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.F', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.CA', '48.CG', '48.NC'], 'contains': ['192.HP', '192.HX', '192.HY', '192.LJ', '192.LL', '192.LY', '192.LZ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922594664024732247801, 378358770650295628183080, 25852272837936812846761, 79804308125641822294440, 25903229683158464676480], 'label': '3072.bgb.96.JC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.DK', 'old_label': '96.ja1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.JC', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760531
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.JD', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.S', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BB', '48.BE', '48.MJ'], 'contains': ['192.HQ', '192.HT', '192.HV', '192.LH', '192.LI', '192.MB', '192.MC'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79804429416356250372480, 378358770648994141276807, 270240484111912758504367, 25852272837936812846761, 25903229683158464676480], 'label': '3072.bgb.96.JD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BO', 'old_label': '96.jb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.JD', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760532
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.JE', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.S', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.CA', '48.CH', '48.NC'], 'contains': ['192.HR', '192.HW', '192.HY', '192.LJ', '192.LL', '192.ME', '192.MG'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [51469042011382569606, 187922594664024732247801, 378358770648994141276807, 79804308125641822294440, 25903229683158464676480], 'label': '3072.bgb.96.JE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.DK', 'old_label': '96.jc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.JE', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760533
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.CA', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.D', '6.F', '6.N', '6.O'], 'contains': ['24.B', '24.DX', '24.EC', '24.ER', '24.ET', '24.HO', '24.HS', '24.HU'], 'core': '24.B', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 122002101738321960, 187922473375925652905521, 133970303627361494479417, 108118165248982343710201, 162070456272950954131199, 53952412691500576681559], 'label': '3072.bgb.12.CA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.ca1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CA', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184760534
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.JF', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '768.I', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DG', '48.DH', '48.MZ'], 'contains': ['192.ID', '192.IF', '192.II', '192.JF', '192.JN', '192.KD', '192.KG'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922473375925652905521, 25903229683158464676480, 108118287251071627990321, 378358905093235639407953, 162070456272950954131199], 'label': '3072.bgb.96.JF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.jd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.JF', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760535
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.JG', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.O', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.CB', '48.CK', '48.MH'], 'contains': ['192.IJ', '192.IL', '192.IQ', '192.KV', '192.KX', '192.LM', '192.LU'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [378358770648994141276807, 79804308125641822294440, 134021394933610431760703, 25903229683158464676480, 53952035291802302422343], 'label': '3072.bgb.96.JG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '96.je1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.JG', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760536
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.JH', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.O', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.CC', '48.CK', '48.MH'], 'contains': ['192.IJ', '192.IL', '192.IO', '192.KV', '192.KZ', '192.LG', '192.LV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [378358770650295628183080, 79804308125641822294440, 134021394933610431760703, 25903229683158464676480, 79855264262271969233416], 'label': '3072.bgb.96.JH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '96.jf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.JH', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760537
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.JI', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.O', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.CB', '48.CK', '48.MK'], 'contains': ['192.IL', '192.IP', '192.IQ', '192.LK', '192.LM', '192.LT', '192.LV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229683158464676480, 134021272934136496216343, 187922594661241166512703, 242089752359655799966096, 79855264262271969233416], 'label': '3072.bgb.96.JI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '96.jg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.JI', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760538
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.JJ', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.O', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.CC', '48.CK', '48.MK'], 'contains': ['192.IL', '192.IO', '192.IP', '192.LG', '192.LK', '192.LU', '192.MA'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [242089752358354392177983, 25903229683158464676480, 134021272934136496216343, 53952035291802302422343, 187922594661241166512703], 'label': '3072.bgb.96.JJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '96.jh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.JJ', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760539
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.JK', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.F', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.CG', '48.CL', '48.MW'], 'contains': ['192.HP', '192.HX', '192.IM', '192.IO', '192.IR', '192.JW', '192.JZ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922473375925652905521, 134021394930826866723126, 25903229683158464676480, 53952035291802302422343, 378358649362364591657542], 'label': '3072.bgb.96.JK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.DK', 'old_label': '96.ji1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.JK', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760540
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.JL', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.S', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.CH', '48.CL', '48.MW'], 'contains': ['192.HR', '192.HW', '192.IM', '192.IQ', '192.IR', '192.JW', '192.KB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922473375925652905521, 134021394930826866723126, 25903229683158464676480, 378358649363678452761737, 79855264262271969233416], 'label': '3072.bgb.96.JL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.DK', 'old_label': '96.jj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.JL', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760541
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.JM', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.F', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.CG', '48.CL', '48.NC'], 'contains': ['192.HP', '192.HW', '192.IM', '192.IO', '192.IS', '192.LL', '192.LZ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [51469042011382569606, 187922594664024732247801, 378358770650295628183080, 79804308125641822294440, 25903229683158464676480], 'label': '3072.bgb.96.JM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.DK', 'old_label': '96.jk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.JM', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760542
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.JN', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.S', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.CH', '48.CL', '48.NC'], 'contains': ['192.HR', '192.HX', '192.IM', '192.IQ', '192.IS', '192.LL', '192.MG'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922594664024732247801, 378358770648994141276807, 25852272837936812846761, 79804308125641822294440, 25903229683158464676480], 'label': '3072.bgb.96.JN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.DK', 'old_label': '96.jl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.JN', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760543
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.JO', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.I', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DI', '48.MZ'], 'contains': ['192.ID', '192.II', '192.IT', '192.JQ', '192.KE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358905094537127039998, 187922473375925652905521, 134021272931340477137406, 25903229683158464676480, 162070456272950954131199], 'label': '3072.bgb.96.JO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.jm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.JO', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760544
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.CB', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.E', '6.G', '6.L', '6.O'], 'contains': ['24.B', '24.DY', '24.EG', '24.EH', '24.EK', '24.HK', '24.HP', '24.HV'], 'core': '24.B', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229681844523013167, 108118165248982343710201, 187922473375925652905521, 133970303627361494479417, 122002101738321960, 1313941673647, 378358649363678452761737, 162070456272950954131199], 'label': '3072.bgb.12.CB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.cb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CB', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184760545
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.JP', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.T', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BQ', '48.BR', '48.NL'], 'contains': ['192.IX', '192.JA', '192.JB', '192.KI', '192.KQ', '192.LW', '192.MB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79804429416356250372480, 350207796319225162214423, 25903229683158464676480, 134021272934136496216343, 216288705272228144236816], 'label': '3072.bgb.96.JP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BX', 'old_label': '96.jn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.JP', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760546
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.JQ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.T', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BR', '48.NL'], 'contains': ['192.IX', '192.JA', '192.KM', '192.KP', '192.LW'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804429416356250372480, 108118287253867647069496, 25903229683158464676480, 216288705272228144236816, 350207796317911301110456], 'label': '3072.bgb.96.JQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BX', 'old_label': '96.jo1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.JQ', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760547
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.JR', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.T', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BQ', '48.NL'], 'contains': ['192.IX', '192.JB', '192.KN', '192.KP', '192.MB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804429416356250372480, 108118287253867647069496, 216288705273529552035263, 25903229683158464676480, 350207796317911301110456], 'label': '3072.bgb.96.JR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BX', 'old_label': '96.jp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.JR', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760548
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.JS', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.T', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.NM'], 'contains': ['192.IY', '192.KS', '192.KT'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [324355779217738848775558, 108118287253867647069496, 242140721662339602266753, 54003382330230002441647, 25903229683158464676480], 'label': '3072.bgb.96.JS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.NM', 'old_label': '96.jq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.JS', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760549
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.JT', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.K', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.OC'], 'contains': ['192.JV', '192.KA', '192.KC', '192.KK', '192.KT', '192.KY', '192.LC'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79804429415054842584367, 133970303627361494479417, 25903229683158464676480, 25852017102974698844878, 242089752359655799966096], 'label': '3072.bgb.96.JT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.OC', 'old_label': '96.jr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.JT', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760550
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.JU', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.K', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DK', '48.OC'], 'contains': ['192.JU', '192.KA', '192.KM', '192.KR', '192.KY'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [133970303627361494479417, 54003382328928594643200, 25903229683158464676480, 25852017102974698844878, 242089752359655799966096], 'label': '3072.bgb.96.JU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GO', 'old_label': '96.js1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.JU', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760551
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.JV', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.K', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DL', '48.OC'], 'contains': ['192.JU', '192.KC', '192.KN', '192.KR', '192.LC'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [242089752358354392177983, 133970303627361494479417, 54003382328928594643200, 25903229683158464676480, 25852017102974698844878], 'label': '3072.bgb.96.JV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GO', 'old_label': '96.jt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.JV', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760552
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.JW', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.K', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DK', '48.DL', '48.OD'], 'contains': ['192.JU', '192.KO', '192.KQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79855142625594763233847, 79855398716250260275073, 187922473375925652905521, 133970303627361494479417, 1313941673647], 'label': '3072.bgb.96.JW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GO', 'old_label': '96.ju1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.JW', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760553
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.JX', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '768.I', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DI', '48.DJ', '48.OS'], 'contains': ['192.JE', '192.JG', '192.JJ', '192.JR', '192.KE', '192.KF', '192.KH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922473021741077083393, 187922473375925652905521, 51212594192254410823, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.96.JX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.jv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.JX', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760554
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.JY', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.I', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DG', '48.OS'], 'contains': ['192.JE', '192.JL', '192.JO', '192.KD', '192.KF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922473375925652905521, 162121669227129588479873, 1313941673647, 25852017101492540879976, 162070456272950954131199], 'label': '3072.bgb.96.JY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.jw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.JY', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760555
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.CC', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.G', '6.G', '6.M', '6.N'], 'contains': ['24.B', '24.EA', '24.ED', '24.EI', '24.EJ'], 'core': '24.B', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 133970303627361494479417, 122002101738321960, 1313941673647, 134021529040297499210286, 162070456272950954131199], 'label': '3072.bgb.12.CC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.cc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CC', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184760556
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.JZ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.I', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DH', '48.OS'], 'contains': ['192.JG', '192.JM', '192.JO', '192.KD', '192.KH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922473021741077083393, 187922473375925652905521, 1313941673647, 25852017101492540879976, 162070456272950954131199], 'label': '3072.bgb.96.JZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.jx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.JZ', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760557
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.KA', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.I', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DJ', '48.MZ'], 'contains': ['192.JF', '192.JP', '192.JQ', '192.KE', '192.KG'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922473375925652905521, 134021272931340477137406, 25903229683158464676480, 378358905093235639407953, 162070456272950954131199], 'label': '3072.bgb.96.KA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.jy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.KA', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760558
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.KB', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.W', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.CB', '48.DA', '48.MH'], 'contains': ['192.KV', '192.KX', '192.LA', '192.LF', '192.LM', '192.LV', '192.ME'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [378358770648994141276807, 79804308125641822294440, 134021394933610431760703, 25903229683158464676480, 79855264262271969233416], 'label': '3072.bgb.96.KB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '96.jz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.KB', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760559
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.KC', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.W', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.CC', '48.DA', '48.MH'], 'contains': ['192.KV', '192.KZ', '192.LA', '192.LF', '192.LG', '192.LU', '192.LY'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [378358770650295628183080, 79804308125641822294440, 134021394933610431760703, 25903229683158464676480, 53952035291802302422343], 'label': '3072.bgb.96.KC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '96.ka1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.KC', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760560
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.KD', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.W', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.CB', '48.DA', '48.MK'], 'contains': ['192.LF', '192.LK', '192.LM', '192.LT', '192.LU', '192.MD', '192.ME'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229683158464676480, 134021272934136496216343, 53952035291802302422343, 187922594661241166512703, 242089752359655799966096], 'label': '3072.bgb.96.KD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '96.kb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.KD', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760561
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.KE', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.W', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.CC', '48.DA', '48.MK'], 'contains': ['192.LF', '192.LG', '192.LK', '192.LV', '192.LY', '192.MA', '192.MD'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [242089752358354392177983, 25903229683158464676480, 134021272934136496216343, 187922594661241166512703, 79855264262271969233416], 'label': '3072.bgb.96.KE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '96.kc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.KE', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760562
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.KF', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '384.FW', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DM', '48.DN', '48.DO', '48.DP', '48.DQ', '48.DR', '48.DS'], 'contains': ['192.A', '192.C', '192.MH', '192.MK', '192.MT', '192.MU', '192.MY', '192.NB'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 122002101738321960, 1313941673647], 'label': '3072.bgb.96.KF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.kd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.KF', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760563
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.KG', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '384.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.A', '48.DM', '48.DT', '48.DU'], 'contains': ['192.A', '192.D', '192.E', '192.F', '192.K', '192.M', '192.MI', '192.MN', '192.MV'], 'core': '192.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 51212588579793007921, 122002101738321960, 1313941673647, 51212962568394582352], 'label': '3072.bgb.96.KG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.ke1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.KG', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760564
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.KH', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.A', '48.DN', '48.DQ', '48.DU', '48.DV', '48.DW', '48.DX', '48.DY', '48.DZ', '48.EA'], 'contains': ['192.A', '192.G', '192.H', '192.MJ', '192.MP', '192.MW', '192.MX'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229681844523013167, 51212588579793007921, 79804308125641822294440, 122002101738321960, 1313941673647], 'label': '3072.bgb.96.KH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.kf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.KH', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184760565
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.KI', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DN', '48.DO', '48.DR', '48.DV', '48.EB', '48.EC', '48.ED'], 'contains': ['192.A', '192.ML', '192.MR', '192.MZ', '192.NA'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79855398717732338388456, 25903229681844523013167, 122002101738321960, 1313941673647, 79804429421968711780537], 'label': '3072.bgb.96.KI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '96.kg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.KI', 'subgroup_fusion': None, 'weyl_group': '128.1578'}
  • id: 184760566
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.CD', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.F'], 'contains': ['24.FG', '24.FH', '24.FI', '24.FM', '24.FN', '24.FO', '24.FQ', '24.GS', '24.GT', '24.GV', '24.HA', '24.HE', '24.HG', '24.HJ', '24.HS'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [187922594664024732247801, 25903229681844523013167, 108118165248982343710201, 53952412691500576681559, 51212588579793007921, 133970303627361494479417, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.12.CD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.cd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CD', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 184760567
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.KJ', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.226', 'aut_weyl_index': 64, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.B', '48.DT', '48.DW'], 'contains': ['192.A', '192.I', '192.J', '192.MM', '192.MQ'], 'core': '192.A', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [25903229681844523013167, 51212588579793007921, 122002101738321960, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.96.KJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.H', 'old_label': '96.kh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.KJ', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 184760568
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.KK', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.C', '48.DT', '48.DX', '48.EB'], 'contains': ['192.A', '192.L', '192.N', '192.MO', '192.MS'], 'core': '192.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 378307680063817574222641, 122002101738321960, 1313941673647], 'label': '3072.bgb.96.KK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.P', 'old_label': '96.ki1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.KK', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760569
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.KL', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.BE', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DM', '48.EE', '48.EL'], 'contains': ['192.O', '192.P', '192.Q', '192.T', '192.MH', '192.MI', '192.MN', '192.NC', '192.NV'], 'core': '384.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229691554491852799, 25903229681844523013167, 122002101738321960, 1313941673647, 51212962568394582352], 'label': '3072.bgb.96.KL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.kj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.KL', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760570
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.KM', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '384.FZ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DQ', '48.EE', '48.EG', '48.EH', '48.EI', '48.EM', '48.FA'], 'contains': ['192.R', '192.MH', '192.MJ', '192.MK', '192.ND', '192.NG', '192.OA', '192.OH'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79855520714221614566521, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647], 'label': '3072.bgb.96.KM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.kk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.KM', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760571
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.KN', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.FZ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DN', '48.EF', '48.EI', '48.EM', '48.EN', '48.EO', '48.FA'], 'contains': ['192.S', '192.MH', '192.MJ', '192.ML', '192.NE', '192.NF', '192.OD', '192.OF'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855520714221614566521, 79855398717732338388456, 25903229681844523013167, 122002101738321960, 1313941673647], 'label': '3072.bgb.96.KN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.kl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.KN', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760572
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.KO', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DR', '48.EF', '48.EH', '48.EJ', '48.EM', '48.EQ', '48.FB'], 'contains': ['192.MH', '192.MK', '192.MR', '192.NH', '192.NP', '192.OU', '192.QQ'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 79804429421968711780537], 'label': '3072.bgb.96.KO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.km1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.KO', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760573
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.KP', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DO', '48.EF', '48.EJ', '48.EM', '48.EN', '48.ET', '48.FB'], 'contains': ['192.MH', '192.ML', '192.MR', '192.NI', '192.NN', '192.PH', '192.QM'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855398717732338388456, 25903229681844523013167, 122002101738321960, 1313941673647, 187922594658424724202816], 'label': '3072.bgb.96.KP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.kn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.KP', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760574
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.KQ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '192.QC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DN', '48.EI', '48.EJ', '48.EQ', '48.ET', '48.EZ', '48.FB'], 'contains': ['192.MH', '192.MP', '192.MR', '192.NJ', '192.NL', '192.PX', '192.QF'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 79804429421968711780537], 'label': '3072.bgb.96.KQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.ko1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.KQ', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760575
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.KR', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '192.MW', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DS', '48.EK', '48.EM', '48.EP', '48.EQ', '48.FA', '48.FB'], 'contains': ['192.MH', '192.MK', '192.NO', '192.NQ', '192.OV'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229691554491852799, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647], 'label': '3072.bgb.96.KR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.kp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.KR', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760576
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.KS', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '192.OK', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DR', '48.EN', '48.ER', '48.ES', '48.ET', '48.FA', '48.FB'], 'contains': ['192.MH', '192.ML', '192.NM', '192.NR', '192.PI'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79855398717732338388456, 25903229681844523013167, 187973685961890096441600, 122002101738321960, 1313941673647], 'label': '3072.bgb.96.KS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '96.kq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.KS', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760577
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.CE', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.F'], 'contains': ['24.FG', '24.FJ', '24.FM', '24.FP', '24.FT', '24.FV', '24.FY', '24.GD', '24.GF', '24.GG', '24.GK', '24.GS', '24.GX', '24.HE', '24.HO'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 187922594664024732247801, 25903229681844523013167, 53952412691500576681559, 187973685961890096441600, 1313941673647, 79804429413572684637382, 25852017102974698844878], 'label': '3072.bgb.12.CE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.ce1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CE', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 184760578
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.KT', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '192.QC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DQ', '48.EL', '48.EO', '48.EU', '48.EV', '48.EW', '48.EX', '48.EY', '48.EZ', '48.FB'], 'contains': ['192.U', '192.V', '192.MH', '192.MP', '192.NK', '192.NS', '192.PY'], 'core': '384.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229681844523013167, 187973685961890096441600, 79804308125641822294440, 122002101738321960, 1313941673647], 'label': '3072.bgb.96.KT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.kr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.KT', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184760579
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.KU', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '384.F', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DU', '48.EE', '48.FC'], 'contains': ['192.W', '192.Z', '192.BA', '192.BO', '192.BQ', '192.MI', '192.MJ', '192.MN', '192.NT'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25852138386775177898303, 25903229681844523013167, 122002101738321960, 1313941673647, 51212962568394582352], 'label': '3072.bgb.96.KU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.ks1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.KU', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760580
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.KV', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '384.J', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.D', '48.DT', '48.FC', '48.FI'], 'contains': ['192.Y', '192.BB', '192.BC', '192.CE', '192.CF', '192.MI', '192.MM', '192.MO', '192.NU'], 'core': '384.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 25852272837936812846761, 122002101738321960, 1313941673647], 'label': '3072.bgb.96.KV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '96.kt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.KV', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760581
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.KW', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '192.CX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.E', '48.DT', '48.FC', '48.FL'], 'contains': ['192.BG', '192.BH', '192.DR', '192.DT', '192.MI', '192.MQ', '192.MS'], 'core': '384.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 378307680063817574222641, 122002101738321960, 1313941673647, 404210922196204071249966], 'label': '3072.bgb.96.KW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '96.ku1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.KW', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760582
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.KX', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '384.BC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DM', '48.EE', '48.EK', '48.FE', '48.FF', '48.FG', '48.FS'], 'contains': ['192.X', '192.BI', '192.MI', '192.MK', '192.NW', '192.NZ'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 404210922196204071249966], 'label': '3072.bgb.96.KX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.kv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.KX', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760583
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.KY', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '192.CX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DU', '48.EL', '48.FD', '48.FH', '48.FI', '48.FJ', '48.FK', '48.FL', '48.FM', '48.FN', '48.FO', '48.FP', '48.FQ', '48.FR', '48.FS'], 'contains': ['192.BD', '192.BE', '192.BF', '192.BJ', '192.DL', '192.MI', '192.MP', '192.NX', '192.NY'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 404210922196204071249966], 'label': '3072.bgb.96.KY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.kw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.KY', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184761626
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '384.HH', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '192.FY', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.FY', '192.QY', '192.QZ'], 'contains': ['768.BM', '768.BX', '768.BY'], 'core': '3072.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [9709968839632, 25852138389591620222016, 108118286902479131308678], 'label': '3072.bgb.384.HH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.IR', 'old_label': '384.gs1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.HH', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184760584
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.KZ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DN', '48.EF', '48.EH', '48.EI', '48.EM', '48.FT', '48.FW'], 'contains': ['192.MJ', '192.MK', '192.MR', '192.OB', '192.OC', '192.OI', '192.OJ'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 133970303635757521608262], 'label': '3072.bgb.96.KZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.kx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.KZ', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184760585
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.LA', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DV', '48.EF', '48.EI', '48.EN', '48.FT', '48.FU', '48.FV'], 'contains': ['192.MJ', '192.ML', '192.MR', '192.OE', '192.OG'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25852138386775177898303, 79855398717732338388456, 25903229681844523013167, 122002101738321960, 1313941673647], 'label': '3072.bgb.96.LA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '96.ky1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.LA', 'subgroup_fusion': None, 'weyl_group': '128.1578'}
  • id: 184760586
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.LB', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DW', '48.FC', '48.FX'], 'contains': ['192.BK', '192.BL', '192.BM', '192.BN', '192.MJ', '192.MM', '192.MQ'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855520714221614566521, 25903229681844523013167, 122002101738321960, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.96.LB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.R', 'old_label': '96.kz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.LB', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760587
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.LC', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DX', '48.FC', '48.FU'], 'contains': ['192.BP', '192.BR', '192.MJ', '192.MO', '192.MS'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 122002101738321960, 1313941673647, 324406870523993839248121], 'label': '3072.bgb.96.LC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.P', 'old_label': '96.la1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.LC', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760588
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.CF', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.I', '6.F'], 'contains': ['24.FH', '24.FJ', '24.FN', '24.FP', '24.FU', '24.FW', '24.FZ', '24.GE', '24.GF', '24.GH', '24.GK', '24.GT', '24.HB', '24.HG', '24.HU'], 'core': '48.D', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 53952412691500576681559, 187973685961890096441600, 133970303627361494479417, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.12.CF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.cf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CF', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 184760589
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.LD', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.A', '48.EI', '48.EO', '48.FD', '48.FW', '48.FX', '48.FY', '48.FZ', '48.GA', '48.GB'], 'contains': ['192.BS', '192.BT', '192.MJ', '192.MP', '192.OK', '192.OL'], 'core': '384.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229681844523013167, 79855398709336311235223, 79804308125641822294440, 122002101738321960, 1313941673647], 'label': '3072.bgb.96.LD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.lb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.LD', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184760590
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.LE', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DN', '48.EI', '48.EJ', '48.FB', '48.GG', '48.GH', '48.GS'], 'contains': ['192.MK', '192.ML', '192.MP', '192.OM', '192.OR', '192.PF', '192.PW'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 122002101738321960, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.96.LE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.lc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.LE', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760591
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.LF', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '384.FZ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DO', '48.EF', '48.FA', '48.FE', '48.GC', '48.GH', '48.GS'], 'contains': ['192.MK', '192.ML', '192.OO', '192.OS', '192.PG'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 79855398717732338388456, 25903229681844523013167, 122002101738321960, 1313941673647], 'label': '3072.bgb.96.LF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.ld1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.LF', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760592
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.LG', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '384.BD', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DM', '48.EE', '48.EP', '48.GC', '48.GD', '48.GJ', '48.GR'], 'contains': ['192.BU', '192.BV', '192.MK', '192.MN', '192.OP', '192.PS'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229337376182892926, 25903229681844523013167, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.LG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.le1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.LG', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760593
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.LH', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DO', '48.EH', '48.EJ', '48.EQ', '48.FF', '48.FT', '48.GD'], 'contains': ['192.MK', '192.MR', '192.OW', '192.OX', '192.QR'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 134021394929311911342598], 'label': '3072.bgb.96.LH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.lf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.LH', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760594
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.LI', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '384.BD', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DP', '48.EG', '48.EP', '48.FE', '48.FG', '48.GD', '48.GN'], 'contains': ['192.MK', '192.OY'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 378358905093235639407953], 'label': '3072.bgb.96.LI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.lg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.LI', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760595
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.LJ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '384.BC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DP', '48.EG', '48.EK', '48.FF', '48.GC', '48.GO', '48.GR'], 'contains': ['192.MK', '192.OZ'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 162121669227129588479873, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.LJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.lh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.LJ', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760596
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.LK', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DR', '48.EM', '48.FT', '48.GE', '48.GF', '48.GH', '48.GS'], 'contains': ['192.MK', '192.ML', '192.ON', '192.PB', '192.QL'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.LK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '96.li1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.LK', 'subgroup_fusion': None, 'weyl_group': '128.1578'}
  • id: 184760597
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.LL', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DQ', '48.EQ', '48.FS', '48.FW', '48.GG', '48.GI', '48.GJ', '48.GK', '48.GL', '48.GM', '48.GN', '48.GO', '48.GP', '48.GQ', '48.GS'], 'contains': ['192.BW', '192.BX', '192.MK', '192.MP', '192.OQ', '192.PA', '192.QE'], 'core': '384.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647], 'label': '3072.bgb.96.LL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.lj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.LL', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184760598
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.LM', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '384.20100', 'aut_weyl_index': 16, 'centralizer': '384.FW', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.F', '48.DS', '48.EH', '48.FG', '48.GR', '48.GS'], 'contains': ['192.MK', '192.OT', '192.PC'], 'core': '384.A', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.96.LM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '96.lk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.LM', 'subgroup_fusion': None, 'weyl_group': '192.1538'}
  • id: 184760599
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '12.CG', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.F'], 'contains': ['24.FI', '24.FO', '24.FT', '24.FU', '24.FV', '24.FW', '24.GB', '24.GD', '24.GE', '24.GG', '24.GH', '24.GN', '24.GQ', '24.HA', '24.HS'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [187922594664024732247801, 25903229681844523013167, 108118165248982343710201, 53952412691500576681559, 187973685961890096441600, 133970303627361494479417, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.12.CG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.cg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CG', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184760600
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.LN', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EB', '48.ER', '48.FU', '48.GE', '48.GT', '48.GX', '48.HE'], 'contains': ['192.BY', '192.BZ', '192.ML', '192.MO', '192.PD', '192.PV'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 122002101738321960, 1313941673647, 134021272934136496216343, 216288705272228144236816], 'label': '3072.bgb.96.LN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.F', 'old_label': '96.ll1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.LN', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184760601
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.LO', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ED', '48.EF', '48.EJ', '48.ET', '48.FT', '48.GT', '48.GU'], 'contains': ['192.ML', '192.MR', '192.PJ', '192.PK', '192.QN'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79855398717732338388456, 25903229681844523013167, 122002101738321960, 1313941673647, 134021394929311911342598], 'label': '3072.bgb.96.LO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '96.lm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.LO', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760602
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.LP', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EB', '48.ES', '48.FU', '48.GF', '48.GU', '48.GZ', '48.HF'], 'contains': ['192.ML', '192.MS'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [51347406816160329727, 79855398717732338388456, 25903229681844523013167, 122002101738321960, 1313941673647], 'label': '3072.bgb.96.LP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.F', 'old_label': '96.ln1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.LP', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184760603
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.LQ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EC', '48.ER', '48.FV', '48.GF', '48.GT', '48.HA', '48.HF'], 'contains': ['192.ML', '192.PL'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855398717732338388456, 25903229681844523013167, 122002101738321960, 1313941673647, 134021529040297499210286], 'label': '3072.bgb.96.LQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.F', 'old_label': '96.lo1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.LQ', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184760604
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.LR', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EC', '48.ES', '48.FV', '48.GE', '48.GU', '48.HD', '48.HE'], 'contains': ['192.ML', '192.QO'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 242140721662339602266753, 122002101738321960, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.96.LR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.F', 'old_label': '96.lp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.LR', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184760605
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.LS', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DV', '48.EO', '48.ET', '48.FH', '48.GG', '48.GH', '48.GV', '48.GW', '48.GX', '48.GY', '48.GZ', '48.HA', '48.HB', '48.HC', '48.HD'], 'contains': ['192.CA', '192.CB', '192.ML', '192.MP', '192.PE', '192.PM', '192.QD'], 'core': '384.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [53952291033879672806278, 79855398717732338388456, 25903229681844523013167, 122002101738321960, 1313941673647], 'label': '3072.bgb.96.LS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.lq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.LS', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184760606
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.LT', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '384.20100', 'aut_weyl_index': 16, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.G', '48.ED', '48.EN', '48.GH', '48.HE', '48.HF'], 'contains': ['192.ML', '192.PN', '192.QP'], 'core': '384.A', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 122002101738321960, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.96.LT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.C', 'old_label': '96.lr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.LT', 'subgroup_fusion': None, 'weyl_group': '384.20100'}
  • id: 184760607
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.LU', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.H', '48.DT', '48.FC', '48.HG'], 'contains': ['192.CC', '192.CD', '192.CG', '192.CH', '192.MM', '192.MN', '192.MS'], 'core': '384.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [54003126248003449434936, 25903229681844523013167, 122002101738321960, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.96.LU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '96.ls1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.LU', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760608
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.LV', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.B', '48.DW', '48.EU', '48.FI', '48.FJ', '48.FX', '48.GI', '48.GV', '48.HG', '48.HH', '48.HI', '48.HJ', '48.HK', '48.HL', '48.HM'], 'contains': ['192.CI', '192.CJ', '192.CK', '192.CL', '192.MM', '192.MP', '192.PO', '192.PP'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.96.LV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.lt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.LV', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184760609
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.LW', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.I', '48.DT', '48.FC', '48.HN'], 'contains': ['192.CM', '192.CQ', '192.CV', '192.DS', '192.MN', '192.MO', '192.MQ'], 'core': '384.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 122002101738321960, 1313941673647, 324355523485385682622200], 'label': '3072.bgb.96.LW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '96.lu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.LW', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760610
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.CH', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.H'], 'contains': ['24.GN', '24.GP', '24.GR', '24.GU', '24.GW', '24.HI', '24.HM'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804308122845802507662, 25903229681844523013167, 108118165248982343710201, 187922473375925652905521, 296092500500710274860657, 25852272837936812846761, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.12.CH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '12.ch1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CH', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 184760611
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.LX', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '384.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DU', '48.EL', '48.FY', '48.GJ', '48.GW', '48.HG', '48.HH', '48.HN', '48.HO', '48.HP', '48.HQ', '48.HR', '48.HS', '48.HT', '48.HU'], 'contains': ['192.CN', '192.CO', '192.CP', '192.CR', '192.DA', '192.MN', '192.MP', '192.PQ', '192.PR'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 25903107685154153232142, 122002101738321960, 1313941673647, 51090958997032170942], 'label': '3072.bgb.96.LX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.lv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.LX', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184760612
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.LY', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EB', '48.FU', '48.HW'], 'contains': ['192.MO', '192.MR', '192.MS'], 'core': '384.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 122002101738321960, 1313941673647, 296041409911409376977422], 'label': '3072.bgb.96.LY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BC', 'old_label': '96.lw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.LY', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760613
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.LZ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '384.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DX', '48.EV', '48.FI', '48.FK', '48.FZ', '48.GK', '48.GX', '48.HI', '48.HN', '48.HO', '48.HV', '48.HW', '48.HX', '48.HY', '48.HZ'], 'contains': ['192.CS', '192.CT', '192.CU', '192.CW', '192.CZ', '192.MO', '192.MP', '192.PT', '192.PU'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647], 'label': '3072.bgb.96.LZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.lx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.LZ', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184760614
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '96.MA', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '48.C', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.C', '48.DW', '48.EW', '48.FL', '48.FM', '48.FX', '48.GL', '48.GY', '48.HN', '48.HP', '48.HV', '48.IA', '48.IB', '48.IC', '48.ID'], 'contains': ['192.CX', '192.CY', '192.DK', '192.MP', '192.MQ'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 25903364135789722998960], 'label': '3072.bgb.96.MA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.ly1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.MA', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760615
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.MB', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '192.QC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DV', '48.EJ', '48.EZ', '48.FN', '48.FW', '48.HJ', '48.HQ', '48.HW', '48.IA', '48.IE'], 'contains': ['192.MP', '192.MR', '192.PZ', '192.QG'], 'core': '384.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 133970303635757521608262], 'label': '3072.bgb.96.MB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.lz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.MB', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184760616
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.MC', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '192.CX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DX', '48.EX', '48.FL', '48.FO', '48.GA', '48.GM', '48.GZ', '48.HG', '48.HK', '48.HR', '48.HW', '48.IB', '48.IF', '48.IG', '48.IL'], 'contains': ['192.DB', '192.DM', '192.MP', '192.MS'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [51347406816160329727, 25903229681844523013167, 25903107685154153232142, 122002101738321960, 1313941673647], 'label': '3072.bgb.96.MC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.ma1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.MC', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760617
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.MD', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '192.CX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DY', '48.EY', '48.FH', '48.FR', '48.FY', '48.GP', '48.HI', '48.HL', '48.HQ', '48.HX', '48.IB', '48.IC', '48.IF', '48.IH', '48.II'], 'contains': ['192.DC', '192.DN', '192.MP', '192.QH'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 404211043484134973872583, 79804308125641822294440, 122002101738321960, 1313941673647], 'label': '3072.bgb.96.MD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.mb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.MD', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760618
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.ME', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '192.QC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DZ', '48.EW', '48.FK', '48.FP', '48.GB', '48.GI', '48.GV', '48.HR', '48.HS', '48.HX', '48.IA', '48.IG', '48.IH', '48.IJ', '48.IM'], 'contains': ['192.DD', '192.DO', '192.MP', '192.QI'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108169512287410083283217, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647], 'label': '3072.bgb.96.ME', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.mc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ME', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760619
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.MF', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '192.CX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EA', '48.EV', '48.FM', '48.FQ', '48.FZ', '48.GM', '48.HB', '48.HH', '48.HM', '48.HS', '48.IC', '48.IE', '48.II', '48.IJ', '48.IL'], 'contains': ['192.DE', '192.DF', '192.MP', '192.QA'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79855264629178445030417, 25903107685154153232142, 122002101738321960, 1313941673647], 'label': '3072.bgb.96.MF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.md1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.MF', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760620
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.MG', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '384.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DY', '48.EY', '48.FD', '48.FN', '48.GQ', '48.GW', '48.HK', '48.HM', '48.HU', '48.HV', '48.HY', '48.ID', '48.IG', '48.IJ', '48.IK'], 'contains': ['192.DG', '192.DP', '192.MP', '192.QJ'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 53952412691500576681559, 25903107685154153232142, 122002101738321960, 1313941673647], 'label': '3072.bgb.96.MG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.me1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.MG', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184760621
    {'ambient': '3072.bgb', 'aut_centralizer_order': 1, 'aut_label': '4.B', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '3072.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.A', '2.D', '2.E'], 'contains': ['8.A', '8.B', '12.BM', '16.F', '16.G'], 'core': '4.B', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [25903229681844523013167, 108118165248982343710201, 187922473375925652905521, 566444897749485959875336, 133970303627361494479417, 404159831259638948150382, 1313941673647, 378358905093235639407953, 162070456272950954131199], 'label': '3072.bgb.4.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': ['2.A', '2.D', '2.E'], 'normal_contains': ['8.A', '8.B'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.B', 'subgroup_fusion': None, 'weyl_group': '3072.bgb'}
  • id: 184760622
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.CI', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.H'], 'contains': ['24.GU', '24.GV', '24.GW', '24.HH', '24.HI', '24.HL', '24.HM'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804308122845802507662, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 270189392822449473928912, 25852272837936812846761, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.12.CI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '12.ci1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CI', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 184760623
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.MH', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '384.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EA', '48.EX', '48.FJ', '48.FP', '48.GA', '48.GK', '48.HC', '48.HL', '48.HP', '48.HT', '48.HZ', '48.ID', '48.IE', '48.IH', '48.IK'], 'contains': ['192.DH', '192.DQ', '192.MP', '192.QK'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.96.MH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.mf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.MH', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184760624
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.MI', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DZ', '48.EU', '48.FO', '48.FQ', '48.GB', '48.GL', '48.GY', '48.HJ', '48.HO', '48.HT', '48.HY', '48.IF', '48.II', '48.IK', '48.IN'], 'contains': ['192.DI', '192.DJ', '192.MP', '192.QB'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 162121413125267185742761, 79804308125641822294440, 122002101738321960, 1313941673647], 'label': '3072.bgb.96.MI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.mg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.MI', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184760625
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.MJ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.X', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DM', '48.IO', '48.IP', '48.IQ', '48.IR', '48.JJ', '48.JS'], 'contains': ['192.DU', '192.DV', '192.DY', '192.DZ', '192.EG', '192.EH', '192.MT', '192.MV', '192.NC', '192.NW', '192.OP'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229337376182892926, 25903229681844523013167, 51212588579793007921, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.MJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.mh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.MJ', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760626
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.MK', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.BF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DM', '48.IS', '48.JJ'], 'contains': ['192.DW', '192.DX', '192.EA', '192.EK', '192.MU', '192.MV', '192.NC', '192.NZ', '192.PS'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229691554491852799, 25852138393689126932998, 25903229681844523013167, 1313941673647, 51212962568394582352], 'label': '3072.bgb.96.MK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.mi1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.MK', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760627
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.ML', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '192.NQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DN', '48.IT', '48.IV', '48.JE', '48.JM', '48.JR', '48.JW'], 'contains': ['192.EB', '192.EC', '192.MT', '192.MW', '192.MZ', '192.NE', '192.NJ', '192.OB', '192.OM'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804308122845802507662, 25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 1313941673647], 'label': '3072.bgb.96.ML', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.mj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ML', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760628
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.MM', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DN', '48.IW', '48.JF', '48.JK', '48.JN', '48.JR', '48.JV'], 'contains': ['192.MT', '192.MX', '192.NA', '192.NF', '192.NL', '192.OC', '192.OR'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 79855520714221614566521, 25903229681844523013167, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.MM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.mk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.MM', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760629
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.MN', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DQ', '48.IR', '48.IU', '48.IX', '48.IY', '48.IZ', '48.JA', '48.JE', '48.JF', '48.JU', '48.JV'], 'contains': ['192.ED', '192.MT', '192.MX', '192.MY', '192.ND', '192.NK', '192.OA', '192.PA'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 1313941673647], 'label': '3072.bgb.96.MN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.ml1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.MN', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760630
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.MO', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DN', '48.JC', '48.JG', '48.JL', '48.JN', '48.JR', '48.JU'], 'contains': ['192.MU', '192.MX', '192.MZ', '192.NE', '192.NL', '192.OI', '192.PF'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [133970182339249961095537, 25903229681844523013167, 51212588579793007921, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.96.MO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.mm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.MO', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760631
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.MP', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '192.NO', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DN', '48.JB', '48.JH', '48.JM', '48.JP', '48.JR', '48.JT'], 'contains': ['192.MU', '192.MW', '192.NA', '192.NF', '192.NJ', '192.OJ', '192.PW'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855398717732338388456, 25903229681844523013167, 1313941673647, 25852017101492540879976, 79804429421968711780537], 'label': '3072.bgb.96.MP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.mn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.MP', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760632
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.MQ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '384.GJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DQ', '48.IS', '48.JD', '48.JG', '48.JH', '48.JK', '48.JL'], 'contains': ['192.EE', '192.MU', '192.MX', '192.NB', '192.NG', '192.NK', '192.OH', '192.QE'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [187922594664024732247801, 25903229681844523013167, 187973685961890096441600, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.96.MQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.mo1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.MQ', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760633
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.CJ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.L'], 'contains': ['24.GX', '24.GY', '24.GZ', '24.HN', '24.HP', '24.HQ', '24.HR'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118421696801471190456, 162070578272437343706839, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647, 79804429413572684637382, 378358649363678452761737], 'label': '3072.bgb.12.CJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '12.cj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CJ', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 184760634
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.MR', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '192.NQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DO', '48.IO', '48.IU', '48.IV', '48.JN', '48.JW'], 'contains': ['192.EF', '192.MT', '192.MZ', '192.NI', '192.OO', '192.OW'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952413035981411118158, 25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 1313941673647], 'label': '3072.bgb.96.MR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.mp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.MR', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760635
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.MS', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DO', '48.IP', '48.IW', '48.JM', '48.JO', '48.JV'], 'contains': ['192.MT', '192.NA', '192.NN', '192.OS', '192.OX'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 1313941673647], 'label': '3072.bgb.96.MS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.mq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.MS', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760636
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.MT', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '384.FW', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DS', '48.IQ', '48.IT', '48.IU', '48.JK', '48.JO'], 'contains': ['192.MT', '192.NB', '192.NO', '192.OT', '192.OV'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [162070578272437343706839, 25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 1313941673647], 'label': '3072.bgb.96.MT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.mr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.MT', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760637
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.MU', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.X', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DP', '48.IO', '48.IP', '48.IQ', '48.IX', '48.JQ', '48.JS'], 'contains': ['192.EI', '192.EJ', '192.MT', '192.OY', '192.OZ'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 162121669227129588479873, 51212588579793007921, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.MU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.ms1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.MU', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760638
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.MV', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DR', '48.IT', '48.IV', '48.IW', '48.JA', '48.JT', '48.JV'], 'contains': ['192.MT', '192.MY', '192.NA', '192.NH', '192.NM', '192.OU', '192.PB'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229691554491852799, 108118165248982343710201, 25903229681844523013167, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.MV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.mt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.MV', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760639
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.MW', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DO', '48.JB', '48.JC', '48.JL', '48.JM', '48.JN', '48.JT'], 'contains': ['192.MU', '192.MZ', '192.NA', '192.NI', '192.NN', '192.PG', '192.QR'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855398717732338388456, 25903229681844523013167, 1313941673647, 108118287251071627990321, 79804429421968711780537], 'label': '3072.bgb.96.MW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.mu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.MW', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760640
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.MX', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.GI', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DR', '48.JB', '48.JC', '48.JK', '48.JL', '48.JO', '48.JP'], 'contains': ['192.MU', '192.NA', '192.NB', '192.NM', '192.NP', '192.QL', '192.QQ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [133970182339249961095537, 79855398717732338388456, 25903229681844523013167, 187973685961890096441600, 1313941673647], 'label': '3072.bgb.96.MX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.mv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.MX', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760641
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.MY', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '192.NQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DQ', '48.JJ', '48.JO', '48.JQ', '48.JR', '48.JT', '48.JW'], 'contains': ['192.EL', '192.EM', '192.MT', '192.MU', '192.MW', '192.ND', '192.NG', '192.NS', '192.OQ'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 1313941673647, 108118287251071627990321], 'label': '3072.bgb.96.MY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.mw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.MY', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760642
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.MZ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '192.NQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DR', '48.JK', '48.JM', '48.JN', '48.JT', '48.JU', '48.JW'], 'contains': ['192.EN', '192.MT', '192.MU', '192.MZ', '192.NH', '192.NP', '192.NR', '192.ON'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [133970182339249961095537, 25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 1313941673647], 'label': '3072.bgb.96.MZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.mx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.MZ', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760643
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.NA', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '192.MU', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DS', '48.JI', '48.JL', '48.JP', '48.JT', '48.JU'], 'contains': ['192.MU', '192.MY', '192.NO', '192.NQ', '192.OT'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [162070578272437343706839, 25903229691554491852799, 25903229681844523013167, 187922473375925652905521, 1313941673647], 'label': '3072.bgb.96.NA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.my1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.NA', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760644
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.CK', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.J', '6.L'], 'contains': ['24.GY', '24.GZ', '24.HB', '24.HQ', '24.HR', '24.HT', '24.HV'], 'core': '48.D', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118421696801471190456, 25903229681844523013167, 108118165248982343710201, 187922473375925652905521, 133970303627361494479417, 1313941673647, 378358649363678452761737, 162070456272950954131199], 'label': '3072.bgb.12.CK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '12.ck1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CK', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 184760645
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '96.NB', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.195', 'aut_weyl_index': 64, 'centralizer': '96.NB', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.K', '48.DS', '48.JS', '48.JV', '48.JW'], 'contains': ['192.EO', '192.MT', '192.NQ', '192.PC'], 'core': '768.A', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.96.NB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '96.mz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.NB', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 184760646
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.NC', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.H', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DU', '48.JJ', '48.KE'], 'contains': ['192.EP', '192.ER', '192.EX', '192.FE', '192.MV', '192.MW', '192.NT', '192.NX', '192.PQ'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229684640542817862, 25903229681844523013167, 51212588579793007921, 1313941673647, 51212962568394582352], 'label': '3072.bgb.96.NC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.na1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.NC', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760647
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.ND', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.C', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DU', '48.IR', '48.IS', '48.JX', '48.JY', '48.JZ', '48.KA'], 'contains': ['192.EQ', '192.ES', '192.EY', '192.FF', '192.MV', '192.MX', '192.NT', '192.NY', '192.PR'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 25852017095880079467006, 25903107685154153232142, 1313941673647, 51090958997032170942], 'label': '3072.bgb.96.ND', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '96.nb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ND', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760648
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.NE', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.Z', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DM', '48.IR', '48.JI', '48.KB', '48.KC', '48.KD', '48.KE'], 'contains': ['192.ET', '192.EU', '192.EZ', '192.FG', '192.MV', '192.MY', '192.NV', '192.NW', '192.OP'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 51212588579793007921, 25852138389591620222016, 1313941673647, 51212962568394582352], 'label': '3072.bgb.96.NE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.nc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.NE', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760649
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.NF', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.BJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DM', '48.IS', '48.KE'], 'contains': ['192.EV', '192.EW', '192.FA', '192.FB', '192.FH', '192.FI', '192.MV', '192.NB', '192.NV', '192.NZ', '192.PS'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25852138393689126932998, 25903229681844523013167, 51212588579793007921, 1313941673647, 51212962568394582352], 'label': '3072.bgb.96.NF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.nd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.NF', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760650
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.NG', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DN', '48.IV', '48.JE', '48.JT', '48.KF', '48.KI', '48.KJ'], 'contains': ['192.MW', '192.MY', '192.MZ', '192.OC', '192.OD', '192.OM', '192.PX'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804308122845802507662, 25903229681844523013167, 187922473375925652905521, 1313941673647, 133970303635757521608262], 'label': '3072.bgb.96.NG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.ne1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.NG', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760651
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.NH', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '384.GI', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DQ', '48.IT', '48.JP', '48.KE', '48.KH', '48.KI', '48.KJ'], 'contains': ['192.FC', '192.FD', '192.MW', '192.MY', '192.NB', '192.OA', '192.OH', '192.OQ', '192.PY'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79855520714221614566521, 25903229681844523013167, 187922473375925652905521, 1313941673647, 108118287251071627990321], 'label': '3072.bgb.96.NH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.nf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.NH', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760652
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.NI', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DN', '48.IW', '48.JA', '48.JF', '48.JL', '48.KG', '48.KJ'], 'contains': ['192.MX', '192.MY', '192.NA', '192.OB', '192.OF', '192.OR', '192.QF'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 51212588579793007921, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.96.NI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.ng1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.NI', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184760653
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.NJ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DV', '48.IV', '48.JB', '48.JM', '48.JR', '48.KF', '48.KJ'], 'contains': ['192.MW', '192.MZ', '192.NA', '192.OE', '192.OG', '192.PE', '192.PZ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952413035981411118158, 79855398717732338388456, 25903229681844523013167, 1313941673647, 79804429421968711780537], 'label': '3072.bgb.96.NJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.nh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.NJ', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760654
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.NK', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DN', '48.IU', '48.JC', '48.JG', '48.JK', '48.KG', '48.KJ'], 'contains': ['192.MX', '192.MZ', '192.NB', '192.OD', '192.OJ', '192.PF', '192.QF'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [133970182339249961095537, 25903229681844523013167, 79804308125641822294440, 1313941673647, 134021272925740469097576], 'label': '3072.bgb.96.NK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.ni1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.NK', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184760655
    {'ambient': '3072.bgb', 'aut_centralizer_order': 1, 'aut_label': '16.A', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '3072.a1', 'complements': ['192.QS', '192.QT', '192.QU', '192.QV'], 'conjugacy_class_count': 1, 'contained_in': ['8.A', '8.B', '8.L', '8.M', '8.N', '8.O'], 'contains': ['48.D', '64.J', '64.K', '64.L'], 'core': '16.A', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 133970303627361494479417, 404159831259638948150382, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.16.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.A', 'normal_contained_in': ['8.A', '8.B'], 'normal_contains': ['48.D'], 'normalizer': '1.a1', 'old_label': '16.a1', 'projective_image': '3072.bgb', 'quotient_action_image': '16.11', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '16.A', 'subgroup_fusion': None, 'weyl_group': '3072.bgb'}
  • id: 184760656
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.NL', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DV', '48.JE', '48.JG', '48.JN', '48.JX', '48.KG'], 'contains': ['192.MX', '192.MZ', '192.OE', '192.PM', '192.QG'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 51212588579793007921, 79804308125641822294440, 134021394933610431760703, 1313941673647], 'label': '3072.bgb.96.NL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.nj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.NL', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760657
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.NM', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '384.GJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DN', '48.IT', '48.JB', '48.JH', '48.JO', '48.KF', '48.KJ'], 'contains': ['192.MW', '192.NA', '192.NB', '192.OF', '192.OI', '192.PW', '192.PX'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855520714221614566521, 79855398717732338388456, 25903229681844523013167, 1313941673647, 25852017101492540879976], 'label': '3072.bgb.96.NM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.nk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.NM', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760658
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.NN', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '384.GJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DV', '48.IW', '48.JC', '48.JF', '48.JH', '48.JY'], 'contains': ['192.MX', '192.NA', '192.OG', '192.QD', '192.QG'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 79855398717732338388456, 25903229681844523013167, 51212588579793007921, 1313941673647], 'label': '3072.bgb.96.NN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.nl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.NN', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760659
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.NO', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.C', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DY', '48.IZ', '48.JD', '48.JX', '48.JY', '48.JZ', '48.KA'], 'contains': ['192.MX', '192.QH', '192.QJ'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 25852017095880079467006, 53952412691500576681559, 25903107685154153232142, 1313941673647], 'label': '3072.bgb.96.NO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '96.nm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.NO', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760660
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '96.NP', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.MH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.A', '48.JE', '48.JH', '48.JR', '48.JZ', '48.KJ'], 'contains': ['192.MW', '192.MX', '192.OK', '192.OL', '192.QC'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79804308122845802507662, 25903229681844523013167, 51212588579793007921, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.96.NP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.nn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.NP', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760661
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.NQ', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '192.1538', 'aut_weyl_index': 32, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.L', '48.A', '48.JF', '48.JG', '48.KA'], 'contains': ['192.B', '192.MX', '192.OL'], 'core': '192.B', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [79855520714221614566521, 25903229681844523013167, 79804308125641822294440, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.96.NQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '96.no1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.NQ', 'subgroup_fusion': None, 'weyl_group': '192.1538'}
  • id: 184760662
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.NR', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DR', '48.IT', '48.IU', '48.JL', '48.KF', '48.KG', '48.KI'], 'contains': ['192.MY', '192.MZ', '192.NB', '192.ON', '192.OU', '192.PI', '192.QQ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [133970182339249961095537, 25903229681844523013167, 187922473375925652905521, 1313941673647, 79804429421968711780537], 'label': '3072.bgb.96.NR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.np1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.NR', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184760663
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.NS', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DO', '48.IV', '48.JU', '48.KB', '48.KG', '48.KI'], 'contains': ['192.MY', '192.MZ', '192.OO', '192.OX', '192.PH'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952413035981411118158, 25903229681844523013167, 187922473375925652905521, 1313941673647, 134021394929311911342598], 'label': '3072.bgb.96.NS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.nq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.NS', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760664
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.NT', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '384.GI', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DO', '48.IW', '48.JA', '48.JP', '48.KC', '48.KF'], 'contains': ['192.MY', '192.NA', '192.OS', '192.OW', '192.QM'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 79855398717732338388456, 25903229681844523013167, 51212588579793007921, 1313941673647], 'label': '3072.bgb.96.NT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.nr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.NT', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760665
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.NU', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.Z', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DP', '48.IY', '48.JI', '48.KB', '48.KC', '48.KD', '48.KH'], 'contains': ['192.MY', '192.OY', '192.OZ'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 51212588579793007921, 25852138389591620222016, 1313941673647, 108118286902479131308678], 'label': '3072.bgb.96.NU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.ns1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.NU', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760666
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '16.B', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '384.5678', 'aut_weyl_index': 16, 'centralizer': '1536.C', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.A', '8.C'], 'contains': ['32.F', '32.K', '32.M', '48.DS', '64.A'], 'core': '192.A', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 566444897749485959875336, 404159831259638948150382, 1313941673647, 486427128433516595381056, 162070456272950954131199], 'label': '3072.bgb.16.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.C', 'old_label': '16.b1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.B', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 184760667
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.NV', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '384.20100', 'aut_weyl_index': 16, 'centralizer': '384.FW', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.M', '48.DS', '48.JA', '48.KD', '48.KI'], 'contains': ['192.MY', '192.OV', '192.PC'], 'core': '768.A', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 51212588579793007921, 133970303627361494479417, 1313941673647], 'label': '3072.bgb.96.NV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '96.nt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.NV', 'subgroup_fusion': None, 'weyl_group': '192.1538'}
  • id: 184760668
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.NW', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DO', '48.IT', '48.JB', '48.JC', '48.JK', '48.KF', '48.KG'], 'contains': ['192.MZ', '192.NA', '192.NB', '192.PG', '192.PH', '192.QM', '192.QR'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855398717732338388456, 25903229681844523013167, 1313941673647, 108118287251071627990321, 187922594658424724202816], 'label': '3072.bgb.96.NW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.nu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.NW', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184760669
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.NX', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ED', '48.IV', '48.JC', '48.JM', '48.JN', '48.KF', '48.KG'], 'contains': ['192.MZ', '192.NA', '192.PJ', '192.PK', '192.PN', '192.QN'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [187922473373129633118743, 79855398717732338388456, 25903229681844523013167, 1313941673647, 79804429421968711780537], 'label': '3072.bgb.96.NX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.nv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.NX', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760670
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.NY', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '192.1540', 'aut_weyl_index': 32, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.N', '48.ED', '48.IW', '48.JB'], 'contains': ['192.NA', '192.QN', '192.QP'], 'core': '768.A', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 51212588579793007921, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.96.NY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.A', 'old_label': '96.nw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.NY', 'subgroup_fusion': None, 'weyl_group': '192.1540'}
  • id: 184760671
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.NZ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.BM', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.EE', '48.IR', '48.JJ', '48.KK', '48.KL', '48.KM', '48.LY'], 'contains': ['192.FJ', '192.FK', '192.FP', '192.FQ', '192.FV', '192.FW', '192.NC', '192.ND', '192.NT', '192.NW', '192.OP'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229691554491852799, 25903229681844523013167, 25852138389591620222016, 1313941673647, 51212962568394582352], 'label': '3072.bgb.96.NZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.nx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.NZ', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760672
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.OA', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.CW', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EE', '48.IS', '48.JJ'], 'contains': ['192.FL', '192.FM', '192.FR', '192.GA', '192.NC', '192.NG', '192.NT', '192.NZ', '192.PS'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25852138386775177898303, 25852138393689126932998, 25903229681844523013167, 1313941673647, 51212962568394582352], 'label': '3072.bgb.96.OA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.ny1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.OA', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760673
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.OB', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.BY', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.EL', '48.IR', '48.IS', '48.KN', '48.KO', '48.KP', '48.KQ'], 'contains': ['192.FN', '192.FO', '192.FS', '192.FT', '192.GF', '192.GG', '192.NC', '192.NK', '192.NV', '192.NY', '192.PR'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107687970595565937, 25903229681844523013167, 25903107685154153232142, 1313941673647, 51090958997032170942], 'label': '3072.bgb.96.OB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '96.nz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.OB', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760674
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.OC', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EM', '48.IT', '48.JU', '48.KS', '48.KU', '48.KW', '48.LZ'], 'contains': ['192.NE', '192.NH', '192.NO', '192.OA', '192.OI', '192.ON', '192.PH'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855520714221614566521, 133970182339249961095537, 25903229681844523013167, 187922473375925652905521, 1313941673647], 'label': '3072.bgb.96.OC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.oa1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.OC', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760675
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.OD', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EM', '48.IU', '48.JT', '48.KR', '48.KT', '48.KW', '48.MA'], 'contains': ['192.ND', '192.NI', '192.NO', '192.OD', '192.OJ', '192.ON', '192.OU'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [133970182339249961095537, 25903229681844523013167, 187922473375925652905521, 1313941673647, 187922594658424724202816], 'label': '3072.bgb.96.OD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.oa2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.OD', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760676
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.OE', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '192.NR', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EF', '48.IV', '48.JN', '48.KU', '48.KW', '48.LD', '48.MC'], 'contains': ['192.FU', '192.NE', '192.NH', '192.NI', '192.OC', '192.OE', '192.OO', '192.PJ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952413035981411118158, 25903229681844523013167, 187922473375925652905521, 1313941673647, 133970303635757521608262], 'label': '3072.bgb.96.OE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.ob1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.OE', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760677
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '16.C', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '192.1537', 'aut_weyl_index': 32, 'centralizer': '1536.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.H'], 'contains': ['32.A', '32.B', '32.C', '32.D', '32.E', '32.H', '32.I', '48.DT', '64.M'], 'core': '192.A', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [51347406816160329727, 378358770650295628183080, 404159952546255909825352, 25903229681844523013167, 25852272837936812846761, 1313941673647, 594545172394561848633606], 'label': '3072.bgb.16.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.C', 'old_label': '16.c1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.C', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 184760678
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.OF', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '384.FZ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.FA', '48.JA', '48.JO', '48.KK', '48.KT', '48.LE'], 'contains': ['192.ND', '192.NM', '192.OF', '192.OS', '192.OV'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 79855398717732338388456, 25903229681844523013167, 187973685961890096441600, 1313941673647], 'label': '3072.bgb.96.OF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.oc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.OF', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760679
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.OG', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EF', '48.IW', '48.JM', '48.KV', '48.LE', '48.LF', '48.LZ'], 'contains': ['192.NF', '192.NH', '192.NN', '192.OB', '192.OG', '192.OS', '192.QN'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229691554491852799, 1313941673647, 25903229681844523013167, 79855398717732338388456, 108118165248982343710201], 'label': '3072.bgb.96.OG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.od1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.OG', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760680
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.OH', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EH', '48.JK', '48.JT', '48.KS', '48.KV', '48.LC', '48.LD'], 'contains': ['192.NG', '192.NH', '192.NP', '192.OC', '192.OJ', '192.OT', '192.QR'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [162070578272437343706839, 25903229681844523013167, 187922473375925652905521, 1313941673647, 133970303635757521608262], 'label': '3072.bgb.96.OH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.oe1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.OH', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760681
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.OI', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EH', '48.JO', '48.JU', '48.KL', '48.KR', '48.LC'], 'contains': ['192.ND', '192.NP', '192.OI', '192.OT', '192.OX'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [162070578272437343706839, 25903229681844523013167, 187922473375925652905521, 1313941673647, 134021394929311911342598], 'label': '3072.bgb.96.OI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.oe2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.OI', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760682
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.OJ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.BM', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.EG', '48.IY', '48.JQ', '48.KK', '48.KL', '48.KM', '48.LY'], 'contains': ['192.FX', '192.FY', '192.ND', '192.OY', '192.OZ'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229691554491852799, 25903229681844523013167, 25852138389591620222016, 1313941673647, 108118286902479131308678], 'label': '3072.bgb.96.OJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.of1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.OJ', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760683
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.OK', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '192.NQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EH', '48.JA', '48.JW', '48.KM', '48.KW', '48.LF'], 'contains': ['192.FZ', '192.ND', '192.NH', '192.OB', '192.OW', '192.PC'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187973685961890096441600, 133970303627361494479417, 1313941673647], 'label': '3072.bgb.96.OK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.og1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.OK', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760684
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.OL', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.FZ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.FA', '48.IT', '48.JL', '48.KT', '48.KU', '48.LJ', '48.LK'], 'contains': ['192.NE', '192.NM', '192.NO', '192.OF', '192.OH', '192.PG', '192.PI'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855520714221614566521, 79855398717732338388456, 25903229681844523013167, 1313941673647, 108118287251071627990321], 'label': '3072.bgb.96.OL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.oh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.OL', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760685
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.OM', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EF', '48.JB', '48.JN', '48.KR', '48.LC', '48.LK', '48.LZ'], 'contains': ['192.NF', '192.NI', '192.NP', '192.OE', '192.OI', '192.PG', '192.QN'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229691554491852799, 1313941673647, 25903229681844523013167, 79855398717732338388456, 108118287251071627990321], 'label': '3072.bgb.96.OM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.oi1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.OM', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760686
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.ON', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EF', '48.JC', '48.JM', '48.KS', '48.LC', '48.LJ', '48.MA'], 'contains': ['192.NE', '192.NN', '192.NP', '192.OG', '192.OJ', '192.PG', '192.PK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 79855398717732338388456, 108118287251071627990321, 133970303635757521608262], 'label': '3072.bgb.96.ON', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.oi2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ON', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760687
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.OO', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EN', '48.IV', '48.JC', '48.KT', '48.KU', '48.LZ', '48.MA'], 'contains': ['192.NE', '192.NI', '192.NM', '192.OD', '192.OG', '192.PH', '192.PN'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [187922473373129633118743, 79855398717732338388456, 25903229681844523013167, 187973685961890096441600, 1313941673647], 'label': '3072.bgb.96.OO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.oj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.OO', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760688
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '16.D', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '384.17949', 'aut_weyl_index': 16, 'centralizer': '1536.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.A', '8.D', '8.E', '8.F'], 'contains': ['32.J', '32.L', '48.A', '64.A'], 'core': '48.A', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 1313941673647, 79804429413572684637382, 486427128433516595381056, 486478219730068018627222, 270189770923792213003566], 'label': '3072.bgb.16.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.H', 'old_label': '16.d1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.D', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 184760689
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.OP', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.GI', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EM', '48.JK', '48.JP', '48.KR', '48.KV', '48.LJ', '48.LK'], 'contains': ['192.NF', '192.NO', '192.NP', '192.OH', '192.OJ', '192.QL', '192.QM'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [133970182339249961095537, 79855398717732338388456, 25903229681844523013167, 1313941673647, 187922594658424724202816], 'label': '3072.bgb.96.OP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.ok1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.OP', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760690
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.OQ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.GH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EM', '48.JL', '48.JO', '48.KS', '48.KV', '48.LI', '48.LK'], 'contains': ['192.NG', '192.NN', '192.NO', '192.OF', '192.OI', '192.QL', '192.QQ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855520714221614566521, 133970182339249961095537, 79855398717732338388456, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.96.OQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.ok2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.OQ', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760691
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.OR', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.GH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EN', '48.IW', '48.JB', '48.LE', '48.LI', '48.LJ'], 'contains': ['192.NF', '192.NM', '192.NN', '192.OF', '192.OG', '192.QM', '192.QP'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 187973685961890096441600, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.96.OR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.ol1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.OR', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760692
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.OS', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '192.NR', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EI', '48.JE', '48.JR', '48.KT', '48.KW', '48.LC', '48.MC'], 'contains': ['192.GB', '192.GC', '192.ND', '192.NE', '192.NJ', '192.OC', '192.OE', '192.OK', '192.OM'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25852138386775177898303, 79804308122845802507662, 25903229681844523013167, 187922473375925652905521, 1313941673647], 'label': '3072.bgb.96.OS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.om1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.OS', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760693
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.OT', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EI', '48.JF', '48.JR', '48.KR', '48.LE', '48.LF', '48.MA'], 'contains': ['192.ND', '192.NF', '192.NL', '192.OB', '192.OG', '192.OL', '192.OR'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187973685961890096441600, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.96.OT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.on1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.OT', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760694
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.OU', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EI', '48.JG', '48.JR', '48.KS', '48.LD', '48.LK', '48.MA'], 'contains': ['192.NE', '192.NG', '192.NL', '192.OE', '192.OJ', '192.OL', '192.PF'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [133970182339249961095537, 25903229681844523013167, 162121668858915397667278, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.96.OU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.oo1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.OU', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760695
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.OV', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EO', '48.JE', '48.JG', '48.KN', '48.KU', '48.MA'], 'contains': ['192.GD', '192.NE', '192.NK', '192.OD', '192.OL', '192.PM'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 187973685961890096441600, 79804308125641822294440, 134021394933610431760703, 1313941673647], 'label': '3072.bgb.96.OV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.op1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.OV', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760696
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.OW', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '192.NM', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EI', '48.JH', '48.JR', '48.KV', '48.LC', '48.LI', '48.LZ'], 'contains': ['192.NF', '192.NG', '192.NJ', '192.OG', '192.OI', '192.OK', '192.PW'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229691554491852799, 79855398717732338388456, 25903229681844523013167, 1313941673647, 25852017101492540879976], 'label': '3072.bgb.96.OW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.oq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.OW', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760697
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.OX', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '384.GJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EO', '48.JF', '48.JH', '48.KO', '48.LE', '48.LK'], 'contains': ['192.GE', '192.NF', '192.NK', '192.OF', '192.OL', '192.QD'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 79855520714221614566521, 79855398717732338388456, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.96.OX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.or1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.OX', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760698
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.OY', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '192.NS', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EJ', '48.IV', '48.JM', '48.KW', '48.KX', '48.LC', '48.MD'], 'contains': ['192.NH', '192.NI', '192.NJ', '192.OM', '192.OX', '192.PK', '192.PZ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804308122845802507662, 25903229681844523013167, 187922473375925652905521, 1313941673647, 134021394929311911342598], 'label': '3072.bgb.96.OY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.os1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.OY', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760699
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '16.E', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '384.5677', 'aut_weyl_index': 16, 'centralizer': '3072.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.A', '8.G'], 'contains': ['32.G', '32.N', '48.ED', '64.A'], 'core': '192.A', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [53952291033879672806278, 566495989041738862713598, 25903229681844523013167, 216288570480689195210176, 1313941673647, 134021272934136496216343, 486427128433516595381056], 'label': '3072.bgb.16.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.G', 'old_label': '16.e1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.E', 'subgroup_fusion': None, 'weyl_group': '384.5677'}
  • id: 184760700
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.OZ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '192.NJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EQ', '48.IT', '48.JT', '48.KV', '48.KW', '48.KX', '48.MB'], 'contains': ['192.NH', '192.NJ', '192.NO', '192.OQ', '192.OU', '192.PX', '192.QR'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 1313941673647, 108118287251071627990321, 79804429421968711780537], 'label': '3072.bgb.96.OZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.ot1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.OZ', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760701
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.PA', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.FB', '48.JA', '48.JK', '48.KU', '48.KX', '48.LE', '48.LP'], 'contains': ['192.NH', '192.NK', '192.NM', '192.OR', '192.OV', '192.QF', '192.QM'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229691554491852799, 108118165248982343710201, 25903229681844523013167, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.96.PA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.ou1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.PA', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760702
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.PB', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '192.NJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EJ', '48.IW', '48.JN', '48.KS', '48.LF', '48.LP', '48.MB'], 'contains': ['192.NH', '192.NL', '192.NN', '192.OR', '192.OW', '192.QG', '192.QN'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 162121668858915397667278, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.96.PB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.ov1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.PB', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760703
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.PC', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '192.NJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ET', '48.IV', '48.JB', '48.KT', '48.KX', '48.LZ', '48.MB'], 'contains': ['192.NI', '192.NJ', '192.NM', '192.PE', '192.PH', '192.PX', '192.QN'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952413035981411118158, 79855398717732338388456, 25903229681844523013167, 187973685961890096441600, 1313941673647], 'label': '3072.bgb.96.PC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.ow1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.PC', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760704
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.PD', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.FB', '48.IU', '48.JL', '48.KU', '48.KX', '48.LK', '48.LU'], 'contains': ['192.NI', '192.NK', '192.NO', '192.PF', '192.PI', '192.QF', '192.QQ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [133970182339249961095537, 25903229681844523013167, 79804308125641822294440, 1313941673647, 79804429421968711780537], 'label': '3072.bgb.96.PD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.ox1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.PD', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760705
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.PE', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '192.NJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EJ', '48.JC', '48.JN', '48.KR', '48.LD', '48.LU', '48.MB'], 'contains': ['192.NI', '192.NL', '192.NP', '192.PF', '192.PJ', '192.QG', '192.QR'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229691554491852799, 133970182339249961095537, 25903229681844523013167, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.96.PE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.oy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.PE', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760706
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.PF', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '192.PW', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.FB', '48.IT', '48.JP', '48.KT', '48.KX', '48.LI', '48.LW'], 'contains': ['192.NJ', '192.NM', '192.NO', '192.PW', '192.PY', '192.QM', '192.QQ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855398717732338388456, 25903229681844523013167, 1313941673647, 187922594658424724202816, 25852017101492540879976], 'label': '3072.bgb.96.PF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.oz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.PF', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760707
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.PG', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '192.NJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EJ', '48.JB', '48.JM', '48.KV', '48.LC', '48.LW', '48.MB'], 'contains': ['192.NJ', '192.NN', '192.NP', '192.PW', '192.PZ', '192.QN', '192.QR'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855398717732338388456, 25903229681844523013167, 1313941673647, 133970303635757521608262, 25852017101492540879976], 'label': '3072.bgb.96.PG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.pa1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.PG', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760708
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '96.PH', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.PH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EZ', '48.JE', '48.JH', '48.KP', '48.KX', '48.MB'], 'contains': ['192.NJ', '192.NK', '192.PX', '192.QC', '192.QG'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79804308122845802507662, 25903229681844523013167, 187973685961890096441600, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.96.PH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.pb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.PH', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760709
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.PI', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ET', '48.IW', '48.JC', '48.LE', '48.LK', '48.LP', '48.LW'], 'contains': ['192.NL', '192.NM', '192.NN', '192.QD', '192.QF', '192.QM', '192.QN'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 79855398717732338388456, 25903229681844523013167, 187973685961890096441600, 1313941673647], 'label': '3072.bgb.96.PI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.pc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.PI', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760710
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '16.F', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '384.5678', 'aut_weyl_index': 16, 'centralizer': '1536.C', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.B', '8.C'], 'contains': ['32.F', '32.O', '48.FG', '64.B'], 'core': '384.A', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 566444897749485959875336, 404159831259638948150382, 1313941673647, 378358905093235639407953, 162070456272950954131199], 'label': '3072.bgb.16.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.C', 'old_label': '16.f1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.F', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 184760711
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.PJ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EQ', '48.JK', '48.JL', '48.KR', '48.KS', '48.LU', '48.LW'], 'contains': ['192.NL', '192.NO', '192.NP', '192.QE', '192.QF', '192.QQ', '192.QR'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [187922594664024732247801, 25903229681844523013167, 79804308125641822294440, 1313941673647, 79804429421968711780537], 'label': '3072.bgb.96.PJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.pd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.PJ', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760712
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.PK', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.BY', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.EY', '48.IZ', '48.JD', '48.KN', '48.KO', '48.KP', '48.KQ'], 'contains': ['192.GH', '192.GI', '192.NK', '192.QH', '192.QJ'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107687970595565937, 25903229681844523013167, 53952412691500576681559, 25903107685154153232142, 1313941673647], 'label': '3072.bgb.96.PK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '96.pe1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.PK', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760713
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.PL', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '192.QC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EZ', '48.JF', '48.JG', '48.KQ', '48.LP', '48.LU'], 'contains': ['192.B', '192.NK', '192.NL', '192.QF', '192.QG'], 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 187973685961890096441600, 79804308125641822294440, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.96.PL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.pf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.PL', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760714
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.PM', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.EL', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.EK', '48.JI', '48.JS', '48.KY', '48.LA', '48.LB', '48.LY'], 'contains': ['192.GL', '192.GV', '192.NQ', '192.NW', '192.OZ'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 162121669227129588479873, 187973685961890096441600, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.PM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.pg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.PM', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760715
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.PN', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.DW', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EL', '48.JJ', '48.KZ'], 'contains': ['192.GJ', '192.GK', '192.GM', '192.HC', '192.NC', '192.NS', '192.NX', '192.PQ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229684640542817862, 25903229691554491852799, 25903229681844523013167, 1313941673647, 51212962568394582352], 'label': '3072.bgb.96.PN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.ph1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.PN', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760716
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.PO', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '192.NQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EM', '48.JL', '48.JW', '48.LC', '48.LD', '48.LZ', '48.MA'], 'contains': ['192.GN', '192.NE', '192.NG', '192.NI', '192.NP', '192.NQ', '192.OB', '192.ON'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229691554491852799, 133970182339249961095537, 25903229681844523013167, 187922473375925652905521, 1313941673647], 'label': '3072.bgb.96.PO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.pi1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.PO', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760717
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.PP', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '192.NG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.FA', '48.JP', '48.JV', '48.KY', '48.LE', '48.LZ'], 'contains': ['192.NF', '192.NM', '192.NQ', '192.OA', '192.OS'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 79855520714221614566521, 25903229681844523013167, 187922473375925652905521, 1313941673647], 'label': '3072.bgb.96.PP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.pj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.PP', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760718
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.PQ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '192.NR', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EM', '48.JT', '48.JV', '48.LC', '48.LE', '48.LF', '48.MC'], 'contains': ['192.GO', '192.ND', '192.NF', '192.NH', '192.NN', '192.NQ', '192.OC', '192.PB'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187973685961890096441600, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.PQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.pk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.PQ', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760719
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.PR', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '192.NF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.FA', '48.JK', '48.JT', '48.LI', '48.LK', '48.LZ', '48.MA'], 'contains': ['192.NF', '192.NG', '192.NM', '192.NO', '192.NR', '192.OD', '192.PG'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855398717732338388456, 25903229681844523013167, 187973685961890096441600, 1313941673647, 108118287251071627990321], 'label': '3072.bgb.96.PR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.pl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.PR', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760720
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.PS', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '192.NR', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EN', '48.JM', '48.JN', '48.LK', '48.LZ', '48.MA', '48.MC'], 'contains': ['192.GP', '192.NE', '192.NF', '192.NI', '192.NN', '192.NR', '192.OE', '192.PN'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [187922473373129633118743, 25903229691554491852799, 79855398717732338388456, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.96.PS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.pm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.PS', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760721
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '16.G', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '384.17949', 'aut_weyl_index': 16, 'centralizer': '768.BG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.B', '8.D', '8.H', '8.I'], 'contains': ['32.J', '32.P', '48.FR', '64.B'], 'core': '96.A', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [25903229681844523013167, 566444897749485959875336, 404159831259638948150382, 79804308125641822294440, 1313941673647, 79804429413572684637382, 404210922196204071249966], 'label': '3072.bgb.16.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.H', 'old_label': '16.g1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.G', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 184760722
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.PT', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '192.NR', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EO', '48.JR', '48.LG', '48.LH', '48.LJ', '48.LZ', '48.MC'], 'contains': ['192.GQ', '192.GR', '192.NE', '192.NF', '192.NS', '192.OK', '192.PE'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952413035981411118158, 25903229691554491852799, 79855398717732338388456, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.96.PT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '96.pn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.PT', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760723
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.PU', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.EM', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.EP', '48.JI', '48.JS', '48.KY', '48.LL', '48.LM', '48.LY'], 'contains': ['192.GS', '192.GW', '192.NQ', '192.OP', '192.OY'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229337376182892926, 25903229681844523013167, 187973685961890096441600, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.PU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.po1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.PU', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760724
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '96.PV', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.PV', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EQ', '48.JP', '48.JW', '48.LA', '48.LC', '48.LL', '48.MB'], 'contains': ['192.GT', '192.GU', '192.NJ', '192.NP', '192.NQ', '192.OQ', '192.OW'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229691554491852799, 25903229681844523013167, 187922473375925652905521, 1313941673647, 108118287251071627990321], 'label': '3072.bgb.96.PV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.pp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.PV', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760725
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.PW', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '192.NJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.FB', '48.JL', '48.JV', '48.LE', '48.LP', '48.MA', '48.MB'], 'contains': ['192.NK', '192.NL', '192.NM', '192.NN', '192.NQ', '192.OR', '192.OU'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 187973685961890096441600, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.PW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.pq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.PW', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760726
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.PX', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '192.NS', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EQ', '48.JU', '48.JV', '48.LB', '48.LD', '48.LF', '48.LM', '48.LN', '48.LO', '48.LP', '48.MD'], 'contains': ['192.NH', '192.NL', '192.NQ', '192.OX', '192.PA'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229691554491852799, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647], 'label': '3072.bgb.96.PX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.pr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.PX', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760727
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.PY', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.EC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ER', '48.LQ', '48.LS'], 'contains': ['192.GX', '192.HA', '192.NR', '192.PD', '192.PL'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 187922473373129633118743, 25903229681844523013167, 404159575154785525538638, 1313941673647], 'label': '3072.bgb.96.PY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CD', 'old_label': '96.ps1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.PY', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760728
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '96.PZ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.PZ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ET', '48.JM', '48.LI', '48.LQ', '48.LR', '48.MB', '48.MC'], 'contains': ['192.GY', '192.GZ', '192.NJ', '192.NN', '192.NR', '192.PE', '192.PJ'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952413035981411118158, 79855398717732338388456, 25903229681844523013167, 1313941673647, 133970303635757521608262], 'label': '3072.bgb.96.PZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '96.pt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.PZ', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760729
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.QA', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '192.NJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.FB', '48.JK', '48.JU', '48.LK', '48.LU', '48.MA', '48.MB'], 'contains': ['192.NK', '192.NL', '192.NO', '192.NP', '192.NR', '192.PF', '192.PH'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [133970182339249961095537, 25903229681844523013167, 187973685961890096441600, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.96.QA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.pu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.QA', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760730
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.QB', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '192.NS', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ET', '48.JN', '48.LS', '48.LT', '48.LU', '48.MA', '48.MD'], 'contains': ['192.NI', '192.NL', '192.NR', '192.PK', '192.PM'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229691554491852799, 25903229681844523013167, 79804308125641822294440, 134021394933610431760703, 1313941673647], 'label': '3072.bgb.96.QB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '96.pv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.QB', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760731
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.QC', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EU', '48.KZ', '48.LV'], 'contains': ['192.HB', '192.NS', '192.PO', '192.QB'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804429416356250372480, 25903229681844523013167, 187973685961890096441600, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.96.QC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.V', 'old_label': '96.pw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.QC', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184760732
    {'ambient': '3072.bgb', 'aut_centralizer_order': 1, 'aut_label': '4.C', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '3072.a1', 'complements': ['768.BL', '768.BK', '768.BS'], 'conjugacy_class_count': 1, 'contained_in': ['2.B', '2.D', '2.F'], 'contains': ['8.A', '8.M', '12.B', '16.K'], 'core': '4.C', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [108118421696801471190456, 25903229681844523013167, 108118165248982343710201, 187922473375925652905521, 566444897749485959875336, 133970303627361494479417, 404159831259638948150382, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.4.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': ['2.B', '2.D', '2.F'], 'normal_contains': ['8.A', '12.B'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '3072.bgb', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.C', 'subgroup_fusion': None, 'weyl_group': '3072.bgb'}
  • id: 184760733
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '16.H', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '384.5678', 'aut_weyl_index': 16, 'centralizer': '1536.C', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.D', '8.C'], 'contains': ['32.F', '32.Q', '48.GR', '64.D'], 'core': '384.A', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [566495989041738862713598, 25903229681844523013167, 296041666021875301271736, 187922473375925652905521, 162121669227129588479873, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.16.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.C', 'old_label': '16.h1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.H', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 184760734
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.QD', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.EG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EV', '48.KZ', '48.LG'], 'contains': ['192.HD', '192.HE', '192.NS', '192.PT', '192.QA'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804429416356250372480, 378358770650295628183080, 25903229681844523013167, 1313941673647, 242140721658215271465607], 'label': '3072.bgb.96.QD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.px1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.QD', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760735
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.QE', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '192.NJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.FB', '48.JO', '48.JT', '48.LJ', '48.LW', '48.LZ', '48.MB'], 'contains': ['192.NM', '192.NN', '192.NO', '192.NP', '192.NS', '192.PW', '192.PX'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855398717732338388456, 25903229681844523013167, 187973685961890096441600, 1313941673647, 25852017101492540879976], 'label': '3072.bgb.96.QE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.py1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.QE', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760736
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '96.QF', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.QF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EZ', '48.JR', '48.LV', '48.LW', '48.LX', '48.MB', '48.MD'], 'contains': ['192.NJ', '192.NL', '192.NS', '192.PZ', '192.QC'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79804308122845802507662, 25903229691554491852799, 25903229681844523013167, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.96.QF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '96.pz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.QF', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760737
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '96.QG', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.QG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.FA', '48.JU', '48.JW', '48.LY', '48.MA', '48.MC'], 'contains': ['192.HF', '192.HG', '192.ND', '192.NE', '192.NQ', '192.NR', '192.OO'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952413035981411118158, 25903229691554491852799, 25903229681844523013167, 187922473375925652905521, 1313941673647], 'label': '3072.bgb.96.QG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.qa1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.QG', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760738
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '96.QH', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.QH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.FB', '48.JT', '48.JW', '48.LZ', '48.MB', '48.MC', '48.MD'], 'contains': ['192.HH', '192.HI', '192.NH', '192.NI', '192.NJ', '192.NQ', '192.NR', '192.NS', '192.OM'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804308122845802507662, 25903229691554491852799, 25903229681844523013167, 187922473375925652905521, 1313941673647], 'label': '3072.bgb.96.QH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.qb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.QH', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760739
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.QI', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.BS', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.EE', '48.IR', '48.KE', '48.KY', '48.ME', '48.MF', '48.MG'], 'contains': ['192.HJ', '192.HK', '192.HZ', '192.IU', '192.NT', '192.NV', '192.NW', '192.OA', '192.OP'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229337376182892926, 122007701746409022, 25903229681844523013167, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.QI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.qc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.QI', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760740
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.QJ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.DE', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EE', '48.IS', '48.KE'], 'contains': ['192.HL', '192.HM', '192.IA', '192.IB', '192.IV', '192.IW', '192.NT', '192.NV', '192.NZ', '192.OH', '192.PS'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107687970595565937, 25852138393689126932998, 25903229681844523013167, 1313941673647, 51212962568394582352], 'label': '3072.bgb.96.QJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.qd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.QJ', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760741
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.QK', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.C', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.FD', '48.JZ', '48.KA', '48.KN', '48.KO', '48.MQ', '48.MR'], 'contains': ['192.IC', '192.JC', '192.NY', '192.OL', '192.QJ'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79855520714221614566521, 25903229681844523013167, 53952412691500576681559, 25903107685154153232142, 1313941673647], 'label': '3072.bgb.96.QK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '96.qe1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.QK', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760742
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.QL', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.BM', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.FE', '48.IO', '48.KB', '48.LY', '48.ME', '48.MV', '48.MZ'], 'contains': ['192.ID', '192.JF', '192.NW', '192.OO', '192.OY'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [53952413035981411118158, 25903229681844523013167, 187922473375925652905521, 1313941673647, 378358905093235639407953], 'label': '3072.bgb.96.QL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.qf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.QL', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760743
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.QM', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.BS', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.FE', '48.IP', '48.KC', '48.KK', '48.KY', '48.MS', '48.NA'], 'contains': ['192.NW', '192.OS', '192.OY'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [108118165248982343710201, 79855398717732338388456, 25903229681844523013167, 1313941673647, 404210922196204071249966], 'label': '3072.bgb.96.QM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.qg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.QM', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760744
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '16.I', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '384.5677', 'aut_weyl_index': 16, 'centralizer': '3072.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.E', '8.G'], 'contains': ['32.G', '32.U', '48.HE', '64.E'], 'core': '384.A', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [53952291033879672806278, 296092500497899884979223, 25903229681844523013167, 1313941673647, 566445019748791678392366, 134021272934136496216343, 270189770923792213003566], 'label': '3072.bgb.16.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.G', 'old_label': '16.i1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.I', 'subgroup_fusion': None, 'weyl_group': '384.5677'}
  • id: 184760745
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.QN', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.Z', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.FG', '48.IQ', '48.JI', '48.KL', '48.MF', '48.MS', '48.MV'], 'contains': ['192.NW', '192.OT', '192.OY'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [162070578272437343706839, 25903229681844523013167, 187922473375925652905521, 1313941673647, 404210922196204071249966], 'label': '3072.bgb.96.QN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.qh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.QN', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760746
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.QO', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.BC', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.EK', '48.IQ', '48.KD', '48.KK', '48.ME', '48.MT', '48.MX'], 'contains': ['192.NW', '192.OV', '192.OZ'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 25852138389591620222016, 1313941673647, 134021272925740469097576, 108118286902479131308678], 'label': '3072.bgb.96.QO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.qi1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.QO', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760747
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.QP', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.DP', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.FF', '48.IO', '48.KC', '48.KM', '48.LA', '48.MF', '48.MX'], 'contains': ['192.IH', '192.JS', '192.NW', '192.OW', '192.OZ'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 25852138389591620222016, 1313941673647, 133970303635757521608262, 108118286902479131308678], 'label': '3072.bgb.96.QP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.qj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.QP', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760748
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.QQ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.CG', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.FF', '48.IP', '48.KB', '48.KL', '48.LB', '48.MG', '48.MT'], 'contains': ['192.NW', '192.OX', '192.OZ'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 162121669227129588479873, 1313941673647, 187922594658424724202816, 25852017102974698844878], 'label': '3072.bgb.96.QQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.qj2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.QQ', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760749
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.QR', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.X', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.O', '48.FG', '48.JS', '48.KD', '48.KM', '48.MG', '48.MZ', '48.NA'], 'contains': ['192.II', '192.KG', '192.NW', '192.OY', '192.PC'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 1313941673647, 378358905093235639407953, 162070456272950954131199], 'label': '3072.bgb.96.QR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.qk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.QR', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760750
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.QS', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.CG', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.FH', '48.JX', '48.KN', '48.MH', '48.MI', '48.MU', '48.NB'], 'contains': ['192.IJ', '192.LA', '192.NY', '192.PM', '192.QH'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 404211043484134973872583, 79804308125641822294440, 134021394933610431760703, 1313941673647], 'label': '3072.bgb.96.QS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.ql1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.QS', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184761627
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '384.HI', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.EL', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.GL', '192.QW', '192.QY'], 'contains': ['768.BO', '768.BU', '768.BY'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [187922473021741077083393, 25852017104276106643073, 162070456280045573438767], 'label': '3072.bgb.384.HI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.DG', 'old_label': '384.gt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.HI', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184760751
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.QT', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.FI', '48.KZ', '48.MJ'], 'contains': ['192.HO', '192.HQ', '192.IK', '192.LE', '192.NU', '192.NX', '192.PO', '192.PT'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804429416356250372480, 378358770650295628183080, 25903229681844523013167, 25852272837936812846761, 1313941673647], 'label': '3072.bgb.96.QT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BO', 'old_label': '96.qm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.QT', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760752
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.QU', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.FI', '48.MH', '48.MK', '48.MM', '48.MN', '48.MW', '48.NC'], 'contains': ['192.HP', '192.HR', '192.IL', '192.LF', '192.NU', '192.NY', '192.PP', '192.PU'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 25852272837936812846761, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.96.QU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '96.qn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.QU', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184760753
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.QV', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.FJ', '48.MI', '48.ML', '48.MM', '48.MN', '48.MW', '48.NC'], 'contains': ['192.IM', '192.LJ', '192.NY', '192.PP', '192.QK'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 1313941673647, 53952035291802302422343, 378358649363678452761737], 'label': '3072.bgb.96.QV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '96.qo1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.QV', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184760754
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.QW', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.FK', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EL', '48.KE', '48.MJ'], 'contains': ['192.HS', '192.HT', '192.IN', '192.LN', '192.NV', '192.NX', '192.PQ', '192.PY'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229684640542817862, 25903107687970595565937, 25903229681844523013167, 1313941673647, 51212962568394582352], 'label': '3072.bgb.96.QW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.qp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.QW', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760755
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '16.J', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '384.5677', 'aut_weyl_index': 16, 'centralizer': '3072.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.G', '8.G'], 'contains': ['32.G', '48.HF', '64.G'], 'core': '384.A', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [53952291033879672806278, 187922217292190117815823, 566495989041738862713598, 25903229681844523013167, 216288570480689195210176, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.16.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.G', 'old_label': '16.j1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.J', 'subgroup_fusion': None, 'weyl_group': '384.5677'}
  • id: 184760756
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.QX', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.FO', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.FK', '48.MH', '48.MK', '48.MO', '48.MP', '48.MW', '48.NC'], 'contains': ['192.IO', '192.IQ', '192.LY', '192.ME', '192.NY', '192.PU', '192.QI'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 162070321828715682652927, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.96.QX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '96.qq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.QX', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760757
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.QY', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.FF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.FQ', '48.KZ', '48.MJ'], 'contains': ['192.HU', '192.HV', '192.NX', '192.QA', '192.QB'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804429416356250372480, 270240484111912758504367, 25903229681844523013167, 1313941673647, 404210922196204071249966], 'label': '3072.bgb.96.QY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BO', 'old_label': '96.qr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.QY', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760758
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '96.QZ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.BT', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.FR', '48.JZ', '48.KP', '48.MM', '48.MO', '48.MU', '48.ND'], 'contains': ['192.NY', '192.QC', '192.QH'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804308122845802507662, 25903229681844523013167, 79804308125641822294440, 1313941673647, 404210922196204071249966], 'label': '3072.bgb.96.QZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.qs1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.QZ', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760759
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.RA', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.FB', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.FH', '48.JY', '48.KO', '48.MK', '48.ML', '48.MY', '48.ND'], 'contains': ['192.IP', '192.MD', '192.NY', '192.QD', '192.QH'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 134021272934136496216343, 404210922196204071249966, 187922594661241166512703], 'label': '3072.bgb.96.RA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.qt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.RA', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184760760
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.RB', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.BY', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.FN', '48.JX', '48.JY', '48.KP', '48.KQ', '48.MQ', '48.MR'], 'contains': ['192.NY', '192.QG', '192.QJ'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 53952412691500576681559, 25903107685154153232142, 1313941673647, 79804429421968711780537], 'label': '3072.bgb.96.RB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '96.qu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.RB', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760761
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.RC', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.FO', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.FP', '48.MI', '48.ML', '48.MO', '48.MP', '48.MW', '48.NC'], 'contains': ['192.HW', '192.HX', '192.NY', '192.QI', '192.QK'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [108169512287410083283217, 25903229681844523013167, 79804308125641822294440, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.96.RC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '96.qv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.RC', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760762
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.RD', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '192.CX', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.P', '48.FR', '48.KA', '48.KQ', '48.MN', '48.MP', '48.MY', '48.NB'], 'contains': ['192.B', '192.NY', '192.QH'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 1313941673647, 79804429413572684637382, 404210922196204071249966], 'label': '3072.bgb.96.RD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.qw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.RD', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760763
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.RE', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '384.DP', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.FS', '48.JJ', '48.KE', '48.LA', '48.MS', '48.MT', '48.MZ'], 'contains': ['192.IE', '192.IF', '192.IG', '192.IT', '192.JP', '192.NW', '192.NX', '192.NZ', '192.OQ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 1313941673647, 108118287251071627990321, 404210922196204071249966], 'label': '3072.bgb.96.RE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.qx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.RE', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760764
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.RF', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '384.CG', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.FS', '48.IR', '48.LB', '48.MQ', '48.MU', '48.MV', '48.MW', '48.MX', '48.MY', '48.NA'], 'contains': ['192.HN', '192.IR', '192.NW', '192.NY', '192.PA'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647, 404210922196204071249966], 'label': '3072.bgb.96.RF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.qy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.RF', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 184760765
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.RG', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '384.FB', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.FS', '48.IS', '48.MR', '48.NB', '48.NC', '48.ND'], 'contains': ['192.HY', '192.IS', '192.NY', '192.NZ', '192.QE'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [187922594664024732247801, 25903229681844523013167, 79804308125641822294440, 1313941673647, 404210922196204071249966], 'label': '3072.bgb.96.RG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.qz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.RG', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184760766
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '16.K', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '384.17949', 'aut_weyl_index': 16, 'centralizer': '1536.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.C', '8.E', '8.H', '8.J'], 'contains': ['32.J', '32.R', '48.B', '64.C'], 'core': '48.B', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [25903229681844523013167, 566444897749485959875336, 404159831259638948150382, 79804308125641822294440, 1313941673647, 79804429413572684637382, 53952035291802302422343], 'label': '3072.bgb.16.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.H', 'old_label': '16.k1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.K', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 184760767
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.RH', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EM', '48.JK', '48.KI', '48.KT', '48.KU', '48.NE', '48.NF'], 'contains': ['192.OC', '192.OD', '192.OH', '192.ON', '192.OV', '192.PH', '192.QQ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [133970182339249961095537, 25903229681844523013167, 187922473375925652905521, 1313941673647, 133970303635757521608262], 'label': '3072.bgb.96.RH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.ra1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.RH', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184761628
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '384.HJ', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.EL', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.GL', '192.QX', '192.QZ'], 'contains': ['768.BO', '768.BU', '768.BY'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [162121669227129588479873, 187973685961890096441600, 25852017102974698844878], 'label': '3072.bgb.384.HJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.DG', 'old_label': '384.gt2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.HJ', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184760768
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.RI', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.FT', '48.JM', '48.KG', '48.KR', '48.KW', '48.LD', '48.NE'], 'contains': ['192.OB', '192.OE', '192.OJ', '192.ON', '192.OX', '192.PJ', '192.QR'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [133970182339249961095537, 25903229681844523013167, 187922473375925652905521, 1313941673647, 134021394929311911342598], 'label': '3072.bgb.96.RI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.rb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.RI', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760769
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.RJ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.FT', '48.JN', '48.KF', '48.KS', '48.KW', '48.LC', '48.NF'], 'contains': ['192.OC', '192.OE', '192.OI', '192.ON', '192.OW', '192.PK', '192.QR'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25852138386775177898303, 133970182339249961095537, 25903229681844523013167, 187922473375925652905521, 1313941673647], 'label': '3072.bgb.96.RJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.rb2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.RJ', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760770
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.RK', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EF', '48.IV', '48.KG', '48.KW', '48.MA', '48.NF', '48.NG'], 'contains': ['192.OB', '192.OD', '192.OE', '192.OO', '192.OU', '192.PH', '192.PK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952413035981411118158, 25903229681844523013167, 187922473375925652905521, 1313941673647, 79804429421968711780537], 'label': '3072.bgb.96.RK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.rc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.RK', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760771
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.RL', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '384.FZ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.FA', '48.IU', '48.KI', '48.KU', '48.ME', '48.NG'], 'contains': ['192.OA', '192.OD', '192.OO', '192.OV', '192.PI'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952413035981411118158, 79855520714221614566521, 25903229681844523013167, 187922473375925652905521, 1313941673647], 'label': '3072.bgb.96.RL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.rd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.RL', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760772
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.RM', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EF', '48.IW', '48.KF', '48.KT', '48.KV', '48.LE', '48.NK'], 'contains': ['192.OC', '192.OF', '192.OG', '192.OS', '192.OU', '192.QM', '192.QN'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 187922473375925652905521, 1313941673647, 79804429421968711780537], 'label': '3072.bgb.96.RM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.re1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.RM', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184760773
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.RN', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EH', '48.IT', '48.JL', '48.KR', '48.KV', '48.NE', '48.NF'], 'contains': ['192.OB', '192.OH', '192.OI', '192.OT', '192.OU', '192.QQ', '192.QR'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [162070578272437343706839, 25903229681844523013167, 187922473375925652905521, 1313941673647, 79804429421968711780537], 'label': '3072.bgb.96.RN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.rf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.RN', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184760774
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.RO', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '384.GI', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EH', '48.IU', '48.JP', '48.KS', '48.MF', '48.NE'], 'contains': ['192.OA', '192.OJ', '192.OT', '192.OW', '192.QQ'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [162070578272437343706839, 79855520714221614566521, 25903229681844523013167, 187922473375925652905521, 1313941673647], 'label': '3072.bgb.96.RO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.rf2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.RO', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760775
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.RP', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.BS', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.EG', '48.IX', '48.KH', '48.KY', '48.ME', '48.MF', '48.MG'], 'contains': ['192.OA', '192.OY', '192.OZ'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [122007701746409022, 25903229681844523013167, 162121669227129588479873, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.RP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.rg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.RP', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760776
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.RQ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EM', '48.IT', '48.JA', '48.LE', '48.NE', '48.NG', '48.NK'], 'contains': ['192.OA', '192.OB', '192.OF', '192.OU', '192.OV', '192.PB', '192.QM'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 1313941673647, 133970303635757521608262, 25852017102974698844878], 'label': '3072.bgb.96.RQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.rh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.RQ', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184760777
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '16.L', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '384.17949', 'aut_weyl_index': 16, 'centralizer': '1536.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.D', '8.D', '8.J', '8.K'], 'contains': ['32.J', '32.S', '48.HU', '64.D'], 'core': '96.A', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [566495989041738862713598, 25903229681844523013167, 53952412691500576681559, 79804308125641822294440, 270240740222366015020798, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.16.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.H', 'old_label': '16.l1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.L', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 184760778
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.RR', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.FT', '48.IV', '48.IW', '48.LC', '48.LF', '48.NE', '48.NK'], 'contains': ['192.OB', '192.OC', '192.OG', '192.OW', '192.OX', '192.PB', '192.QN'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 1313941673647, 79804429421968711780537, 25852017102974698844878], 'label': '3072.bgb.96.RR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.ri1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.RR', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760779
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.RS', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EH', '48.JV', '48.KI', '48.KW', '48.MG', '48.NK'], 'contains': ['192.OA', '192.OC', '192.OU', '192.OX', '192.PC'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79855520714221614566521, 25903229681844523013167, 187922473375925652905521, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.96.RS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.rj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.RS', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760780
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.RT', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EF', '48.JB', '48.KG', '48.KS', '48.KT', '48.LK', '48.NE'], 'contains': ['192.OE', '192.OF', '192.OJ', '192.PG', '192.PH', '192.QN', '192.QQ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855398717732338388456, 25903229681844523013167, 1313941673647, 108118287251071627990321, 134021394929311911342598], 'label': '3072.bgb.96.RT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.rk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.RT', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184760781
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.RU', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '384.GH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EF', '48.JC', '48.KF', '48.KR', '48.KU', '48.LI', '48.NE'], 'contains': ['192.OD', '192.OG', '192.OI', '192.PG', '192.PJ', '192.QM', '192.QQ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25852138386775177898303, 79855398717732338388456, 25903229681844523013167, 1313941673647, 108118287251071627990321], 'label': '3072.bgb.96.RU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.rk2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.RU', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760782
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.RV', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EN', '48.KF', '48.KG', '48.KT', '48.KU', '48.LK', '48.NG'], 'contains': ['192.OD', '192.OE', '192.OF', '192.PH', '192.PI', '192.PN', '192.QM'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855520714221614566521, 187922473373129633118743, 79855398717732338388456, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.96.RV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.rl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.RV', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184760783
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.RW', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.FT', '48.JB', '48.JC', '48.KR', '48.KS', '48.KV'], 'contains': ['192.OG', '192.OI', '192.OJ', '192.QL', '192.QN', '192.QR'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [133970182339249961095537, 79855398717732338388456, 25903229681844523013167, 1313941673647, 134021394929311911342598], 'label': '3072.bgb.96.RW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.rm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.RW', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184760784
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.RX', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EI', '48.JE', '48.KJ', '48.KW', '48.LZ', '48.NE', '48.NG'], 'contains': ['192.OA', '192.OB', '192.OD', '192.OE', '192.OK', '192.OM', '192.PX'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855520714221614566521, 79804308122845802507662, 25903229681844523013167, 187922473375925652905521, 1313941673647], 'label': '3072.bgb.96.RX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.rn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.RX', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760785
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.RY', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.FW', '48.JR', '48.KJ', '48.KV', '48.KW', '48.LC', '48.NE'], 'contains': ['192.OB', '192.OC', '192.OI', '192.OJ', '192.OK', '192.OQ', '192.PZ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 1313941673647, 133970303635757521608262, 108118287251071627990321], 'label': '3072.bgb.96.RY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.ro1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.RY', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760786
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.RZ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EI', '48.JF', '48.KJ', '48.KS', '48.KU', '48.LE', '48.NK'], 'contains': ['192.OA', '192.OC', '192.OF', '192.OG', '192.OL', '192.OR', '192.QF'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 1313941673647, 79804429421968711780537, 25852017102974698844878], 'label': '3072.bgb.96.RZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.rp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.RZ', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184760787
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.SA', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.FW', '48.JE', '48.JF', '48.LD', '48.LF', '48.MQ', '48.NF', '48.NH', '48.NI', '48.NJ', '48.NK'], 'contains': ['192.OB', '192.OC', '192.OL', '192.PA', '192.QG'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647, 133970303635757521608262], 'label': '3072.bgb.96.SA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.rq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.SA', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760788
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '16.M', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '384.17949', 'aut_weyl_index': 16, 'centralizer': '1536.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.E', '8.F', '8.H', '8.K'], 'contains': ['32.J', '32.T', '48.HZ', '64.E'], 'core': '96.A', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [25903229681844523013167, 566444897749485959875336, 404159831259638948150382, 79804308125641822294440, 1313941673647, 79804429413572684637382, 378358649363678452761737], 'label': '3072.bgb.16.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.H', 'old_label': '16.m1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.M', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 184760789
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.SB', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '384.GH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EO', '48.KJ', '48.KT', '48.LI', '48.NG', '48.NL', '48.NM'], 'contains': ['192.IX', '192.IY', '192.OD', '192.OF', '192.OK', '192.PE', '192.PY'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952413035981411118158, 79855520714221614566521, 79855398717732338388456, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.96.SB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '96.rr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.SB', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760790
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.SC', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EI', '48.JG', '48.KJ', '48.KR', '48.KU', '48.LK', '48.NF'], 'contains': ['192.OD', '192.OE', '192.OH', '192.OI', '192.OL', '192.PF', '192.QF'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [133970182339249961095537, 25903229681844523013167, 79855398709336311235223, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.96.SC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.rs1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.SC', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184760791
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.SD', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.C', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.FY', '48.JZ', '48.KA', '48.KN', '48.KO', '48.NH', '48.NN'], 'contains': ['192.IZ', '192.JD', '192.OL', '192.PR', '192.QH'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79855520714221614566521, 25903229681844523013167, 25903107685154153232142, 1313941673647, 51090958997032170942], 'label': '3072.bgb.96.SD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '96.rt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.SD', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760792
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.SE', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.I', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.FZ', '48.LG', '48.NL'], 'contains': ['192.JA', '192.JB', '192.OK', '192.PT', '192.QA'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804429416356250372480, 378358770650295628183080, 25903229681844523013167, 324406991811924875755576, 1313941673647], 'label': '3072.bgb.96.SE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BX', 'old_label': '96.ru1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.SE', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760793
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.SF', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '384.GJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EI', '48.JH', '48.KJ', '48.KT', '48.KV', '48.LJ', '48.NE'], 'contains': ['192.OF', '192.OG', '192.OH', '192.OJ', '192.OK', '192.PW', '192.PX'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25852138386775177898303, 79855398717732338388456, 25903229681844523013167, 1313941673647, 25852017101492540879976], 'label': '3072.bgb.96.SF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.rv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.SF', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760794
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.SG', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '384.GJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.FW', '48.JG', '48.JH', '48.KR', '48.KS', '48.MR', '48.NN'], 'contains': ['192.OI', '192.OJ', '192.OL', '192.QE', '192.QG'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [187922594664024732247801, 25903229681844523013167, 79804308125641822294440, 1313941673647, 133970303635757521608262], 'label': '3072.bgb.96.SG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.rw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.SG', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760795
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '96.SH', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '192.NJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EJ', '48.IV', '48.KF', '48.KW', '48.MB', '48.NE', '48.NV'], 'contains': ['192.OM', '192.OU', '192.OW', '192.PH', '192.PJ', '192.PX', '192.PZ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804308122845802507662, 25903229681844523013167, 187922473375925652905521, 1313941673647, 187922594658424724202816], 'label': '3072.bgb.96.SH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.rx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.SH', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760796
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.SI', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.FB', '48.IT', '48.KI', '48.KT', '48.KX', '48.NG', '48.NV'], 'contains': ['192.OM', '192.OU', '192.OV', '192.PH', '192.PI', '192.PX', '192.PY'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804308122845802507662, 25903229681844523013167, 187922473375925652905521, 1313941673647, 79804429421968711780537], 'label': '3072.bgb.96.SI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.ry1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.SI', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760797
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '96.SJ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '192.NJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GG', '48.JR', '48.KJ', '48.KX', '48.MB', '48.NU', '48.OT'], 'contains': ['192.OM', '192.OQ', '192.OR', '192.PE', '192.PF', '192.PW', '192.QC'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [187922594664024732247801, 108118165248982343710201, 25903229681844523013167, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.96.SJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.rz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.SJ', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760798
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.SK', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GS', '48.JK', '48.JL', '48.KR', '48.KS', '48.NU', '48.OE'], 'contains': ['192.ON', '192.OR', '192.OT', '192.PF', '192.PG', '192.QE', '192.QL'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 25852138393689126932998, 25903229681844523013167, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.96.SK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.sa1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.SK', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184760799
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '16.N', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '192.956', 'aut_weyl_index': 32, 'centralizer': '768.BG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.F', '8.E', '8.I', '8.K'], 'contains': ['32.J', '48.C', '64.F'], 'core': '48.C', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [486427128437815115841359, 378307814169184473345982, 25903229681844523013167, 486426872699855848892862, 79804308125641822294440, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.16.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.H', 'old_label': '16.n1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.N', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 184760800
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.SL', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.BM', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.GC', '48.IO', '48.KB', '48.LY', '48.ME', '48.NS', '48.OS'], 'contains': ['192.JE', '192.JG', '192.OO', '192.OP', '192.OZ'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 162121669227129588479873, 1313941673647, 162070456274433112077942, 25852017102974698844878], 'label': '3072.bgb.96.SL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.sb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.SL', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760801
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.SM', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GH', '48.JM', '48.KF', '48.KT', '48.LZ', '48.NU', '48.OT'], 'contains': ['192.OM', '192.ON', '192.OS', '192.PE', '192.PG', '192.PN', '192.PW'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [162070578272437343706839, 108118165248982343710201, 79855398717732338388456, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.96.SM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.sc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.SM', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760802
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.SN', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GH', '48.JN', '48.KG', '48.KU', '48.MA', '48.OE', '48.OT'], 'contains': ['192.ON', '192.OO', '192.OR', '192.PF', '192.PG', '192.PM', '192.PN'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [162070578272437343706839, 108118165248982343710201, 25903229681844523013167, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.96.SN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.sd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.SN', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760803
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.SO', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.BS', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.GC', '48.IP', '48.KC', '48.KK', '48.KY', '48.NO', '48.OU'], 'contains': ['192.OP', '192.OS', '192.OZ'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 25852138389591620222016, 1313941673647, 134021272934136496216343, 51090960298439969137], 'label': '3072.bgb.96.SO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.se1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.SO', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760804
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.SP', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.Z', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.GR', '48.IQ', '48.JI', '48.KL', '48.MF', '48.NO', '48.NS'], 'contains': ['192.OP', '192.OT', '192.OZ'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922594664024732247801, 25903229337376182892926, 25903229681844523013167, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.SP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.sf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.SP', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760805
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.SQ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.BD', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.EP', '48.IQ', '48.KD', '48.KK', '48.ME', '48.NP', '48.OH'], 'contains': ['192.OP', '192.OV', '192.OY'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 25852138389591620222016, 1313941673647, 134021272925740469097576, 51212962568394582352], 'label': '3072.bgb.96.SQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.sg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.SQ', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760806
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.SR', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.DQ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.GD', '48.IO', '48.KC', '48.KM', '48.LL', '48.MF', '48.OH'], 'contains': ['192.JK', '192.JT', '192.OP', '192.OW', '192.OY'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 25852138389591620222016, 1313941673647, 133970303635757521608262, 51212962568394582352], 'label': '3072.bgb.96.SR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.sh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.SR', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760807
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.SS', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.CH', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.GD', '48.IP', '48.KB', '48.KL', '48.LM', '48.MG', '48.NP'], 'contains': ['192.OP', '192.OX', '192.OY'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229337376182892926, 25903229681844523013167, 1313941673647, 187922594658424724202816, 25852017102974698844878], 'label': '3072.bgb.96.SS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.sh2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.SS', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760808
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.ST', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '384.DQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GJ', '48.JJ', '48.KE', '48.LL', '48.NO', '48.NP', '48.OS'], 'contains': ['192.JH', '192.JI', '192.JJ', '192.JL', '192.JM', '192.OP', '192.OQ', '192.PQ', '192.PS'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229337376182892926, 25903229681844523013167, 1313941673647, 25852017101492540879976, 25852017102974698844878], 'label': '3072.bgb.96.ST', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.si1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ST', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760809
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.SU', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '384.GI', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GS', '48.JO', '48.JP', '48.KV', '48.MS', '48.NO', '48.NU'], 'contains': ['192.OQ', '192.OS', '192.OT', '192.PW', '192.QL'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [187922594664024732247801, 108118165248982343710201, 79855398717732338388456, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.96.SU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.sj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.SU', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760810
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '16.O', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '384.17949', 'aut_weyl_index': 16, 'centralizer': '768.BG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.G', '8.F', '8.I', '8.J'], 'contains': ['32.J', '48.IL', '64.G'], 'core': '96.A', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [79855142625594763233847, 25903229681844523013167, 566444897749485959875336, 404159831259638948150382, 79804308125641822294440, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.16.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.H', 'old_label': '16.o1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.O', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 184760811
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.SV', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EQ', '48.JO', '48.KI', '48.KX', '48.MT', '48.NE', '48.NP'], 'contains': ['192.OQ', '192.OV', '192.OX', '192.PX', '192.QQ'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 1313941673647, 108118287251071627990321, 134021394929311911342598], 'label': '3072.bgb.96.SV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.sk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.SV', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760812
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.SW', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '384.DQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GN', '48.JQ', '48.KH', '48.LL', '48.MS', '48.MZ', '48.NP'], 'contains': ['192.JN', '192.JQ', '192.OQ', '192.OY'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 1313941673647, 108118287251071627990321, 378358905093235639407953], 'label': '3072.bgb.96.SW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.sl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.SW', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760813
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.SX', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '384.DP', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GO', '48.JQ', '48.KH', '48.LA', '48.MT', '48.NO', '48.OS'], 'contains': ['192.JO', '192.JR', '192.OQ', '192.OZ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 162121669227129588479873, 1313941673647, 25852017101492540879976, 25852017102974698844878], 'label': '3072.bgb.96.SX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.sm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.SX', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760814
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.SY', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EJ', '48.IW', '48.KG', '48.KR', '48.KX', '48.LP', '48.NK'], 'contains': ['192.OR', '192.OU', '192.OX', '192.QF', '192.QG', '192.QM', '192.QN'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 1313941673647, 187922594658424724202816, 25852017102974698844878], 'label': '3072.bgb.96.SY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.sn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.SY', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760815
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.SZ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GS', '48.IT', '48.JT', '48.LC', '48.NE', '48.NU', '48.OT'], 'contains': ['192.OM', '192.ON', '192.OQ', '192.OT', '192.PB', '192.PG', '192.PW'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 133970182339249961095537, 25903229681844523013167, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.SZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.so1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.SZ', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760816
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '96.TA', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '192.NS', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GG', '48.JE', '48.MD', '48.MU', '48.NQ', '48.NR', '48.NT', '48.NV', '48.NW', '48.NX', '48.NY', '48.NZ', '48.OT'], 'contains': ['192.OM', '192.PA', '192.PM', '192.QC'], 'core': '768.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [79804308122845802507662, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647], 'label': '3072.bgb.96.TA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.sp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.TA', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184760817
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.TB', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GS', '48.IU', '48.JU', '48.LD', '48.MV', '48.NF', '48.NS', '48.OA', '48.OB', '48.OE', '48.OT'], 'contains': ['192.ON', '192.OO', '192.OT', '192.PA', '192.PF'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 133970182339249961095537, 25903229681844523013167, 187922473375925652905521, 1313941673647], 'label': '3072.bgb.96.TB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.sq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.TB', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760818
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.TC', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '192.NR', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GH', '48.IV', '48.MC', '48.NG', '48.OC', '48.OD', '48.OT'], 'contains': ['192.JU', '192.JV', '192.OM', '192.OO', '192.PB', '192.PE', '192.PN'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79804308122845802507662, 108118165248982343710201, 25903229681844523013167, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.TC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '96.sr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.TC', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760819
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.TD', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GI', '48.MW', '48.NQ', '48.OF', '48.OG'], 'contains': ['192.JW', '192.PA', '192.PP', '192.QI'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.96.TD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '96.ss1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.TD', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184760820
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.TE', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '384.CH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GJ', '48.IR', '48.LM', '48.NH', '48.NR', '48.NS', '48.OH', '48.OI', '48.OU'], 'contains': ['192.JX', '192.JY', '192.OP', '192.PA', '192.PR'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25852138757799544092222, 25903229681844523013167, 25852138389591620222016, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.TE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.st1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.TE', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184760821
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '16.P', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '192.955', 'aut_weyl_index': 32, 'centralizer': '1536.C', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.I', '8.C'], 'contains': ['32.K', '32.O', '32.Q', '48.JS', '64.H', '64.N'], 'core': '768.A', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [162070577934876685646657, 25903229681844523013167, 187922473375925652905521, 404159831259638948150382, 1313941673647, 486427128433516595381056, 162070456272950954131199], 'label': '3072.bgb.16.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.C', 'old_label': '16.p1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.P', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 184760822
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.TF', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GK', '48.MW', '48.NT', '48.OF', '48.OK'], 'contains': ['192.JZ', '192.KB', '192.PA', '192.PU', '192.QK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.96.TF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '96.su1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.TF', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184760823
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.TG', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '768.K', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GE', '48.OC', '48.OJ'], 'contains': ['192.KA', '192.KC', '192.PB', '192.PV', '192.QO'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [242089752358354392177983, 25903229681844523013167, 133970303627361494479417, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.TG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.EH', 'old_label': '96.sv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.TG', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760824
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.TH', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.D', '48.GH', '48.IW', '48.LE', '48.NU', '48.OJ', '48.OL'], 'contains': ['192.OR', '192.OS', '192.PB', '192.QD', '192.QP'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 187922473375925652905521, 133970303627361494479417, 1313941673647], 'label': '3072.bgb.96.TH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '96.sw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.TH', 'subgroup_fusion': None, 'weyl_group': '128.1578'}
  • id: 184760825
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.TI', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EQ', '48.IU', '48.JA', '48.LP', '48.MX', '48.NF', '48.NK', '48.NV', '48.OH', '48.OM', '48.ON'], 'contains': ['192.OU', '192.OV', '192.OW', '192.PA', '192.QF'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647, 79804429421968711780537], 'label': '3072.bgb.96.TI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.sx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.TI', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760826
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.TJ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '384.CH', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.GN', '48.IX', '48.IY', '48.LM', '48.LN', '48.MV', '48.NA', '48.NI', '48.NJ', '48.NW', '48.OA', '48.OH', '48.OM', '48.OO', '48.OV'], 'contains': ['192.OY', '192.PA'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647, 378358905093235639407953], 'label': '3072.bgb.96.TJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.sy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.TJ', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184760827
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.TK', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '384.CG', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.GO', '48.IX', '48.IY', '48.LB', '48.LO', '48.MX', '48.NI', '48.NJ', '48.NS', '48.NX', '48.OB', '48.ON', '48.OP', '48.OU', '48.OW'], 'contains': ['192.OZ', '192.PA'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [162070577934876685646657, 25903229681844523013167, 25852138389591620222016, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.TK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.sz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.TK', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184760828
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.TL', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '384.CG', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.GP', '48.IZ', '48.LO', '48.MU', '48.MY', '48.NH', '48.OA', '48.OF', '48.ON', '48.OV'], 'contains': ['192.PA', '192.QH'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 404211043484134973872583, 187922473375925652905521, 1313941673647], 'label': '3072.bgb.96.TL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.ta1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.TL', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 184760829
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.TM', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '384.CH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GQ', '48.IZ', '48.LN', '48.MQ', '48.NR', '48.OB', '48.OI', '48.OM', '48.OW'], 'contains': ['192.PA', '192.QJ'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 53952412691500576681559, 25852138389591620222016, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.TM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.tb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.TM', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184760830
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.TN', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.D', '48.GG', '48.JF', '48.LP', '48.MY', '48.OE', '48.OG', '48.OI', '48.OK', '48.OO', '48.OP', '48.OQ', '48.OR'], 'contains': ['192.B', '192.OR', '192.PA', '192.QD'], 'core': '192.B', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.96.TN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.tc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.TN', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184760831
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.TO', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '192.NQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GS', '48.JW', '48.KI', '48.KW', '48.MZ', '48.OS', '48.OT'], 'contains': ['192.KD', '192.KE', '192.OM', '192.ON', '192.OO', '192.OQ', '192.PC'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 1313941673647, 108118287251071627990321, 162070456272950954131199], 'label': '3072.bgb.96.TO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.td1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.TO', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760832
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '16.Q', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '192.956', 'aut_weyl_index': 32, 'centralizer': '1536.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.I', '8.D'], 'contains': ['32.L', '32.P', '32.S', '48.KA', '64.H'], 'core': '192.B', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [121659103022301503, 25903229681844523013167, 79804308125641822294440, 1313941673647, 79804429413572684637382, 486427128433516595381056, 270189770923792213003566], 'label': '3072.bgb.16.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.D', 'old_label': '16.q1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.Q', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 184760833
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.TP', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.X', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.Q', '48.GR', '48.JS', '48.KD', '48.KM', '48.MG', '48.OS', '48.OU'], 'contains': ['192.KF', '192.KH', '192.OP', '192.OZ', '192.PC'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 162121669227129588479873, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.96.TP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.te1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.TP', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760834
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.TQ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.D', '48.GS', '48.JA', '48.JV', '48.LF', '48.NA', '48.NK', '48.OT', '48.OU', '48.OV', '48.OW'], 'contains': ['192.OR', '192.OS', '192.PA', '192.PB', '192.PC'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 133970303627361494479417, 1313941673647], 'label': '3072.bgb.96.TQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '96.tf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.TQ', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760835
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.TR', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ER', '48.OX', '48.PE'], 'contains': ['192.PD', '192.PI', '192.PL'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 404159696441402621126383, 134021394933610431760703, 1313941673647], 'label': '3072.bgb.96.TR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CD', 'old_label': '96.tg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.TR', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760836
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.TS', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.EC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GT', '48.LQ', '48.PE'], 'contains': ['192.KL', '192.KU', '192.PD', '192.PJ', '192.PL'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 187922473373129633118743, 25903229681844523013167, 1313941673647, 242089752368057879612857], 'label': '3072.bgb.96.TS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CD', 'old_label': '96.th1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.TS', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760837
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.TT', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GT', '48.LS', '48.OX'], 'contains': ['192.PD', '192.PK', '192.PL'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [324355779217738848775558, 378358770650295628183080, 187922473373129633118743, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.96.TT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CD', 'old_label': '96.th2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.TT', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760838
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.TU', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '384.EC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GX', '48.LG', '48.LQ', '48.NL', '48.OC', '48.OX', '48.OY'], 'contains': ['192.KI', '192.KJ', '192.KK', '192.KM', '192.KN', '192.PD', '192.PE', '192.PT', '192.PV'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 54003382330230002441647, 1313941673647, 134021272934136496216343, 216288705272228144236816], 'label': '3072.bgb.96.TU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BA', 'old_label': '96.ti1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.TU', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 184760839
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.TV', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ET', '48.KF', '48.KX', '48.LJ', '48.NG', '48.OX', '48.OZ'], 'contains': ['192.PE', '192.PI', '192.PK', '192.PX', '192.QM'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952413035981411118158, 79855398717732338388456, 25903229681844523013167, 1313941673647, 187922594658424724202816], 'label': '3072.bgb.96.TV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '96.tj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.TV', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760840
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.TW', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '384.EC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.HA', '48.LH', '48.LQ', '48.NM', '48.OD', '48.OX', '48.PA'], 'contains': ['192.KO', '192.KS', '192.PE', '192.PL'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952413035981411118158, 79855398717732338388456, 25903229681844523013167, 162121291492681005016326, 1313941673647], 'label': '3072.bgb.96.TW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BA', 'old_label': '96.tk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.TW', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 184760841
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.TX', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '384.EB', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.HB', '48.LG', '48.LR', '48.NL', '48.OD', '48.OZ', '48.PA'], 'contains': ['192.KP', '192.KQ', '192.PE', '192.QA'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952413035981411118158, 79855142625594763233847, 79855398717732338388456, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.96.TX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BA', 'old_label': '96.tl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.TX', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760842
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.TY', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '384.EB', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.HD', '48.LH', '48.LR', '48.NM', '48.OC', '48.OY', '48.OZ'], 'contains': ['192.KR', '192.KT', '192.PE', '192.QO'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 242140721662339602266753, 54003382330230002441647, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.96.TY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BA', 'old_label': '96.tm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.TY', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760843
    {'ambient': '3072.bgb', 'aut_centralizer_order': 1, 'aut_label': '4.D', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '3072.a1', 'complements': ['768.BT'], 'conjugacy_class_count': 1, 'contained_in': ['2.A', '2.F', '2.G'], 'contains': ['8.A', '8.N', '12.CA', '16.H', '16.L'], 'core': '4.D', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 187922473375925652905521, 404159831259638948150382, 133970303627361494479417, 566444897749485959875336, 108118165248982343710201, 162070456272950954131199, 53952412691500576681559], 'label': '3072.bgb.4.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': ['2.A', '2.F', '2.G'], 'normal_contains': ['8.A'], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': '3072.bgb', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.D', 'subgroup_fusion': None, 'weyl_group': '3072.bgb'}
  • id: 184760844
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '16.R', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '192.955', 'aut_weyl_index': 32, 'centralizer': '1536.C', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.I', '8.C'], 'contains': ['32.M', '32.O', '32.Q', '48.KD', '64.H'], 'core': '768.A', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 216288570480689195210176, 486427128433516595381056, 133970303627361494479417, 108118165248982343710201, 108118286902479131308678], 'label': '3072.bgb.16.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.C', 'old_label': '16.r1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.R', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 184760845
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.TZ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '384.GH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GH', '48.JB', '48.LI', '48.LJ', '48.NU', '48.OY', '48.PA'], 'contains': ['192.PE', '192.PG', '192.PW', '192.QL', '192.QP'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 79804429416356250372480, 25903229681844523013167, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.96.TZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '96.tn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.TZ', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760846
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.UA', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EJ', '48.JC', '48.KG', '48.KS', '48.KX', '48.LU', '48.NF'], 'contains': ['192.PF', '192.PH', '192.PK', '192.QF', '192.QG', '192.QQ', '192.QR'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [133970182339249961095537, 25903229681844523013167, 79804308125641822294440, 1313941673647, 133970303635757521608262], 'label': '3072.bgb.96.UA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.to1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.UA', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760847
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.UB', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GV', '48.MH', '48.MI', '48.NQ', '48.PB'], 'contains': ['192.KV', '192.PM', '192.PP', '192.QI'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 134021394933610431760703, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.96.UB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '96.tp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.UB', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184760848
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.UC', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.CH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GW', '48.JX', '48.KN', '48.NR', '48.PC'], 'contains': ['192.KW', '192.LB', '192.PM', '192.PR', '192.QJ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 25903107685154153232142, 1313941673647, 53952291036675691857216, 51090958997032170942], 'label': '3072.bgb.96.UC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '96.tq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.UC', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760849
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.UD', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '768.K', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.HE', '48.OC', '48.PD'], 'contains': ['192.KY', '192.LC', '192.PN', '192.PV', '192.QO'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 242140721662339602266753, 1313941673647, 162070456275746973182137, 134021272934136496216343], 'label': '3072.bgb.96.UD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.EH', 'old_label': '96.tr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.UD', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760850
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.UE', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GX', '48.LS', '48.MH', '48.NT', '48.PE', '48.PF'], 'contains': ['192.KX', '192.KZ', '192.PD', '192.PM', '192.PU'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 79804308125641822294440, 134021394933610431760703, 1313941673647], 'label': '3072.bgb.96.UE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '96.ts1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.UE', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 184760851
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.UF', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GH', '48.JC', '48.LK', '48.NU', '48.OE', '48.PD', '48.PG'], 'contains': ['192.PF', '192.PG', '192.PN', '192.QD', '192.QL'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 187922594664024732247801, 79855398717732338388456, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.96.UF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '96.tt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.UF', 'subgroup_fusion': None, 'weyl_group': '128.1578'}
  • id: 184760852
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.UG', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ET', '48.KG', '48.KU', '48.LU', '48.NV', '48.PE', '48.PH'], 'contains': ['192.PH', '192.PI', '192.PJ', '192.PM', '192.QF'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 134021394933610431760703, 1313941673647, 79804429421968711780537], 'label': '3072.bgb.96.UG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '96.tu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.UG', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760853
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.UH', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.HA', '48.LS', '48.LT', '48.NY', '48.PE', '48.PH', '48.PI'], 'contains': ['192.PL', '192.PM'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [187922217290876255985856, 25903229681844523013167, 25903107685154153232142, 1313941673647, 53952291036675691857216], 'label': '3072.bgb.96.UH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BE', 'old_label': '96.tv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.UH', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184760854
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.UI', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.HC', '48.LT', '48.MI', '48.NT', '48.PF', '48.PH'], 'contains': ['192.PM', '192.QK'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 134021394933610431760703, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.96.UI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '96.tw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.UI', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 184760855
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '16.S', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '192.956', 'aut_weyl_index': 32, 'centralizer': '1536.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.J', '8.H'], 'contains': ['32.P', '32.R', '32.T', '48.MN', '64.I'], 'core': '192.B', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [25903229681844523013167, 404159831259638948150382, 79804308125641822294440, 1313941673647, 79804429413572684637382, 53952035291802302422343, 378358649363678452761737], 'label': '3072.bgb.16.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.H', 'old_label': '16.s1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.S', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 184760856
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.UJ', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GG', '48.JG', '48.LU', '48.NB', '48.OE', '48.PB', '48.PC', '48.PF', '48.PI', '48.PJ'], 'contains': ['192.B', '192.PF', '192.PM', '192.QE'], 'core': '192.B', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 1313941673647, 108118287251071627990321, 79804429413572684637382], 'label': '3072.bgb.96.UJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.tx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.UJ', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184760857
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.UK', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.HH', '48.KZ', '48.MJ'], 'contains': ['192.LD', '192.LI', '192.PO', '192.PQ', '192.QA'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79855142625594763233847, 25903229684640542817862, 25903229681844523013167, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.96.UK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BO', 'old_label': '96.ty1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.UK', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760858
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.UL', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.HI', '48.MH', '48.MK', '48.MM', '48.MN', '48.OF', '48.PK'], 'contains': ['192.LG', '192.LM', '192.PP', '192.PU', '192.QH'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 79804308125641822294440, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.96.UL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '96.tz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.UL', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184760859
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.UM', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EU', '48.MJ', '48.PM'], 'contains': ['192.LH', '192.PO', '192.PY', '192.QB'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804429416356250372480, 25903229681844523013167, 108169377837562135992360, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.96.UM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.V', 'old_label': '96.ua1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.UM', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184760860
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.UN', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.HJ', '48.LV', '48.PM'], 'contains': ['192.PO', '192.PZ', '192.QB'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804308122845802507662, 25903229681844523013167, 1313941673647, 187922594658424724202816, 53952035291802302422343], 'label': '3072.bgb.96.UN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CJ', 'old_label': '96.ub1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.UN', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760861
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.UO', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GV', '48.MK', '48.ML', '48.OG', '48.PL'], 'contains': ['192.LK', '192.PP', '192.QD', '192.QI'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 79855398717732338388456, 25903229681844523013167, 256460345499052777, 1313941673647], 'label': '3072.bgb.96.UO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '96.uc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.UO', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184760862
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.UP', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GI', '48.NC', '48.PB', '48.PK', '48.PL'], 'contains': ['192.LL', '192.PP', '192.QE', '192.QI'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [187922594664024732247801, 108169512287410083283217, 25903229681844523013167, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.96.UP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '96.ud1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.UP', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184760863
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.UQ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.HL', '48.MI', '48.ML', '48.MM', '48.MN', '48.OF', '48.PK'], 'contains': ['192.PP', '192.QH', '192.QK'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 25852272837936812846761, 79804308125641822294440, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.96.UQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '96.ue1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.UQ', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184760864
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.UR', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.B', '48.LV', '48.MM', '48.NQ', '48.PL', '48.PM'], 'contains': ['192.PO', '192.PP', '192.QC'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79804308122845802507662, 25903229681844523013167, 79804308125641822294440, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.96.UR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '96.uf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.UR', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184760865
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.US', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '192.955', 'aut_weyl_index': 32, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.R', '48.B', '48.MN', '48.OG', '48.PB'], 'contains': ['192.B', '192.PP'], 'core': '192.B', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 1313941673647, 79804429413572684637382, 53952035291802302422343], 'label': '3072.bgb.96.US', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.D', 'old_label': '96.ug1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.US', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 184760866
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '24.A', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '384.17948', 'aut_weyl_index': 16, 'centralizer': '384.A', 'complements': ['128.O', '128.P'], 'conjugacy_class_count': 1, 'contained_in': ['8.E', '12.I', '12.R'], 'contains': ['48.A', '48.B', '48.C', '48.DW', '48.FX'], 'core': '24.A', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [79855520714221614566521, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 79804429413572684637382, 53952035291802302422343], 'label': '3072.bgb.24.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': ['6.A'], 'normal_contains': ['48.A', '48.B', '48.C'], 'normalizer': '1.a1', 'old_label': '24.a1', 'projective_image': '3072.bgb', 'quotient_action_image': '24.12', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.A', 'subgroup_fusion': None, 'weyl_group': '384.17948'}
  • id: 184760867
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.UT', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.HO', '48.KZ', '48.MJ'], 'contains': ['192.LP', '192.LQ', '192.LX', '192.MC', '192.PQ', '192.PT', '192.QB'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804429416356250372480, 378358770650295628183080, 25903229681844523013167, 216288448822893847639681, 1313941673647], 'label': '3072.bgb.96.UT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BO', 'old_label': '96.uh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.UT', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760868
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '96.UU', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.V', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.HU', '48.JZ', '48.KP', '48.NR', '48.PN'], 'contains': ['192.PR', '192.QC', '192.QJ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804429415054842584367, 25903229681844523013167, 25903107685154153232142, 1313941673647, 51090958997032170942], 'label': '3072.bgb.96.UU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '96.ui1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.UU', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760869
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.UV', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.FH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GW', '48.JY', '48.KO', '48.OI', '48.PN'], 'contains': ['192.LR', '192.MF', '192.PR', '192.QD', '192.QJ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 79855398717732338388456, 25903229681844523013167, 53952412691500576681559, 1313941673647], 'label': '3072.bgb.96.UV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '96.uj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.UV', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760870
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.UW', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.BY', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.HQ', '48.JX', '48.JY', '48.KP', '48.KQ', '48.NH', '48.NN'], 'contains': ['192.PR', '192.QG', '192.QH'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 25903107685154153232142, 1313941673647, 79804429421968711780537, 51090958997032170942], 'label': '3072.bgb.96.UW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '96.uk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.UW', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760871
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.UX', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.S', '48.HU', '48.KA', '48.KQ', '48.OI', '48.PC'], 'contains': ['192.B', '192.PR', '192.QJ'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 53952412691500576681559, 79804308125641822294440, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.96.UX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '96.ul1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.UX', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760872
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.UY', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '384.FH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GJ', '48.IS', '48.NN', '48.PC', '48.PN'], 'contains': ['192.LO', '192.LS', '192.PR', '192.PS', '192.QE'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 25903107685154153232142, 1313941673647, 25852017101492540879976, 51090958997032170942], 'label': '3072.bgb.96.UY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.C', 'old_label': '96.um1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.UY', 'subgroup_fusion': None, 'weyl_group': '64.32'}
  • id: 184760873
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.UZ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.FJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EV', '48.MJ', '48.NL'], 'contains': ['192.LW', '192.MB', '192.PT', '192.PY', '192.QA'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804429416356250372480, 378358770650295628183080, 270240484111912758504367, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.96.UZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.un1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.UZ', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760874
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '96.VA', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.DO', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.HZ', '48.MM', '48.MO', '48.NT', '48.PO'], 'contains': ['192.PU', '192.QC', '192.QK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770650295628183080, 79804308122845802507662, 25903229681844523013167, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.96.VA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '96.uo1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.VA', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760875
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.VB', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GK', '48.NC', '48.PF', '48.PK', '48.PO'], 'contains': ['192.LZ', '192.MG', '192.PU', '192.QE', '192.QK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [187922594664024732247801, 378358770650295628183080, 25903229681844523013167, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.96.VB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '96.up1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.VB', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184760876
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.VC', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.FO', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.HX', '48.MH', '48.MK', '48.MO', '48.MP', '48.OF', '48.PK'], 'contains': ['192.LU', '192.LV', '192.PU', '192.QH', '192.QI'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 108169512287410083283217, 25903229681844523013167, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.96.VC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '96.uq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.VC', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760877
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.B', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '1536.408610986', 'aut_weyl_index': 4, 'centralizer': '768.A', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.A', '12.A', '12.B', '12.C', '12.BM', '12.CA', '12.CB', '12.CC'], 'contains': ['48.D', '48.GG', '48.GH', '48.GS', '48.NU', '48.OE', '48.OT'], 'core': '24.B', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 133970303627361494479417, 122002101738321960, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.24.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': ['8.A', '12.A', '12.B', '12.C'], 'normal_contains': ['48.D', '96.A'], 'normalizer': '1.a1', 'old_label': '24.b1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.B', 'subgroup_fusion': None, 'weyl_group': '768.1087581'}
  • id: 184760878
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.VD', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.T', '48.HZ', '48.MN', '48.MP', '48.OK', '48.PF'], 'contains': ['192.B', '192.PU', '192.QK'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 1313941673647, 79804429413572684637382, 378358649363678452761737], 'label': '3072.bgb.96.VD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '96.ur1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.VD', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760879
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.VE', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.T', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GE', '48.OY', '48.PD'], 'contains': ['192.PV', '192.QL', '192.QO'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [133970182339249961095537, 25903229681844523013167, 242140721662339602266753, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.96.VE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.EH', 'old_label': '96.us1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.VE', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760880
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.VF', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.T', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.U', '48.HE', '48.OJ', '48.OY'], 'contains': ['192.PV', '192.QO', '192.QP'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [53952291033879672806278, 296092500497899884979223, 25903229681844523013167, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.96.VF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.EH', 'old_label': '96.ut1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.VF', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760881
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.VG', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GX', '48.MK', '48.OJ', '48.OK', '48.PD', '48.PO'], 'contains': ['192.LT', '192.MA', '192.PU', '192.PV', '192.QD'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [242089752358354392177983, 25903229681844523013167, 1313941673647, 134021272934136496216343, 187922594661241166512703], 'label': '3072.bgb.96.VG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '96.uu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.VG', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 184760882
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.VH', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EJ', '48.JB', '48.KF', '48.KV', '48.KX', '48.LW', '48.NE'], 'contains': ['192.PW', '192.PX', '192.PZ', '192.QM', '192.QN', '192.QQ', '192.QR'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855398717732338388456, 25903229681844523013167, 1313941673647, 25852017101492540879976, 134021394929311911342598], 'label': '3072.bgb.96.VH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '96.uv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.VH', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184760883
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '96.VI', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '192.PY', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GG', '48.JH', '48.LW', '48.ND', '48.NU', '48.PL', '48.PN', '48.PO', '48.PP', '48.PQ'], 'contains': ['192.PW', '192.QC', '192.QD', '192.QE'], 'core': '768.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [53952291033879672806278, 79804429416356250372480, 79855398717732338388456, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.96.VI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.uw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.VI', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184760884
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '96.VJ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '192.QC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.EZ', '48.KJ', '48.KX', '48.LW', '48.NV', '48.PM', '48.PR'], 'contains': ['192.PX', '192.PY', '192.PZ', '192.QC', '192.QF'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79804308122845802507662, 25903229681844523013167, 79804308125641822294440, 1313941673647, 79804429421968711780537], 'label': '3072.bgb.96.VJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '96.ux1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.VJ', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760885
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '96.VK', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.VK', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.IM', '48.LX', '48.MO', '48.NQ', '48.PL', '48.PR'], 'contains': ['192.QC', '192.QI'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108169512287410083283217, 79804308122845802507662, 25903229681844523013167, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.96.VK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '96.uy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.VK', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760886
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.VL', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.IN', '48.LV', '48.LX', '48.NZ', '48.PM', '48.PP', '48.PR'], 'contains': ['192.QB', '192.QC'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [51469043514137246038, 79804308122845802507662, 25903229681844523013167, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.96.VL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BC', 'old_label': '96.uz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.VL', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760887
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.VM', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.HC', '48.ML', '48.OK', '48.OL', '48.PG', '48.PO'], 'contains': ['192.QD', '192.QK'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 134021272934136496216343, 378358649363678452761737, 187922594661241166512703], 'label': '3072.bgb.96.VM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '96.va1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.VM', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 184760888
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.C', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.D'], 'contains': ['48.F', '48.J', '48.K', '48.N', '48.Q', '48.S', '48.V', '48.BA', '48.BF', '48.BH', '48.BK', '48.CG', '48.CJ', '48.CT', '48.CV'], 'core': '3072.a1', 'coset_action_label': '24T7075', 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 187922473375925652905521, 134021394930826866723126, 25903229683158464676480, 296041409911409376977422, 378358649362364591657542, 79855264262271969233416], 'label': '3072.bgb.24.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '24.c1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.C', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 184760889
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.VN', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.HD', '48.OJ', '48.OL', '48.OR', '48.PD', '48.PG', '48.PQ'], 'contains': ['192.QD', '192.QO'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 134021272934136496216343, 216237613982764859689536, 187922594661241166512703], 'label': '3072.bgb.96.VN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.CB', 'old_label': '96.vb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.VN', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184760890
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.VO', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '384.FB', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GP', '48.JD', '48.NB', '48.ND', '48.NN', '48.PK'], 'contains': ['192.QE', '192.QH'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [187922594664024732247801, 25903229681844523013167, 404211043484134973872583, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.96.VO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.vc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.VO', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184760891
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.VP', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '384.FH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.GQ', '48.JD', '48.MR', '48.PC', '48.PN'], 'contains': ['192.QE', '192.QJ'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 53952412691500576681559, 25903107685154153232142, 1313941673647, 25852017101492540879976], 'label': '3072.bgb.96.VP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.C', 'old_label': '96.vd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.VP', 'subgroup_fusion': None, 'weyl_group': '64.32'}
  • id: 184760892
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.VQ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.FO', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.IH', '48.MI', '48.ML', '48.MO', '48.MP', '48.OF', '48.PK'], 'contains': ['192.QH', '192.QI', '192.QK'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 162070321828715682652927, 79804308125641822294440, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.96.VQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '96.ve1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.VQ', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184760893
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.VR', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.215', 'aut_weyl_index': 96, 'centralizer': '192.QC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.IM', '48.MP', '48.OG', '48.OQ', '48.PB', '48.PJ'], 'contains': ['192.B', '192.QI'], 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118421696801471190456, 25903229681844523013167, 79804308125641822294440, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.96.VR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '96.vf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.VR', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184760894
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '128.A', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.GM', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.F', '32.G', '32.J', '64.A', '64.B', '64.C', '64.D', '64.E', '64.F', '64.G'], 'contains': ['256.A', '384.A', '512.A'], 'core': '384.A', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [25903229681844523013167, 566444897749485959875336, 404159831259638948150382, 1313941673647], 'label': '3072.bgb.128.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.C', 'old_label': '128.a1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.A', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 184760895
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '128.B', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '768.Z', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.K', '32.L', '32.M', '32.N', '64.A', '64.H'], 'contains': ['256.A', '384.FW', '512.B'], 'core': '768.A', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [25903229681844523013167, 216288570480689195210176, 1313941673647, 486427128433516595381056], 'label': '3072.bgb.128.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.A', 'old_label': '128.b1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.B', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 184760896
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '128.C', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.GM', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.O', '32.P', '64.B', '64.H', '64.I'], 'contains': ['256.A', '384.FY', '512.C'], 'core': '768.A', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [25903229681844523013167, 404159831259638948150382, 1313941673647, 404210922196204071249966], 'label': '3072.bgb.128.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.C', 'old_label': '128.c1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.C', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 184760897
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '128.D', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '768.BC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.R', '64.C', '64.I'], 'contains': ['256.A', '384.GC', '512.D'], 'core': '768.A', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [25903229681844523013167, 270240740222366015020798, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.128.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.D', 'old_label': '128.d1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.D', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 184760898
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '128.E', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '768.Z', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.Q', '32.S', '64.D', '64.H'], 'contains': ['256.A', '384.GD', '512.E'], 'core': '768.A', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [25903229681844523013167, 378307936172768329324920, 1313941673647, 51212962568394582352], 'label': '3072.bgb.128.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.A', 'old_label': '128.e1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.E', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 184760899
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.D', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.S', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.D'], 'contains': ['48.F', '48.I', '48.L', '48.M', '48.R', '48.T', '48.V', '48.BB', '48.BF', '48.BG', '48.BL', '48.CH', '48.CI', '48.CT', '48.CW'], 'core': '3072.a1', 'coset_action_label': '24T7077', 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 187922473375925652905521, 134021394930826866723126, 25903229683158464676480, 378358649363678452761737, 296041409911409376977422, 79855264262271969233416], 'label': '3072.bgb.24.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '24.d1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.D', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760900
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '128.F', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '768.BC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.T', '32.U', '64.E', '64.I'], 'contains': ['256.A', '384.GE', '512.F'], 'core': '768.A', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 404159831259638948150382, 1313941673647], 'label': '3072.bgb.128.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.D', 'old_label': '128.f1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.F', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 184760901
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '128.G', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.14', 'aut_weyl_index': 256, 'centralizer': '768.Z', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.A', '64.M'], 'contains': ['256.B', '256.C', '256.E', '256.I', '384.GL'], 'core': '3072.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [512279023525993448904377, 25903108050746727640336, 216288570482003057040143, 486427128433516595381056], 'label': '3072.bgb.128.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.M', 'old_label': '128.g1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.G', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 184760902
    {'ambient': '3072.bgb', 'aut_centralizer_order': 12, 'aut_label': '128.H', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '512.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.B', '64.M'], 'contains': ['256.B', '256.D', '256.G', '384.GM'], 'core': '3072.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [51347037126292956736, 512279023525993448904377, 216288570482003057040143, 486427128433516595381056], 'label': '3072.bgb.128.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.M', 'old_label': '128.h1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.H', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760903
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '128.I', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.14', 'aut_weyl_index': 256, 'centralizer': '1536.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.C', '64.M'], 'contains': ['256.B', '256.F', '256.H', '384.GO'], 'core': '3072.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [378358905460129661894279, 51347406816160329727, 378358770650295628183080, 620448401365031515454761], 'label': '3072.bgb.128.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.M', 'old_label': '128.i1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.I', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 184760904
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '128.J', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.14', 'aut_weyl_index': 256, 'centralizer': '768.BC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.D', '64.M'], 'contains': ['256.C', '256.D', '256.F', '256.J', '384.GQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [378359026752338661681217, 378358770650295628183080, 51469040697520739881, 540644093954862016504456], 'label': '3072.bgb.128.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.M', 'old_label': '128.j1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.J', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 184760905
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '128.K', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.14', 'aut_weyl_index': 256, 'centralizer': '768.BG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.E', '64.M'], 'contains': ['256.C', '256.G', '256.H', '384.GS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [51347406816160329727, 404159952546255909825352, 594545172395863256432041, 378307935804560365900801], 'label': '3072.bgb.128.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.M', 'old_label': '128.k1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.K', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 184760906
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '128.L', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.14', 'aut_weyl_index': 256, 'centralizer': '1536.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.H', '64.M'], 'contains': ['256.D', '256.E', '256.H', '384.GY'], 'core': '3072.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [566495989041738862713598, 53952035293116243360136, 79804173335443638313656, 270240861515876502434616], 'label': '3072.bgb.128.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.M', 'old_label': '128.l1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.L', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 184760907
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '128.M', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.14', 'aut_weyl_index': 256, 'centralizer': '1536.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.I', '64.M'], 'contains': ['256.E', '256.F', '256.G', '384.HA'], 'core': '3072.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [324406735730979173366422, 378358770650295628183080, 512330114830760308086479, 51212962568394582352], 'label': '3072.bgb.128.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.M', 'old_label': '128.m1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.M', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 184760908
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '128.N', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '1536.C', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.K', '64.N'], 'contains': ['256.K', '384.HE', '512.B'], 'core': '3072.a1', 'coset_action_label': None, 'count': 128, 'diagramx': None, 'generators': [187973685954795477134032, 404159831259638948150382, 486427128433516595381056, 162121668868625366436606], 'label': '3072.bgb.128.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.N', 'old_label': '128.n1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.N', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 184760909
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '128.O', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '1536.C', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.O', '64.N'], 'contains': ['256.K', '384.HR', '512.C'], 'core': '3072.a1', 'coset_action_label': None, 'count': 128, 'diagramx': None, 'generators': [162070456271649546332752, 162121668867311424773041, 378359026753640149313262, 378358905093235639407953], 'label': '3072.bgb.128.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.N', 'old_label': '128.o1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.O', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 184761014
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.DO', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.VA', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.CV', '96.DB', '96.DV', '96.EG', '96.FT', '96.FU', '96.ME'], 'contains': ['384.Q', '384.FO'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108169512287410083283217, 54003503618341535825287, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.192.DO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '192.dd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DO', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760910
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.E', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.F', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.D'], 'contains': ['48.G', '48.I', '48.K', '48.M', '48.O', '48.S', '48.U', '48.BA', '48.BD', '48.BG', '48.BI', '48.CG', '48.CI', '48.CU', '48.CX'], 'core': '3072.a1', 'coset_action_label': '24T7085', 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 187922473375925652905521, 134021394930826866723126, 25903229683158464676480, 53952035291802302422343, 296041409911409376977422, 378358649362364591657542], 'label': '3072.bgb.24.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '24.e1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.E', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184760911
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '128.P', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '1536.C', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.Q', '64.N'], 'contains': ['256.K', '384.HT', '512.E'], 'core': '3072.a1', 'coset_action_label': None, 'count': 128, 'diagramx': None, 'generators': [187922473375925652905521, 378307936172768329324920, 162121669227129588479873, 162070456272950954131199], 'label': '3072.bgb.128.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.N', 'old_label': '128.p1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.P', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 184760912
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.A', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '192.955', 'aut_weyl_index': 32, 'centralizer': '192.A', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.A', '96.KF', '96.KG', '96.KH', '96.KI', '96.KJ', '96.KK'], 'contains': ['384.A', '384.B', '384.FW'], 'core': '192.A', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [25903229681844523013167, 51212588579793007921, 122002101738321960, 1313941673647], 'label': '3072.bgb.192.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.A', 'normal_contained_in': ['48.A'], 'normal_contains': ['384.A'], 'normalizer': '1.a1', 'old_label': '192.a1', 'projective_image': '3072.bgb', 'quotient_action_image': '192.955', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '192.A', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 184760913
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '192.B', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '48.C', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.K', '96.A', '96.NQ', '96.PL', '96.RD', '96.TN', '96.UJ', '96.US', '96.UX', '96.VD', '96.VR'], 'contains': ['384.GG'], 'core': '192.B', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.192.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.B', 'normal_contained_in': ['48.D', '96.A'], 'normal_contains': ['768.A'], 'normalizer': '1.a1', 'old_label': '192.b1', 'projective_image': '3072.bgb', 'quotient_action_image': '48.48', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '192.B', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 184760914
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.C', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.MV', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.B', '96.C', '96.D', '96.E', '96.F', '96.G', '96.KF'], 'contains': ['384.B', '384.C', '384.H', '384.X', '384.Z', '384.BF', '384.BJ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922473375925652905521, 187973685961890096441600, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.192.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.c1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.C', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760915
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.D', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.B', '96.C', '96.D', '96.E', '96.H', '96.I', '96.KG'], 'contains': ['384.B', '384.D', '384.L', '384.BA', '384.BB', '384.BH', '384.BI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [51212588579793007921, 122002101738321960, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.d1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.D', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760916
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.E', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.E', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.E', '96.J', '96.L', '96.M', '96.P', '96.KG'], 'contains': ['384.B', '384.E', '384.M', '384.BA', '384.GL'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 51212588579793007921, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.e1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.E', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760917
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.F', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.K', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.D', '96.K', '96.N', '96.O', '96.P', '96.KG'], 'contains': ['384.B', '384.E', '384.V', '384.BB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 25852017095880079467006, 1313941673647, 25852016759807766522832], 'label': '3072.bgb.192.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.f1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.F', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760918
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.G', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.MI', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.F', '96.H', '96.J', '96.K', '96.Q', '96.R', '96.V', '96.W', '96.X', '96.Y', '96.KH'], 'contains': ['384.B', '384.F', '384.P', '384.BC', '384.BE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [51212588579793007921, 79804308125641822294440, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.192.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.g1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.G', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760919
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.H', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.MN', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.G', '96.I', '96.P', '96.S', '96.T', '96.U', '96.KH'], 'contains': ['384.B', '384.F', '384.Q', '384.BD', '384.BE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 51212588579793007921, 79804308125641822294440, 25903229683158464676480], 'label': '3072.bgb.192.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.h1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.H', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760920
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.I', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.MI', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.L', '96.O', '96.Q', '96.S', '96.Z', '96.BC', '96.KJ'], 'contains': ['384.B', '384.J', '384.R', '384.GM', '384.GN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [51212587278385209726, 25903229681844523013167, 122002101738321960, 53952035291802302422343], 'label': '3072.bgb.192.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '192.i1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.I', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760921
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.F', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.D'], 'contains': ['48.G', '48.J', '48.L', '48.N', '48.P', '48.T', '48.U', '48.BB', '48.BD', '48.BH', '48.BJ', '48.CH', '48.CJ', '48.CU', '48.CY'], 'core': '3072.a1', 'coset_action_label': '24T7076', 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 187922473375925652905521, 134021394930826866723126, 25903229683158464676480, 53952035291802302422343, 378358649363678452761737, 296041409911409376977422], 'label': '3072.bgb.24.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '24.f1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.F', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 184760922
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.J', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.M', '96.N', '96.R', '96.S', '96.BA', '96.BB', '96.KJ'], 'contains': ['384.B', '384.J', '384.S', '384.GN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 51212588579793007921, 122002101738321960, 53952035291802302422343], 'label': '3072.bgb.192.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '192.j1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.J', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760923
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.K', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.F', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.C', '96.J', '96.T', '96.Z', '96.BA', '96.KG'], 'contains': ['384.B', '384.M', '384.T', '384.BH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 25852017095880079467006, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.k1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.K', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760924
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.L', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.E', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.L', '96.N', '96.U', '96.V', '96.Z', '96.BB', '96.KK'], 'contains': ['384.B', '384.O', '384.W', '384.GO'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 378307680063817574222641, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.192.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '192.l1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.L', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760925
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.M', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.M', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.B', '96.K', '96.T', '96.BB', '96.BC', '96.KG'], 'contains': ['384.B', '384.T', '384.V', '384.BI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 51212588579793007921, 1313941673647, 25852016759807766522832], 'label': '3072.bgb.192.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.m1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.M', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760926
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.N', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.T', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.M', '96.O', '96.U', '96.W', '96.BA', '96.BC', '96.KK'], 'contains': ['384.B', '384.U', '384.W'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770648994141276807, 378307680063817574222641, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.192.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '192.n1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.N', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760927
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.O', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.EY', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.C', '96.E', '96.BE', '96.BG', '96.BI', '96.BJ', '96.KL'], 'contains': ['384.C', '384.D', '384.M', '384.BK', '384.BV', '384.CN', '384.EQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903107682370587468807, 25903229691554491852799, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.o1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.O', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760928
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.P', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.FF', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.B', '96.D', '96.BD', '96.BF', '96.BI', '96.BK', '96.KL'], 'contains': ['384.C', '384.D', '384.V', '384.BL', '384.BZ', '384.CR', '384.FR'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903107682370587468807, 25903229691554491852799, 1313941673647, 25852016759807766522832], 'label': '3072.bgb.192.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.p1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.P', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760929
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.Q', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.EQ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.D', '96.E', '96.BF', '96.BG', '96.BH', '96.BL', '96.KL'], 'contains': ['384.C', '384.E', '384.L', '384.BK', '384.BL', '384.CN', '384.CR'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229691554491852799, 122002101738321960, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.q1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.Q', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760930
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.R', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.NT', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.F', '96.G', '96.BD', '96.BE', '96.BF', '96.BG', '96.KM'], 'contains': ['384.C', '384.F', '384.H', '384.BM', '384.BS', '384.CW', '384.DE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79855520714221614566521, 187922473375925652905521, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.192.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.r1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.R', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760931
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.S', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '384.FZ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BM', '96.BN', '96.KN'], 'contains': ['384.C', '384.G', '384.I', '384.BO', '384.BR', '384.CZ', '384.DD'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [79855520714221614566521, 79855398717732338388456, 122002101738321960, 1313941673647], 'label': '3072.bgb.192.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.EO', 'old_label': '192.s1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.S', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760932
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.G', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.T'], 'contains': ['48.Y', '48.BC', '48.BJ', '48.BO', '48.BQ', '48.BT', '48.BV', '48.BX', '48.BZ', '48.CB', '48.CE', '48.CN', '48.CR', '48.CZ', '48.DC'], 'core': '3072.a1', 'coset_action_label': '24T7088', 'count': 24, 'diagramx': None, 'generators': [122002101738321960, 324406991811924875755576, 25903229683158464676480, 134021272934136496216343, 53952035291802302422343, 187922594661241166512703, 242089752359655799966096], 'label': '3072.bgb.24.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '24.g1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.G', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184760933
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.T', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.ES', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.B', '96.C', '96.BD', '96.BE', '96.BH', '96.BQ', '96.KL'], 'contains': ['384.C', '384.L', '384.T', '384.BV', '384.BZ', '384.EQ', '384.FR'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [9709968839632, 122002101738321960, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.t1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.T', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760934
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.U', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.QZ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.F', '96.BH', '96.BJ', '96.BK', '96.BM', '96.BO', '96.BP', '96.BR', '96.BS', '96.BT', '96.BU', '96.BV', '96.BW', '96.BX', '96.KT'], 'contains': ['384.C', '384.P', '384.BY', '384.CG', '384.FB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [187973685961890096441600, 79804308125641822294440, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.192.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '192.u1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.U', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760935
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.V', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.UU', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.G', '96.BI', '96.BL', '96.BN', '96.BQ', '96.BY', '96.KT'], 'contains': ['384.C', '384.Q', '384.BY', '384.CH', '384.FH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 187973685961890096441600, 79804308125641822294440, 25903229683158464676480], 'label': '3072.bgb.192.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '192.v1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.V', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760936
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.W', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.W', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.H', '96.I', '96.BD', '96.BE', '96.BF', '96.BG', '96.KU'], 'contains': ['384.D', '384.F', '384.L', '384.CI', '384.CJ', '384.DB', '384.DC'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25852138386775177898303, 122002101738321960, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.w1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.W', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760937
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.X', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.ER', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.B', '96.C', '96.BD', '96.BE', '96.CE', '96.CX', '96.KX'], 'contains': ['384.D', '384.H', '384.T', '384.CK', '384.CQ', '384.DR', '384.FS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922473375925652905521, 122002101738321960, 25903229683158464676480, 404210922196204071249966], 'label': '3072.bgb.192.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.x1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.X', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760938
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.Y', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '384.J', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.CG', '96.CH', '96.KV'], 'contains': ['384.D', '384.K', '384.N', '384.CL', '384.CM', '384.EI', '384.EJ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [25903107682370587468807, 378358770650295628183080, 25852272837936812846761, 25903229683158464676480], 'label': '3072.bgb.192.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.FI', 'old_label': '192.y1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.Y', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760939
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.Z', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.Z', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.J', '96.P', '96.BG', '96.BZ', '96.CA', '96.KU'], 'contains': ['384.E', '384.F', '384.M', '384.CI', '384.GP'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 51091300648929957136, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.z1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.Z', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760940
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.BA', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.BO', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.K', '96.P', '96.BF', '96.CB', '96.CC', '96.KU'], 'contains': ['384.E', '384.F', '384.V', '384.CJ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 25852138386775177898303, 1313941673647, 25852016759807766522832], 'label': '3072.bgb.192.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.ba1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BA', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760941
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.BB', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '192.BB', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.L', '96.N', '96.BZ', '96.CB', '96.CI', '96.CZ', '96.KV'], 'contains': ['384.E', '384.J', '384.O', '384.CL', '384.GQ', '384.GR'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 25852272837936812846761, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.192.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '192.bb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BB', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760942
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.BC', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '192.CE', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.M', '96.O', '96.CA', '96.CC', '96.CJ', '96.CZ', '96.KV'], 'contains': ['384.E', '384.J', '384.U', '384.CM'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [51469042011382569606, 378358770648994141276807, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.192.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '192.bc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BC', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760943
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.H', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.T'], 'contains': ['48.Y', '48.BC', '48.BI', '48.BN', '48.BR', '48.BS', '48.BU', '48.BW', '48.BY', '48.CC', '48.CD', '48.CM', '48.CR', '48.CZ', '48.DD'], 'core': '3072.a1', 'coset_action_label': '24T7089', 'count': 24, 'diagramx': None, 'generators': [242089752358354392177983, 122002101738321960, 324406991811924875755576, 25903229683158464676480, 134021272934136496216343, 53952035291802302422343, 187922594661241166512703], 'label': '3072.bgb.24.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '24.h1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.H', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184760944
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.BD', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.CN', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.H', '96.BJ', '96.BK', '96.CD', '96.CF', '96.CG', '96.CK', '96.CL', '96.CN', '96.CP', '96.CQ', '96.CR', '96.CU', '96.CX', '96.KY'], 'contains': ['384.D', '384.P', '384.CO', '384.CU', '384.FI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 54003503618341535825287, 25903229683158464676480, 404210922196204071249966], 'label': '3072.bgb.192.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '192.bd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BD', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760945
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.BE', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.CM', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.J', '96.K', '96.BH', '96.CI', '96.CJ', '96.CM', '96.CO', '96.CS', '96.CT', '96.CX', '96.KY'], 'contains': ['384.E', '384.P', '384.T', '384.CO', '384.CP'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804308125641822294440, 122002101738321960, 25903229683158464676480, 404210922196204071249966], 'label': '3072.bgb.192.BE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.bd2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BE', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760946
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.BF', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.FG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.I', '96.BI', '96.CE', '96.CH', '96.CV', '96.DD', '96.KY'], 'contains': ['384.D', '384.Q', '384.CP', '384.CT', '384.FG'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 79804308125641822294440, 25903229683158464676480, 404210922196204071249966], 'label': '3072.bgb.192.BF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.be1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BF', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760947
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.BG', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.CM', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.L', '96.O', '96.BZ', '96.CC', '96.CM', '96.DC', '96.KW'], 'contains': ['384.E', '384.R', '384.W', '384.GS', '384.GT'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [404210922197505558871681, 122002101738321960, 25903229683158464676480, 378307680062503632549246], 'label': '3072.bgb.192.BG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '192.bf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BG', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184760948
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.BH', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '192.CX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.M', '96.N', '96.CA', '96.CB', '96.CO', '96.DC', '96.KW'], 'contains': ['384.E', '384.S', '384.W'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [404210922197505558871681, 378307680063817574222641, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.192.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '192.bg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BH', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760949
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.BI', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.EP', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.D', '96.E', '96.BF', '96.BG', '96.CX', '96.DD', '96.KX'], 'contains': ['384.D', '384.E', '384.H', '384.CK', '384.CQ', '384.CS', '384.CV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922473375925652905521, 404210922197505558871681, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.192.BI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.bh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BI', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760950
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.BJ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '96.FL', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.P', '96.BL', '96.CW', '96.CY', '96.CZ', '96.DA', '96.DB', '96.DC', '96.DD', '96.KY'], 'contains': ['384.E', '384.Q', '384.CT', '384.CU'], 'core': '3072.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [54003503618341535825287, 404210922197505558871681, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.192.BJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '192.bi1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BJ', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760951
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.BK', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.MI', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.Q', '96.S', '96.BZ', '96.CC', '96.DE', '96.DH', '96.LB'], 'contains': ['384.F', '384.J', '384.R', '384.GU', '384.GV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 79855520714221614566521, 25903229683158464676480, 53952035291802302422343], 'label': '3072.bgb.192.BK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '192.bj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BK', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760952
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.BL', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.DI', '96.DK', '96.LB'], 'contains': ['384.G', '384.K', '384.R', '384.GU', '384.GW'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [122000787877207687, 79855520714221614566521, 25903229681844523013167, 53952035291802302422343], 'label': '3072.bgb.192.BL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.FX', 'old_label': '192.bj2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BL', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760953
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.BM', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.R', '96.S', '96.CA', '96.CB', '96.DF', '96.DG', '96.LB'], 'contains': ['384.F', '384.J', '384.S', '384.GW'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 53952291032377091563446, 25903229683158464676480, 53952035291802302422343], 'label': '3072.bgb.192.BM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '192.bk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BM', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760954
    {'ambient': '3072.bgb', 'aut_centralizer_order': 1, 'aut_label': '4.E', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '3072.a1', 'complements': ['768.BK', '768.BL', '768.BS'], 'conjugacy_class_count': 1, 'contained_in': ['2.C', '2.D', '2.G'], 'contains': ['8.A', '8.O', '12.CB', '16.I', '16.M'], 'core': '4.E', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [25903229681844523013167, 108118165248982343710201, 187922473375925652905521, 566444897749485959875336, 133970303627361494479417, 404159831259638948150382, 1313941673647, 378358649363678452761737, 162070456272950954131199], 'label': '3072.bgb.4.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': ['2.C', '2.D', '2.G'], 'normal_contains': ['8.A'], 'normalizer': '1.a1', 'old_label': '4.e1', 'projective_image': '3072.bgb', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.E', 'subgroup_fusion': None, 'weyl_group': '3072.bgb'}
  • id: 184760955
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.I', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.T'], 'contains': ['48.Z', '48.BE', '48.BL', '48.BN', '48.BQ', '48.BT', '48.BU', '48.BW', '48.BZ', '48.CB', '48.CD', '48.CP', '48.CS', '48.DB', '48.DE'], 'core': '3072.a1', 'coset_action_label': '24T7087', 'count': 24, 'diagramx': None, 'generators': [122002101738321960, 324406991811924875755576, 25903229683158464676480, 134021272934136496216343, 187922594661241166512703, 242089752359655799966096, 79855264262271969233416], 'label': '3072.bgb.24.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '24.i1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.I', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184760956
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.BN', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.DJ', '96.DK', '96.LB'], 'contains': ['384.G', '384.K', '384.S', '384.GV', '384.GW'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79855520712907753462326, 122000787877207687, 25903229681844523013167, 53952035291802302422343], 'label': '3072.bgb.192.BN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.FX', 'old_label': '192.bk2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BN', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760957
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.BO', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.BA', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.J', '96.T', '96.BE', '96.DE', '96.DF', '96.KU'], 'contains': ['384.F', '384.M', '384.T', '384.DB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 25852138386775177898303, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.BO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.bl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BO', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760958
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.BP', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.E', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.U', '96.V', '96.BZ', '96.CB', '96.DE', '96.DG', '96.LC'], 'contains': ['384.F', '384.O', '384.W', '384.GX'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 122002101738321960, 25903229683158464676480, 324406870523993839248121], 'label': '3072.bgb.192.BP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '192.bm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BP', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760959
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.BQ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.BQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.K', '96.T', '96.BD', '96.DG', '96.DH', '96.KU'], 'contains': ['384.F', '384.T', '384.V', '384.DC'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 51091300648929957136, 1313941673647, 25852016759807766522832], 'label': '3072.bgb.192.BQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.bn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BQ', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760960
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.BR', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.T', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.U', '96.W', '96.CA', '96.CC', '96.DF', '96.DH', '96.LC'], 'contains': ['384.F', '384.U', '384.W'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770648994141276807, 122002101738321960, 25903229683158464676480, 324406870523993839248121], 'label': '3072.bgb.192.BR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '192.bo1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BR', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760961
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.BS', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.BM', '96.CD', '96.DI', '96.DJ', '96.DM', '96.DN', '96.DO', '96.DP', '96.DQ', '96.DR', '96.LD'], 'contains': ['384.G', '384.P', '384.DF', '384.DH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855398709336311235223, 79804308125641822294440, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.192.BS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '192.bp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BS', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 184760962
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.BT', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.BN', '96.CW', '96.DK', '96.DL', '96.DS', '96.DT', '96.LD'], 'contains': ['384.G', '384.Q', '384.DG', '384.DH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 79855398709336311235223, 79804308125641822294440, 25903229683158464676480], 'label': '3072.bgb.192.BT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.U', 'old_label': '192.bq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BT', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 184760963
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.BU', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.FE', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.B', '96.D', '96.BD', '96.BF', '96.DW', '96.DX', '96.LG'], 'contains': ['384.H', '384.L', '384.V', '384.DN', '384.DS', '384.ER', '384.FV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [368207923870206, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.192.BU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.br1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BU', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760964
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.BV', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.EX', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.C', '96.E', '96.BE', '96.BG', '96.DX', '96.DY', '96.LG'], 'contains': ['384.H', '384.L', '384.M', '384.DN', '384.DO', '384.ER', '384.EU'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229337376182892926, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.192.BV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.bs1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BV', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760965
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.BW', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.NX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.F', '96.CX', '96.DU', '96.DW', '96.DY', '96.EA', '96.EB', '96.EC', '96.ED', '96.EE', '96.LL'], 'contains': ['384.H', '384.P', '384.DP', '384.DW', '384.FK'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 187922473375925652905521, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.192.BW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.bt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BW', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760966
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.J', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.T'], 'contains': ['48.Z', '48.BE', '48.BK', '48.BO', '48.BR', '48.BS', '48.BV', '48.BX', '48.BY', '48.CC', '48.CE', '48.CO', '48.CS', '48.DB', '48.DF'], 'core': '3072.a1', 'coset_action_label': '24T7092', 'count': 24, 'diagramx': None, 'generators': [242089752358354392177983, 122002101738321960, 324406991811924875755576, 25903229683158464676480, 134021272934136496216343, 187922594661241166512703, 79855264262271969233416], 'label': '3072.bgb.24.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '24.j1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.J', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184760967
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.BX', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.PQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.G', '96.CE', '96.DD', '96.DV', '96.DX', '96.DZ', '96.LL'], 'contains': ['384.H', '384.Q', '384.DQ', '384.DW', '384.FK'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 108118165248982343710201, 187922473375925652905521, 25903229683158464676480], 'label': '3072.bgb.192.BX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.bu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BX', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760968
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.BY', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '384.EV', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.EJ', '96.EK', '96.LN'], 'contains': ['384.I', '384.N', '384.U', '384.DZ', '384.ED', '384.EX', '384.FT'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [122002101738321960, 25903229683158464676480, 134021272934136496216343, 216288705272228144236816], 'label': '3072.bgb.192.BY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.GX', 'old_label': '192.bv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BY', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760969
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.BZ', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '384.EV', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.EK', '96.EL', '96.LN'], 'contains': ['384.I', '384.N', '384.O', '384.DZ', '384.EA', '384.EX', '384.FA'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [216288705273529552035263, 122002101738321960, 25903229683158464676480, 134021272934136496216343], 'label': '3072.bgb.192.BZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.GX', 'old_label': '192.bw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BZ', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760970
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.CA', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.QA', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.BM', '96.CF', '96.EF', '96.EI', '96.EJ', '96.EL', '96.EM', '96.EN', '96.EO', '96.EP', '96.LS'], 'contains': ['384.I', '384.P', '384.EB', '384.EG', '384.FJ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 53952291033879672806278, 79855398717732338388456, 1313941673647], 'label': '3072.bgb.192.CA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '192.bx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CA', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760971
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.CB', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.PT', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.BN', '96.CY', '96.EG', '96.EH', '96.EK', '96.EQ', '96.LS'], 'contains': ['384.I', '384.Q', '384.EC', '384.EG', '384.FJ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 79855398717732338388456, 122002101738321960, 1313941673647], 'label': '3072.bgb.192.CB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '192.by1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CB', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760972
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.CC', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.E', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.L', '96.BA', '96.CA', '96.DE', '96.ES', '96.ET', '96.LU'], 'contains': ['384.J', '384.M', '384.W', '384.GY'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 1313941673647, 79804173335443638313656, 53952035291802302422343], 'label': '3072.bgb.192.CC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '192.bz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CC', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760973
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.CD', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.E', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.M', '96.Z', '96.BZ', '96.DF', '96.ES', '96.ET', '96.LU'], 'contains': ['384.J', '384.M', '384.W', '384.GZ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 54003126248003449434936, 1313941673647, 79855264262271969233416], 'label': '3072.bgb.192.CD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '192.bz2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CD', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760974
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.CE', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '192.BC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.Z', '96.BB', '96.CI', '96.DE', '96.DG', '96.EV', '96.KV'], 'contains': ['384.J', '384.O', '384.T', '384.EI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [51469042011382569606, 378358770650295628183080, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.192.CE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '192.ca1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CE', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760975
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.CF', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '192.CF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.BA', '96.BC', '96.CJ', '96.DF', '96.DH', '96.EV', '96.KV'], 'contains': ['384.J', '384.T', '384.U', '384.EJ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770648994141276807, 25852272837936812846761, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.192.CF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '192.cb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CF', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760976
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.CG', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.T', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.N', '96.BC', '96.CC', '96.DG', '96.ES', '96.EZ', '96.LU'], 'contains': ['384.J', '384.V', '384.W'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 54003126248003449434936, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.192.CG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '192.cc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CG', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760977
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.K', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.N'], 'contains': ['48.DM', '48.DO', '48.DP', '48.FE', '48.FF', '48.GC', '48.GD', '48.IO', '48.IP', '48.KB', '48.KC'], 'core': '192.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25852017094578671678641, 25903229681844523013167, 25852138389591620222016, 122002101738321960, 1313941673647, 134021272934136496216343, 51090960298439969137], 'label': '3072.bgb.24.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '24.k1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.K', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 184760978
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.CH', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.T', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.O', '96.BB', '96.CB', '96.DH', '96.ES', '96.EZ', '96.LU'], 'contains': ['384.J', '384.V', '384.W'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 1313941673647, 79804173335443638313656, 79855264262271969233416], 'label': '3072.bgb.192.CH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '192.cc2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CH', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760979
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.CI', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.MI', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.Q', '96.R', '96.BO', '96.CI', '96.CJ', '96.CK', '96.DU', '96.ER', '96.ET', '96.EZ', '96.LV'], 'contains': ['384.J', '384.P', '384.EK', '384.EM'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 54003503618341535825287, 25903229683158464676480, 53952035291802302422343], 'label': '3072.bgb.192.CI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.cd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CI', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761015
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.DP', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.DP', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.BY', '96.CW', '96.DS', '96.EH', '96.FD', '96.GG', '96.MG'], 'contains': ['384.Q', '384.FP'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 122004885304085057, 79855399081842795124439, 1313941673647], 'label': '3072.bgb.192.DP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.U', 'old_label': '192.de1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DP', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760980
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.CJ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.BP', '96.CG', '96.DI', '96.DJ', '96.EF', '96.EU', '96.EX', '96.EY', '96.FA', '96.FB', '96.LV'], 'contains': ['384.K', '384.P', '384.EK', '384.EN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804308125641822294440, 122002101738321960, 25903229683158464676480, 53952035291802302422343], 'label': '3072.bgb.192.CJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '192.cd2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CJ', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 184760981
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.CK', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.MO', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.S', '96.CZ', '96.EG', '96.ES', '96.EV', '96.EW', '96.LV'], 'contains': ['384.J', '384.Q', '384.EL', '384.EN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 79804308125641822294440, 25903229683158464676480, 53952035291802302422343], 'label': '3072.bgb.192.CK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.P', 'old_label': '192.ce1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CK', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760982
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.CL', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.CH', '96.DA', '96.DK', '96.DV', '96.FC', '96.FD', '96.LV'], 'contains': ['384.K', '384.Q', '384.EL', '384.EM'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [54003503618341535825287, 122002101738321960, 25903229683158464676480, 53952035291802302422343], 'label': '3072.bgb.192.CL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BH', 'old_label': '192.ce2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CL', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 184760983
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.CM', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.BJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.L', '96.Z', '96.BZ', '96.DE', '96.FE', '96.FL', '96.LW'], 'contains': ['384.M', '384.O', '384.R', '384.HA', '384.HB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 324355523484084195000247, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.192.CM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '192.cf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CM', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760984
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.CN', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.BF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.H', '96.BH', '96.DW', '96.DY', '96.ER', '96.FF', '96.FG', '96.FH', '96.FI', '96.FJ', '96.LX'], 'contains': ['384.L', '384.P', '384.EP', '384.ES', '384.FD'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [122004885304085057, 122002101738321960, 1313941673647, 51090958997032170942], 'label': '3072.bgb.192.CN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.cg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CN', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760985
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.CO', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.CO', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.I', '96.BL', '96.BQ', '96.DL', '96.DX', '96.EH', '96.LX'], 'contains': ['384.L', '384.Q', '384.EO', '384.ET', '384.FM'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107685154153232142, 122002101738321960, 1313941673647, 51090958997032170942], 'label': '3072.bgb.192.CO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '192.ch1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CO', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760986
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.CP', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.CP', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.P', '96.T', '96.BI', '96.DX', '96.ES', '96.FE', '96.LX'], 'contains': ['384.M', '384.Q', '384.V', '384.EO', '384.EP'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 122004885304085057, 1313941673647, 51090958997032170942], 'label': '3072.bgb.192.CP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.ch2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CP', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760987
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.CQ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.M', '96.BA', '96.CA', '96.DF', '96.FE', '96.FM', '96.LW'], 'contains': ['384.M', '384.S', '384.U'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770648994141276807, 324355523484084195000247, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.192.CQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '192.ci1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CQ', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760988
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.L', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.D', '12.E', '12.N'], 'contains': ['48.E', '48.F', '48.G', '48.H', '48.DM', '48.DQ', '48.DU', '48.EE', '48.EL', '48.FS', '48.GJ', '48.IR', '48.IS', '48.JJ', '48.KE'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25852138757799544092222, 25903229681844523013167, 51212588579793007921, 25852138389591620222016, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.24.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.l1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.L', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184760989
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.CR', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '192.BJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.J', '96.BJ', '96.DM', '96.DY', '96.EI', '96.ET', '96.EU', '96.FK', '96.FL', '96.FM', '96.FN', '96.FO', '96.LX'], 'contains': ['384.M', '384.P', '384.ES', '384.ET'], 'core': '3072.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903107682370587468807, 25852138757799544092222, 25903107685154153232142, 1313941673647], 'label': '3072.bgb.192.CR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '192.cj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CR', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 184760990
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.CS', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.DN', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.BR', '96.CG', '96.DN', '96.EJ', '96.EL', '96.FK', '96.FP', '96.FQ', '96.FR', '96.FS', '96.LZ'], 'contains': ['384.N', '384.P', '384.EW', '384.EY', '384.FC'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 378358770650295628183080, 54003503618341535825287, 25903229683158464676480], 'label': '3072.bgb.192.CS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '192.ck1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CS', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760991
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.CT', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.CT', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.U', '96.CZ', '96.EK', '96.EV', '96.FE', '96.FU', '96.LZ'], 'contains': ['384.O', '384.Q', '384.U', '384.EV', '384.EW'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770650295628183080, 54003503618341535825287, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.192.CT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.P', 'old_label': '192.cl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CT', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760992
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.CU', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.CU', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.CH', '96.DB', '96.DZ', '96.EK', '96.EW', '96.FT', '96.LZ'], 'contains': ['384.N', '384.Q', '384.EV', '384.EZ', '384.FL'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 378358770650295628183080, 79804308125641822294440, 25903229683158464676480], 'label': '3072.bgb.192.CU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '192.cl2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CU', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184760993
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.CV', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.N', '96.BB', '96.CB', '96.DG', '96.FE', '96.FV', '96.LW'], 'contains': ['384.O', '384.S', '384.V'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 122002101738321960, 25903229683158464676480, 324355523485385682622200], 'label': '3072.bgb.192.CV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '192.cm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CV', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184760994
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.CW', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '192.BJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.V', '96.BS', '96.CI', '96.CL', '96.DO', '96.EA', '96.EL', '96.EX', '96.FF', '96.FL', '96.FV', '96.FW', '96.LZ'], 'contains': ['384.O', '384.P', '384.EY', '384.EZ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [378358770650295628183080, 79804308125641822294440, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.192.CW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '192.cn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CW', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 184760995
    {'ambient': '3072.bgb', 'aut_centralizer_order': 256, 'aut_label': '192.CX', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.DG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.Q', '96.BT', '96.CM', '96.CN', '96.DI', '96.EB', '96.EM', '96.FG', '96.FL', '96.FP', '96.FX', '96.FY', '96.MA'], 'contains': ['384.P', '384.R'], 'core': '3072.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [377744146017650047, 79804308125641822294440, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.192.CX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '192.co1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CX', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184760996
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '192.CY', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '48.C', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.R', '96.BU', '96.CO', '96.CP', '96.DJ', '96.EC', '96.EN', '96.FH', '96.FM', '96.FQ', '96.FV', '96.FZ', '96.MA'], 'contains': ['384.P', '384.S'], 'core': '3072.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79804308125641822294440, 122002101738321960, 25903229683158464676480, 25903364135789722998960], 'label': '3072.bgb.192.CY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '192.cp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CY', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184760997
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.CZ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '192.DL', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.W', '96.BV', '96.CJ', '96.CQ', '96.DP', '96.ED', '96.EJ', '96.EY', '96.FI', '96.FM', '96.FX', '96.GA', '96.LZ'], 'contains': ['384.P', '384.U', '384.FC', '384.FL'], 'core': '3072.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [378358770648994141276807, 79804308125641822294440, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.192.CZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '192.cq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CZ', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 184760998
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.DA', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '192.DL', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.K', '96.BK', '96.DQ', '96.DW', '96.EO', '96.EZ', '96.FA', '96.FR', '96.FV', '96.FX', '96.GB', '96.GC', '96.LX'], 'contains': ['384.P', '384.V', '384.FD', '384.FM'], 'core': '3072.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903107682370587468807, 25903107685154153232142, 1313941673647, 51090958997032170942], 'label': '3072.bgb.192.DA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '192.cr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DA', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 184760999
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.M', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.A', '12.F', '12.G'], 'contains': ['48.DN', '48.DO', '48.DR', '48.DV', '48.ED', '48.EF', '48.EJ', '48.EN', '48.ET', '48.FT', '48.GH', '48.IV', '48.IW', '48.JB', '48.JC', '48.JM', '48.JN', '48.KF', '48.KG'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 133970303627361494479417, 122002101738321960, 1313941673647], 'label': '3072.bgb.24.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.m1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.M', 'subgroup_fusion': None, 'weyl_group': '128.1578'}
  • id: 184761000
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.DB', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.CM', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.V', '96.W', '96.BW', '96.CM', '96.CO', '96.CR', '96.EE', '96.ET', '96.EZ', '96.FJ', '96.MC'], 'contains': ['384.P', '384.W'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25852394494243815333247, 122004885304085057, 122002101738321960, 1313941673647], 'label': '3072.bgb.192.DB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.cs1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DB', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761001
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.DC', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.FY', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.BX', '96.CF', '96.DM', '96.DQ', '96.EX', '96.EY', '96.FS', '96.FY', '96.FZ', '96.GD', '96.MD'], 'contains': ['384.P', '384.FN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [404211043484134973872583, 79804308125641822294440, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.192.DC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '192.ct1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DC', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761002
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.DD', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.QZ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.X', '96.BT', '96.BU', '96.CL', '96.CQ', '96.CS', '96.DR', '96.DU', '96.EF', '96.FJ', '96.FN', '96.FS', '96.GB', '96.GE', '96.ME'], 'contains': ['384.P', '384.FO'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 54003503618341535825287, 25903229683158464676480, 133970560084911187416382], 'label': '3072.bgb.192.DD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '192.cu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DD', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761003
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.DE', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.CN', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.Y', '96.BS', '96.BV', '96.CN', '96.CP', '96.CT', '96.DN', '96.EE', '96.EP', '96.ER', '96.FB', '96.FN', '96.GB', '96.GD', '96.MF'], 'contains': ['384.P', '384.FE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 53952034948635409649297, 25903107685154153232142, 1313941673647], 'label': '3072.bgb.192.DE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '192.cv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DE', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761004
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.DF', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.FY', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.BR', '96.CU', '96.DO', '96.DP', '96.EP', '96.EU', '96.FA', '96.FY', '96.FZ', '96.GE', '96.MF'], 'contains': ['384.P', '384.FE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855264629178445030417, 122004885304085057, 122002101738321960, 1313941673647], 'label': '3072.bgb.192.DF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '192.cv2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DF', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761005
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.DG', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.DN', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.BX', '96.CD', '96.EI', '96.EO', '96.FB', '96.FP', '96.FQ', '96.FW', '96.GA', '96.GE', '96.MG'], 'contains': ['384.P', '384.FP'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952412691500576681559, 122004885304085057, 122002101738321960, 1313941673647], 'label': '3072.bgb.192.DG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '192.cw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DG', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761006
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.DH', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.BF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.Y', '96.BW', '96.CK', '96.CS', '96.EA', '96.ED', '96.FG', '96.FH', '96.FO', '96.GC', '96.MH'], 'contains': ['384.P', '384.FQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 54003503618341535825287, 25903229683158464676480, 378358649362364591657542], 'label': '3072.bgb.192.DH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.cx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DH', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761007
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.DI', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.NX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.X', '96.BO', '96.CR', '96.CT', '96.EB', '96.EC', '96.FF', '96.FI', '96.FO', '96.GC', '96.MI'], 'contains': ['384.P', '384.FF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [162121413125267185742761, 79804308125641822294440, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.192.DI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.cy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DI', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761008
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.DJ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.QA', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.BP', '96.CU', '96.DR', '96.EM', '96.EN', '96.FK', '96.FR', '96.FW', '96.GA', '96.GD', '96.MI'], 'contains': ['384.P', '384.FF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 187922216921192616009606, 54003503618341535825287, 25903229683158464676480], 'label': '3072.bgb.192.DJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '192.cy2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DJ', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761009
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '192.DK', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.C', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.S', '96.DC', '96.DK', '96.FE', '96.GF', '96.GG', '96.MA'], 'contains': ['384.Q', '384.R', '384.S'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [377744146017650047, 54003503618341535825287, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.192.DK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.R', 'old_label': '192.cz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DK', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761010
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.N', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.D', '12.H', '12.I'], 'contains': ['48.I', '48.J', '48.DQ', '48.DW', '48.DZ', '48.EU', '48.EW', '48.GI', '48.GL'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 122002101738321960, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.24.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.n1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.N', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184761011
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.DL', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '96.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.T', '96.BQ', '96.CE', '96.DS', '96.EQ', '96.EV', '96.FC', '96.FT', '96.GF', '96.KY'], 'contains': ['384.Q', '384.T', '384.FG', '384.FI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [54003503618341535825287, 122002101738321960, 25903229683158464676480, 404210922196204071249966], 'label': '3072.bgb.192.DL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '192.da1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DL', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761012
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.DM', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.CX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.U', '96.DC', '96.DT', '96.ES', '96.FD', '96.GF', '96.MC'], 'contains': ['384.Q', '384.W'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [51347406816160329727, 25903107685154153232142, 122002101738321960, 1313941673647], 'label': '3072.bgb.192.DM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.R', 'old_label': '192.db1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DM', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761013
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.DN', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.FP', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.BY', '96.CY', '96.DL', '96.EQ', '96.EW', '96.FU', '96.MD'], 'contains': ['384.Q', '384.FN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 404211043482821032924936, 79804308125641822294440, 25903229683158464676480], 'label': '3072.bgb.192.DN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '192.dc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DN', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761016
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.DQ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.DQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.CV', '96.DA', '96.DT', '96.DZ', '96.FC', '96.GG', '96.MH'], 'contains': ['384.Q', '384.FQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [54003503618341535825287, 122002101738321960, 25903229683158464676480, 378358649363678452761737], 'label': '3072.bgb.192.DQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BH', 'old_label': '192.df1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DQ', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761017
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.DR', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.CM', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.Z', '96.BC', '96.CM', '96.DE', '96.DH', '96.GF', '96.KW'], 'contains': ['384.R', '384.T', '384.W'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378307680063817574222641, 122002101738321960, 25903229683158464676480, 404210922196204071249966], 'label': '3072.bgb.192.DR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '192.dg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DR', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761018
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.DS', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.DL', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.O', '96.BC', '96.CC', '96.DH', '96.FE', '96.FX', '96.LW'], 'contains': ['384.R', '384.U', '384.V'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770648994141276807, 122002101738321960, 25903229683158464676480, 324355523485385682622200], 'label': '3072.bgb.192.DS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '192.dh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DS', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761019
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.DT', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '192.CX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.BA', '96.BB', '96.CO', '96.DF', '96.DG', '96.GF', '96.KW'], 'contains': ['384.S', '384.T', '384.W'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [122002101738321960, 25903229683158464676480, 378307680062503632549246, 404210922196204071249966], 'label': '3072.bgb.192.DT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '192.di1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DT', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761020
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.DU', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.DU', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.B', '96.E', '96.GI', '96.GN', '96.GT', '96.GU', '96.MJ'], 'contains': ['384.X', '384.BA', '384.BI', '384.BL', '384.BV', '384.CK', '384.DN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229337376182892926, 51212588579793007921, 1313941673647, 51212595674412385793], 'label': '3072.bgb.192.DU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.dj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DU', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761021
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.O', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.D', '12.H', '12.J'], 'contains': ['48.K', '48.L', '48.DQ', '48.DX', '48.EA', '48.EV', '48.EX', '48.GK', '48.GM'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 378358649363678452761737, 296041409911409376977422], 'label': '3072.bgb.24.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.o1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.O', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184761022
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.DV', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.DV', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.C', '96.D', '96.GH', '96.GO', '96.GT', '96.GU', '96.MJ'], 'contains': ['384.X', '384.BB', '384.BH', '384.BK', '384.BZ', '384.CK', '384.DN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229337376182892926, 25852017095880079467006, 1313941673647, 51212595674412385793], 'label': '3072.bgb.192.DV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.dj2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DV', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761023
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.DW', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.EZ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.C', '96.E', '96.GK', '96.GQ', '96.GU', '96.GV', '96.MK'], 'contains': ['384.Z', '384.BA', '384.BH', '384.BK', '384.BV', '384.CQ', '384.EU'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229691554491852799, 25852138393689126932998, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.DW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.dk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DW', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761024
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.DX', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.FG', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.B', '96.D', '96.GJ', '96.GP', '96.GU', '96.GW', '96.MK'], 'contains': ['384.Z', '384.BB', '384.BI', '384.BL', '384.BZ', '384.CQ', '384.FV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229691554491852799, 25852138393689126932998, 1313941673647, 25852016759807766522832], 'label': '3072.bgb.192.DX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.dl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DX', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761025
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.DY', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.DY', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.E', '96.GL', '96.GO', '96.GV', '96.GX', '96.HB', '96.MJ'], 'contains': ['384.X', '384.BA', '384.BK', '384.CS', '384.DO', '384.HC'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229337376182892926, 51212588579793007921, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.192.DY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '192.dm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DY', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761026
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.DZ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.EG', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.D', '96.GM', '96.GN', '96.GW', '96.GX', '96.HC', '96.MJ'], 'contains': ['384.X', '384.BB', '384.BL', '384.CS', '384.DS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [368207923870206, 25852017095880079467006, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.192.DZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '192.dn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DZ', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761027
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.EA', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.ET', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.D', '96.E', '96.GP', '96.GQ', '96.GT', '96.GX', '96.MK'], 'contains': ['384.Z', '384.BA', '384.BB', '384.BK', '384.BL', '384.CV', '384.ER'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229691554491852799, 1313941673647, 51091307562878992073, 51212962568394582352], 'label': '3072.bgb.192.EA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.do1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.EA', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761028
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.EB', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.NQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.HF', '96.ML'], 'contains': ['384.Y', '384.BC', '384.BG', '384.BP', '384.BW', '384.CX', '384.DI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79804308122845802507662, 25903229681844523013167, 187922473375925652905521, 187973685961890096441600], 'label': '3072.bgb.192.EB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.JW', 'old_label': '192.dp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.EB', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761029
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.EC', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.NQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.HG', '96.ML'], 'contains': ['384.Y', '384.BD', '384.BG', '384.BP', '384.BX', '384.CX', '384.DJ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 79804308124159744181057], 'label': '3072.bgb.192.EC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.JW', 'old_label': '192.dq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.EC', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761030
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.ED', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.NC', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.F', '96.G', '96.GH', '96.GI', '96.GN', '96.GO', '96.MN'], 'contains': ['384.X', '384.BE', '384.BF', '384.BM', '384.BY', '384.CW', '384.DW'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [108118165248982343710201, 187922473375925652905521, 187973685961890096441600, 25903229683158464676480], 'label': '3072.bgb.192.ED', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.dr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.ED', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761031
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.EE', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.NV', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.F', '96.G', '96.GJ', '96.GK', '96.GP', '96.GQ', '96.MQ'], 'contains': ['384.Z', '384.BE', '384.BJ', '384.BS', '384.BY', '384.DE', '384.FK'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922594664024732247801, 187973685961890096441600, 79804308125641822294440, 25903229683158464676480], 'label': '3072.bgb.192.EE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.ds1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.EE', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761032
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.P', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.6536092', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.K', '12.N', '12.O'], 'contains': ['48.DP', '48.DQ', '48.EG', '48.GN', '48.GO', '48.IX', '48.IY', '48.JQ', '48.KH'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [162070577934876685646657, 25903229681844523013167, 51212588579793007921, 25852138389591620222016, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.24.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.p1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.P', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 184761033
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.EF', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.NQ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.GL', '96.GM', '96.GR', '96.GS', '96.HF', '96.HG', '96.MR'], 'contains': ['384.X', '384.BG', '384.BU', '384.DL', '384.DT'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [53952413035981411118158, 187922473375925652905521, 187973685961890096441600, 25903229683158464676480], 'label': '3072.bgb.192.EF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.dt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.EF', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761034
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.EG', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.DZ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.C', '96.GI', '96.GR', '96.GV', '96.GY', '96.HD', '96.MJ'], 'contains': ['384.X', '384.BH', '384.BV', '384.DO', '384.DR'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229337376182892926, 25852017095880079467006, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.192.EG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '192.du1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.EG', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761035
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.EH', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.EH', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.B', '96.GH', '96.GS', '96.GW', '96.GY', '96.HE', '96.MJ'], 'contains': ['384.X', '384.BI', '384.BZ', '384.DR', '384.DS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [368207923870206, 51212588579793007921, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.192.EH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '192.dv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.EH', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761036
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.EI', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.EI', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.GL', '96.GS', '96.GZ', '96.HA', '96.HC', '96.HD', '96.MU'], 'contains': ['384.X', '384.DU', '384.DV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25852017095880079467006, 162121669227129588479873, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.192.EI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.dw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.EI', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761037
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.EJ', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.EJ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.GM', '96.GR', '96.GZ', '96.HA', '96.HB', '96.HE', '96.MU'], 'contains': ['384.X', '384.DU', '384.DV', '384.HD'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [162121669227129588479873, 51212588579793007921, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.192.EJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.dw2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.EJ', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761038
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.EK', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.EU', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.B', '96.C', '96.GJ', '96.GK', '96.GT', '96.GY', '96.MK'], 'contains': ['384.Z', '384.BH', '384.BI', '384.BV', '384.BZ', '384.ER', '384.FS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [9709968839632, 1313941673647, 51091307562878992073, 51212962568394582352], 'label': '3072.bgb.192.EK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.dx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.EK', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761039
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.EL', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.PM', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.F', '96.GT', '96.GV', '96.GW', '96.GZ', '96.HF', '96.MY'], 'contains': ['384.X', '384.Z', '384.BC', '384.BM', '384.BS', '384.CG', '384.DP'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922473375925652905521, 187973685961890096441600, 25903229683158464676480, 108118287251071627990321], 'label': '3072.bgb.192.EL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '192.dy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.EL', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761040
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.EM', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.PU', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.G', '96.GU', '96.GX', '96.GY', '96.HA', '96.HG', '96.MY'], 'contains': ['384.X', '384.Z', '384.BD', '384.BM', '384.BS', '384.CH', '384.DQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922473375925652905521, 187973685961890096441600, 134021272931340477137406, 25903229683158464676480], 'label': '3072.bgb.192.EM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '192.dz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.EM', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761041
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.EN', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.NQ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.HF', '96.HG', '96.MZ'], 'contains': ['384.Y', '384.Z', '384.BG', '384.BT', '384.CB', '384.CE', '384.DK'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [133970182339249961095537, 25903229681844523013167, 187922473375925652905521, 187973685961890096441600], 'label': '3072.bgb.192.EN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.JW', 'old_label': '192.ea1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.EN', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761042
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.EO', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.NB', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.HB', '96.HC', '96.HD', '96.HE', '96.HF', '96.HG', '96.NB'], 'contains': ['384.X', '384.Y', '384.CC', '384.CD', '384.DY', '384.HE', '384.HF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 162070456272950954131199], 'label': '3072.bgb.192.EO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.eb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.EO', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761043
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.Q', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.E', '12.H', '12.O'], 'contains': ['48.DQ', '48.DY', '48.EY', '48.GP', '48.GQ', '48.IZ', '48.JD'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229681844523013167, 53952412691500576681559, 51212588579793007921, 25852138389591620222016, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.24.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.q1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.Q', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184761044
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.EP', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.BI', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.H', '96.J', '96.GT', '96.GV', '96.HH', '96.HJ', '96.NC'], 'contains': ['384.BA', '384.BC', '384.BH', '384.CI', '384.CO', '384.DB', '384.ES'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [2796019804937, 51212588579793007921, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.EP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.ec1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.EP', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761045
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.EQ', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.Q', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.I', '96.J', '96.GI', '96.GK', '96.GO', '96.GQ', '96.ND'], 'contains': ['384.BA', '384.BE', '384.BH', '384.CI', '384.CP', '384.DB', '384.ET'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25852138757799544092222, 25852017095880079467006, 25903107685154153232142, 1313941673647], 'label': '3072.bgb.192.EQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.ed1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.EQ', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761046
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.ER', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.X', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.H', '96.K', '96.GT', '96.GW', '96.HH', '96.HK', '96.NC'], 'contains': ['384.BB', '384.BC', '384.BI', '384.CJ', '384.CO', '384.DC', '384.FD'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [2796019804937, 51212588579793007921, 1313941673647, 25852016759807766522832], 'label': '3072.bgb.192.ER', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.ee1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.ER', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761047
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.ES', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.T', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.I', '96.K', '96.GH', '96.GJ', '96.GN', '96.GP', '96.ND'], 'contains': ['384.BB', '384.BE', '384.BI', '384.CJ', '384.CP', '384.DC', '384.FM'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25852017095880079467006, 25903107685154153232142, 1313941673647, 51090958997032170942], 'label': '3072.bgb.192.ES', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.ef1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.ES', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761048
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.ET', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.EA', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.C', '96.E', '96.GI', '96.GO', '96.HI', '96.HJ', '96.NE'], 'contains': ['384.BA', '384.BF', '384.BH', '384.CK', '384.CN', '384.DO', '384.EQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [51212588579793007921, 25852138389591620222016, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.ET', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.eg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.ET', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761049
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.EU', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.EK', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.B', '96.D', '96.GH', '96.GN', '96.HI', '96.HK', '96.NE'], 'contains': ['384.BB', '384.BF', '384.BI', '384.CK', '384.CR', '384.DS', '384.FR'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [51212588579793007921, 25852138389591620222016, 1313941673647, 25852016759807766522832], 'label': '3072.bgb.192.EU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.eh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.EU', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761050
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.EV', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.EV', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.B', '96.E', '96.GK', '96.GP', '96.HH', '96.HI', '96.NF'], 'contains': ['384.BA', '384.BI', '384.BJ', '384.CQ', '384.CR', '384.EQ', '384.ER'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [51212588579793007921, 1313941673647, 51091307562878992073, 51212962568394582352], 'label': '3072.bgb.192.EV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.ei1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.EV', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761051
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.EW', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.EW', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.C', '96.D', '96.GJ', '96.GQ', '96.HH', '96.HI', '96.NF'], 'contains': ['384.BB', '384.BH', '384.BJ', '384.CN', '384.CQ', '384.ER', '384.FR'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25852017095880079467006, 1313941673647, 51091307562878992073, 51212962568394582352], 'label': '3072.bgb.192.EW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.ei2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.EW', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761052
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.EX', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.BV', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.I', '96.P', '96.GU', '96.GX', '96.HI', '96.HL', '96.NC'], 'contains': ['384.BA', '384.BB', '384.BD', '384.CI', '384.CJ', '384.CT', '384.EO'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229684640542817862, 51212588579793007921, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.EX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.ej1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.EX', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761053
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.EY', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.O', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.H', '96.P', '96.GN', '96.GO', '96.GP', '96.GQ', '96.ND'], 'contains': ['384.BA', '384.BB', '384.BE', '384.CI', '384.CJ', '384.CU', '384.EP'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [122004885304085057, 51212588579793007921, 1313941673647, 51090958997032170942], 'label': '3072.bgb.192.EY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.ek1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.EY', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761054
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.R', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.6407063', 'aut_weyl_index': 12, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.A', '12.E', '12.I', '12.J', '12.K', '12.L', '12.M'], 'contains': ['48.A', '48.DN', '48.DQ', '48.DV', '48.EI', '48.EO', '48.EZ', '48.FW', '48.GG', '48.JE', '48.JF', '48.JG', '48.JH', '48.JR', '48.KJ'], 'core': '48.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 122002101738321960, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.24.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.r1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.R', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 184761055
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.EZ', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.DW', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.D', '96.E', '96.GN', '96.GO', '96.HH', '96.HL', '96.NE'], 'contains': ['384.BA', '384.BB', '384.BF', '384.CN', '384.CR', '384.CS', '384.DN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [51212588579793007921, 1313941673647, 51091303465372291183, 51212962568394582352], 'label': '3072.bgb.192.EZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.el1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.EZ', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761056
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.FA', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.FA', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.E', '96.GQ', '96.HJ', '96.HL', '96.NF'], 'contains': ['384.BA', '384.BJ', '384.CN', '384.CV', '384.EU'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25852138393689126932998, 51212588579793007921, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.FA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.em1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.FA', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761057
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.FB', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.FH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.D', '96.GP', '96.HK', '96.HL', '96.NF'], 'contains': ['384.BB', '384.BJ', '384.CR', '384.CV', '384.FV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25852138393689126932998, 25852017095880079467006, 1313941673647, 25852016759807766522832], 'label': '3072.bgb.192.FB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.en1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.FB', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761058
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.FC', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.NZ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.F', '96.HH', '96.HJ', '96.HK', '96.NH'], 'contains': ['384.BC', '384.BF', '384.BJ', '384.CW', '384.DE', '384.DP', '384.FB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79855520714221614566521, 187922473375925652905521, 25903229683158464676480, 108118287251071627990321], 'label': '3072.bgb.192.FC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.eo1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.FC', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761059
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.FD', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.PS', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.G', '96.HI', '96.HL', '96.HM', '96.NH'], 'contains': ['384.BD', '384.BF', '384.BJ', '384.CW', '384.DE', '384.DQ', '384.FH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79855520714221614566521, 187922473375925652905521, 134021272931340477137406, 25903229683158464676480], 'label': '3072.bgb.192.FD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.ep1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.FD', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761060
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.FE', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.BU', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.I', '96.T', '96.GU', '96.GY', '96.HI', '96.HM', '96.NC'], 'contains': ['384.BD', '384.BH', '384.BI', '384.DB', '384.DC', '384.EO', '384.FG'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229684640542817862, 25852017095880079467006, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.FE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.eq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.FE', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761061
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.FF', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.P', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.H', '96.T', '96.GH', '96.GI', '96.GJ', '96.GK', '96.ND'], 'contains': ['384.BE', '384.BH', '384.BI', '384.DB', '384.DC', '384.EP', '384.FI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25852017095880079467006, 122004885304085057, 1313941673647, 51090958997032170942], 'label': '3072.bgb.192.FF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.er1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.FF', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761062
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.FG', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.DX', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.B', '96.C', '96.GH', '96.GI', '96.HH', '96.HM', '96.NE'], 'contains': ['384.BF', '384.BH', '384.BI', '384.DN', '384.DR', '384.EQ', '384.FR'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25852017095880079467006, 1313941673647, 51091303465372291183, 51212962568394582352], 'label': '3072.bgb.192.FG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.es1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.FG', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761063
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.FH', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.FB', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.C', '96.GK', '96.HJ', '96.HM', '96.NF'], 'contains': ['384.BH', '384.BJ', '384.EQ', '384.EU', '384.FS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25852138393689126932998, 25852017095880079467006, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.FH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.et1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.FH', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761064
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.FI', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.FI', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.B', '96.GJ', '96.HK', '96.HM', '96.NF'], 'contains': ['384.BI', '384.BJ', '384.FR', '384.FS', '384.FV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25852138393689126932998, 51212588579793007921, 1313941673647, 25852016759807766522832], 'label': '3072.bgb.192.FI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.eu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.FI', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761065
    {'ambient': '3072.bgb', 'aut_centralizer_order': 1, 'aut_label': '4.F', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '3072.a1', 'complements': ['768.BT', '768.BK', '768.BS', '768.BL'], 'conjugacy_class_count': 1, 'contained_in': ['2.B', '2.E', '2.G'], 'contains': ['8.A', '12.C', '16.N'], 'core': '4.F', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 187922473375925652905521, 486426872699855848892862, 404159831259638948150382, 133970303627361494479417, 566444897749485959875336, 108118165248982343710201, 162070456272950954131199], 'label': '3072.bgb.4.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.F', 'normal_contained_in': ['2.B', '2.E', '2.G'], 'normal_contains': ['8.A', '12.C'], 'normalizer': '1.a1', 'old_label': '4.f1', 'projective_image': '3072.bgb', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.F', 'subgroup_fusion': None, 'weyl_group': '3072.bgb'}
  • id: 184761066
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.S', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.F'], 'contains': ['48.DR', '48.EB', '48.EC', '48.ER', '48.ES', '48.GE', '48.GF'], 'core': '192.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [242089752358354392177983, 25903229681844523013167, 133970303627361494479417, 122002101738321960, 242140843656207303055942, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.24.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.F', 'old_label': '24.s1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.S', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761067
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.FJ', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.FJ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BD', '96.BG', '96.GI', '96.GN', '96.GT', '96.GU', '96.NZ'], 'contains': ['384.BL', '384.BM', '384.BV', '384.CI', '384.CK', '384.DC', '384.DN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [9709968839632, 1313941673647, 51091303465372291183, 51212962568394582352], 'label': '3072.bgb.192.FJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.ev1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.FJ', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761068
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.FK', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.FK', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BE', '96.BF', '96.GH', '96.GO', '96.GT', '96.GU', '96.NZ'], 'contains': ['384.BK', '384.BM', '384.BZ', '384.CJ', '384.CK', '384.DB', '384.DN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229691554491852799, 1313941673647, 51091303465372291183, 51212962568394582352], 'label': '3072.bgb.192.FK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.ev2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.FK', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761629
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '384.HK', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.EM', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.GS', '192.QW', '192.QZ'], 'contains': ['768.BO', '768.BW', '768.BX'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [25903229337376182892926, 25852017104276106643073, 162070456280045573438767], 'label': '3072.bgb.384.HK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.DI', 'old_label': '384.gu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.HK', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761069
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.FL', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.HZ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BE', '96.BG', '96.GK', '96.GQ', '96.GU', '96.GV', '96.OA'], 'contains': ['384.BK', '384.BS', '384.BV', '384.CI', '384.CQ', '384.DB', '384.EU'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25852138386775177898303, 25852138393689126932998, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.FL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.ew1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.FL', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761070
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.FM', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.IU', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BD', '96.BF', '96.GJ', '96.GP', '96.GU', '96.GW', '96.OA'], 'contains': ['384.BL', '384.BS', '384.BZ', '384.CJ', '384.CQ', '384.DC', '384.FV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25852138386775177898303, 25852138393689126932998, 1313941673647, 25852016759807766522832], 'label': '3072.bgb.192.FM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.ex1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.FM', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761071
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.FN', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.FN', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BH', '96.BI', '96.GH', '96.GK', '96.GO', '96.GP', '96.OB'], 'contains': ['384.BK', '384.BY', '384.BZ', '384.CP', '384.CR', '384.EP', '384.EQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903107687970595565937, 122004885304085057, 1313941673647, 51090958997032170942], 'label': '3072.bgb.192.FN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.ey1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.FN', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761072
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.FO', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.FO', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BH', '96.BI', '96.GI', '96.GJ', '96.GN', '96.GQ', '96.OB'], 'contains': ['384.BL', '384.BV', '384.BY', '384.CN', '384.CP', '384.EP', '384.FR'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [122007701746409022, 122004885304085057, 1313941673647, 51090958997032170942], 'label': '3072.bgb.192.FO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.ey2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.FO', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761073
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.FP', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.FP', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BG', '96.GO', '96.GV', '96.GX', '96.HN', '96.IR', '96.NZ'], 'contains': ['384.BK', '384.BM', '384.CI', '384.CS', '384.DO', '384.HG'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229691554491852799, 25852138389591620222016, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.FP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '192.ez1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.FP', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761074
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.FQ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.FV', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BF', '96.GN', '96.GW', '96.GX', '96.HO', '96.IS', '96.NZ'], 'contains': ['384.BL', '384.BM', '384.CJ', '384.CS', '384.DS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [9709968839632, 25852138389591620222016, 1313941673647, 25852016759807766522832], 'label': '3072.bgb.192.FQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '192.fa1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.FQ', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761075
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.FR', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.HJ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BF', '96.BG', '96.GP', '96.GQ', '96.GT', '96.GX', '96.OA'], 'contains': ['384.BK', '384.BL', '384.BS', '384.CI', '384.CJ', '384.CV', '384.ER'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [51091300648929957136, 1313941673647, 51091307562878992073, 51212962568394582352], 'label': '3072.bgb.192.FR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.fb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.FR', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761076
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.FS', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.FS', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BJ', '96.BL', '96.GO', '96.GQ', '96.HP', '96.HR', '96.OB'], 'contains': ['384.BK', '384.BY', '384.CN', '384.CU', '384.ET'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [122007701746409022, 25852138757799544092222, 25903107685154153232142, 1313941673647], 'label': '3072.bgb.192.FS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '192.fc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.FS', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761077
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.T', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.C', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.C', '12.N'], 'contains': ['48.DM', '48.DP', '48.DS', '48.EK', '48.EP', '48.FG', '48.GR', '48.IQ', '48.JI', '48.JS', '48.KD'], 'core': '192.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 162121669227129588479873, 187973685961890096441600, 122002101738321960, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.24.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '24.t1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.T', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184761078
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.FT', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.GF', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BK', '96.BL', '96.GN', '96.GP', '96.HQ', '96.HS', '96.OB'], 'contains': ['384.BL', '384.BY', '384.CR', '384.CU', '384.FM'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107687970595565937, 25903107685154153232142, 1313941673647, 51090958997032170942], 'label': '3072.bgb.192.FT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '192.fd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.FT', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761079
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.FU', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.NR', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.IV', '96.IW', '96.OE'], 'contains': ['384.BO', '384.BT', '384.BU', '384.CY', '384.DA', '384.DM', '384.EE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [53952413035981411118158, 187922473375925652905521, 1313941673647, 133970303635757521608262], 'label': '3072.bgb.192.FU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.MC', 'old_label': '192.fe1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.FU', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761080
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.FV', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.FQ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BE', '96.GI', '96.GV', '96.GY', '96.HT', '96.IT', '96.NZ'], 'contains': ['384.BM', '384.BV', '384.DB', '384.DO', '384.DR'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [9709968839632, 25852138389591620222016, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.FV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '192.ff1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.FV', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761081
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.FW', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.FW', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BD', '96.GH', '96.GW', '96.GY', '96.HU', '96.IU', '96.NZ'], 'contains': ['384.BM', '384.BZ', '384.DC', '384.DR', '384.DS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229691554491852799, 25852138389591620222016, 1313941673647, 25852016759807766522832], 'label': '3072.bgb.192.FW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '192.fg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.FW', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761082
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.FX', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.FX', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.GZ', '96.HA', '96.HN', '96.HU', '96.IS', '96.IT', '96.OJ'], 'contains': ['384.BM', '384.DU', '384.DV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229691554491852799, 25852138389591620222016, 1313941673647, 108118286902479131308678], 'label': '3072.bgb.192.FX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.fh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.FX', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761083
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.FY', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.FY', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.GZ', '96.HA', '96.HO', '96.HT', '96.IR', '96.IU', '96.OJ'], 'contains': ['384.BM', '384.DU', '384.DV', '384.HH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [9709968839632, 25852138389591620222016, 1313941673647, 108118286902479131308678], 'label': '3072.bgb.192.FY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.fh2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.FY', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761084
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.FZ', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.NQ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.HF', '96.HG', '96.HN', '96.HO', '96.HT', '96.HU', '96.OK'], 'contains': ['384.BM', '384.BT', '384.CX', '384.DT', '384.DY'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [108118165248982343710201, 187973685961890096441600, 133970303627361494479417, 25903229683158464676480], 'label': '3072.bgb.192.FZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.fi1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.FZ', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761085
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.GA', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.HK', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BD', '96.BE', '96.GJ', '96.GK', '96.GT', '96.GY', '96.OA'], 'contains': ['384.BS', '384.BV', '384.BZ', '384.DB', '384.DC', '384.ER', '384.FS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25852138386775177898303, 1313941673647, 51091307562878992073, 51212962568394582352], 'label': '3072.bgb.192.GA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.fj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.GA', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761086
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.GB', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.NR', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.IV', '96.OS'], 'contains': ['384.BN', '384.BQ', '384.BW', '384.CY', '384.DA', '384.DF', '384.DI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25852138386775177898303, 79804308122845802507662, 25903229681844523013167, 187922473375925652905521], 'label': '3072.bgb.192.GB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.MC', 'old_label': '192.fk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.GB', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761087
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.GC', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.NR', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.IW', '96.OS'], 'contains': ['384.BN', '384.BQ', '384.BX', '384.CY', '384.DA', '384.DG', '384.DJ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25852138386775177898303, 25903229681844523013167, 187922473375925652905521, 79804308124159744181057], 'label': '3072.bgb.192.GC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.MC', 'old_label': '192.fl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.GC', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761088
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.U', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.A', '12.N', '12.O'], 'contains': ['48.DN', '48.DO', '48.DQ', '48.DR', '48.DS', '48.EH', '48.EM', '48.EQ', '48.FA', '48.FB', '48.GS', '48.IT', '48.IU', '48.JA', '48.JK', '48.JL', '48.JO', '48.JP', '48.JT', '48.JU', '48.JV', '48.JW', '48.KI'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 133970303627361494479417, 122002101738321960, 1313941673647], 'label': '3072.bgb.24.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.u1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.U', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 184761089
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.GD', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BM', '96.BN', '96.HP', '96.HQ', '96.HV', '96.HW', '96.OV'], 'contains': ['384.BO', '384.BY', '384.CZ', '384.DH', '384.EG'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187973685961890096441600, 79804308125641822294440, 134021394933610431760703, 25903229683158464676480], 'label': '3072.bgb.192.GD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BN', 'old_label': '192.fm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.GD', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761090
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.GE', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.GJ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BM', '96.BN', '96.HR', '96.HS', '96.HX', '96.HY', '96.OX'], 'contains': ['384.BR', '384.BY', '384.DD', '384.DH', '384.FJ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [53952291033879672806278, 79855520714221614566521, 79855398717732338388456, 1313941673647], 'label': '3072.bgb.192.GE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BN', 'old_label': '192.fn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.GE', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761091
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.GF', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.FT', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BJ', '96.BQ', '96.GI', '96.GK', '96.HV', '96.HX', '96.OB'], 'contains': ['384.BV', '384.BY', '384.EQ', '384.ET', '384.FI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107687970595565937, 25852138757799544092222, 25903107685154153232142, 1313941673647], 'label': '3072.bgb.192.GF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '192.fo1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.GF', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761092
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.GG', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.GG', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BK', '96.BQ', '96.GH', '96.GJ', '96.HW', '96.HY', '96.OB'], 'contains': ['384.BY', '384.BZ', '384.FI', '384.FM', '384.FR'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [122007701746409022, 25903107685154153232142, 1313941673647, 51090958997032170942], 'label': '3072.bgb.192.GG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '192.fp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.GG', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761093
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.GH', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.GH', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BX', '96.BY', '96.HP', '96.HS', '96.HW', '96.HX', '96.PK'], 'contains': ['384.BY', '384.FN', '384.FP'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [122007701746409022, 53952412691500576681559, 122004885304085057, 1313941673647], 'label': '3072.bgb.192.GH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BN', 'old_label': '192.fq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.GH', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761094
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.GI', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.GI', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BX', '96.BY', '96.HQ', '96.HR', '96.HV', '96.HY', '96.PK'], 'contains': ['384.BY', '384.FN', '384.FP'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903107687970595565937, 53952412691500576681559, 122004885304085057, 1313941673647], 'label': '3072.bgb.192.GI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BN', 'old_label': '192.fq2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.GI', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761095
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.GJ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.IR', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BH', '96.BJ', '96.GT', '96.GV', '96.HZ', '96.IA', '96.PN'], 'contains': ['384.BK', '384.BV', '384.CG', '384.CO', '384.ES'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229691554491852799, 2796019804937, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.GJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.fr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.GJ', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761096
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.GK', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.HN', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BH', '96.BK', '96.GT', '96.GW', '96.IB', '96.IC', '96.PN'], 'contains': ['384.BL', '384.BZ', '384.CG', '384.CO', '384.FD'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229691554491852799, 2796019804937, 1313941673647, 25852016759807766522832], 'label': '3072.bgb.192.GK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.fs1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.GK', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761097
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.GL', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.EL', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.HB', '96.HC', '96.ID', '96.IE', '96.IR', '96.IS', '96.PM'], 'contains': ['384.CC', '384.CS', '384.DV', '384.HI', '384.HJ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [162121669227129588479873, 187973685961890096441600, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.192.GL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.ft1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.GL', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761098
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.GM', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.JY', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.BI', '96.BL', '96.GU', '96.GX', '96.PN'], 'contains': ['384.BK', '384.BL', '384.CH', '384.CT', '384.EO'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229684640542817862, 25903229691554491852799, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.GM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.fu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.GM', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761099
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.V', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.E', '12.P', '12.Q'], 'contains': ['48.DU', '48.DV', '48.DY', '48.FH', '48.FN', '48.GW', '48.HQ', '48.JX', '48.JY'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 79855398717732338388456, 25903229681844523013167, 53952412691500576681559, 51212588579793007921, 122002101738321960, 1313941673647], 'label': '3072.bgb.24.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.v1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.V', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184761100
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.GN', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.NQ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.HF', '96.HG', '96.PO'], 'contains': ['384.BP', '384.BS', '384.BU', '384.CB', '384.CD', '384.CX', '384.DK'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [25903229691554491852799, 133970182339249961095537, 25903229681844523013167, 187922473375925652905521], 'label': '3072.bgb.192.GN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.JW', 'old_label': '192.fv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.GN', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761101
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.GO', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.NR', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.IV', '96.IW', '96.PQ'], 'contains': ['384.BN', '384.BR', '384.BT', '384.CA', '384.CD', '384.CY', '384.DX'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187973685961890096441600, 25852017102974698844878], 'label': '3072.bgb.192.GO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.MC', 'old_label': '192.fw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.GO', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761102
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.GP', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.NR', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.IV', '96.IW', '96.PS'], 'contains': ['384.BQ', '384.BR', '384.BU', '384.CA', '384.CE', '384.DA', '384.EH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [187922473373129633118743, 25903229691554491852799, 79855398717732338388456, 1313941673647], 'label': '3072.bgb.192.GP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.MC', 'old_label': '192.fx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.GP', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761103
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.GQ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.NR', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BM', '96.IF', '96.IG', '96.IH', '96.II', '96.IV', '96.PT'], 'contains': ['384.BO', '384.BR', '384.CG', '384.DF', '384.EB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79855398716250260275073, 25903229691554491852799, 79855398717732338388456, 1313941673647], 'label': '3072.bgb.192.GQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BA', 'old_label': '192.fy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.GQ', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761104
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.GR', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.NR', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.BN', '96.IW', '96.PT'], 'contains': ['384.BO', '384.BR', '384.CH', '384.DG', '384.EC'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [53952413035981411118158, 25903229691554491852799, 79855398717732338388456, 1313941673647], 'label': '3072.bgb.192.GR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CQ', 'old_label': '192.fz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.GR', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761105
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.GS', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.EM', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.HB', '96.HD', '96.IJ', '96.IK', '96.IR', '96.IT', '96.PU'], 'contains': ['384.CC', '384.DO', '384.DU', '384.HK', '384.HL'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229337376182892926, 187973685961890096441600, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.192.GS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.ga1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.GS', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761106
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.GT', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.PV', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.HF', '96.ID', '96.IK', '96.IL', '96.PV'], 'contains': ['384.BW', '384.CB', '384.CC', '384.DP', '384.DT'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229691554491852799, 187922473375925652905521, 25903229683158464676480, 108118287251071627990321], 'label': '3072.bgb.192.GT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.gb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.GT', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761107
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.GU', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.PV', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.HG', '96.IE', '96.IJ', '96.IM', '96.PV'], 'contains': ['384.BX', '384.CB', '384.CC', '384.DQ', '384.DT'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229691554491852799, 187922473375925652905521, 134021272931340477137406, 25903229683158464676480], 'label': '3072.bgb.192.GU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.gc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.GU', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761108
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.GV', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.EL', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.HD', '96.HE', '96.ID', '96.IM', '96.IT', '96.IU', '96.PM'], 'contains': ['384.CC', '384.DR', '384.DV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [162121669227129588479873, 1313941673647, 25852017102974698844878, 162070456280045573438767], 'label': '3072.bgb.192.GV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.gd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.GV', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761109
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.GW', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.EM', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.HC', '96.HE', '96.IJ', '96.IL', '96.IS', '96.IU', '96.PU'], 'contains': ['384.CC', '384.DS', '384.DU'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [368207923870206, 1313941673647, 25852017102974698844878, 162070456280045573438767], 'label': '3072.bgb.192.GW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.ge1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.GW', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761110
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.W', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.D', '12.P', '12.R'], 'contains': ['48.O', '48.P', '48.Q', '48.R', '48.W', '48.X', '48.DT', '48.DU', '48.DW', '48.DX', '48.FC', '48.FI', '48.FL', '48.HG', '48.HN'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 122002101738321960, 324406870523993839248121, 79804308125641822294440, 378358770650295628183080, 25852272837936812846761], 'label': '3072.bgb.24.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.w1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.W', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184761111
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.GX', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.EC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.IN', '96.IO', '96.PY'], 'contains': ['384.CF', '384.EA', '384.EF', '384.HM'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [378358770650295628183080, 404159575154785525538638, 162121668865829346659896, 25903229683158464676480], 'label': '3072.bgb.192.GX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.LQ', 'old_label': '192.gf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.GX', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761112
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.GY', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.PZ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.IO', '96.IP', '96.IQ', '96.IV', '96.PZ'], 'contains': ['384.BW', '384.CA', '384.CF', '384.EB', '384.EE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79855398716250260275073, 79855398717732338388456, 1313941673647, 133970303635757521608262], 'label': '3072.bgb.192.GY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GO', 'old_label': '192.gg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.GY', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761113
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.GZ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.PZ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.IN', '96.IW', '96.PZ'], 'contains': ['384.BX', '384.CA', '384.CF', '384.EC', '384.EE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [53952413035981411118158, 79855398717732338388456, 1313941673647, 133970303635757521608262], 'label': '3072.bgb.192.GZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GO', 'old_label': '192.gh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.GZ', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761114
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.HA', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.EC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.IN', '96.IP', '96.PY'], 'contains': ['384.CF', '384.ED', '384.EF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [378358770648994141276807, 404159575154785525538638, 162121668865829346659896, 25903229683158464676480], 'label': '3072.bgb.192.HA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.LQ', 'old_label': '192.gi1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.HA', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761115
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.HB', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.FY', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BO', '96.BP', '96.HZ', '96.IA', '96.IB', '96.IC', '96.QC'], 'contains': ['384.CG', '384.EK', '384.FF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79804429416356250372480, 187973685961890096441600, 25903229683158464676480, 53952035291802302422343], 'label': '3072.bgb.192.HB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BO', 'old_label': '192.gj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.HB', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761116
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.HC', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.JX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.BI', '96.BQ', '96.GU', '96.GY', '96.PN'], 'contains': ['384.BV', '384.BZ', '384.CH', '384.EO', '384.FG'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [9709968839632, 25903229684640542817862, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.HC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.gk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.HC', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761117
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.HD', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.IJ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BR', '96.BS', '96.HZ', '96.IB', '96.IF', '96.IG', '96.QD'], 'contains': ['384.CG', '384.EY', '384.FE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804429416356250372480, 378358770650295628183080, 25903229683158464676480, 242140721658215271465607], 'label': '3072.bgb.192.HD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '192.gl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.HD', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761118
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.HE', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.LA', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BR', '96.BV', '96.IA', '96.IC', '96.IF', '96.IH', '96.QD'], 'contains': ['384.CG', '384.FC', '384.FE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804429416356250372480, 378358770648994141276807, 25903229683158464676480, 242140721658215271465607], 'label': '3072.bgb.192.HE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '192.gm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.HE', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761119
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.HF', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.QG', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.HF', '96.HG', '96.IR', '96.IS', '96.IT', '96.IU', '96.QG'], 'contains': ['384.BM', '384.BP', '384.CC', '384.CE', '384.DL', '384.HN', '384.HO', '384.HP'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [53952413035981411118158, 25903229691554491852799, 187922473375925652905521, 25903229683158464676480], 'label': '3072.bgb.192.HF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.gn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.HF', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761120
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.HG', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '96.QG', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.IV', '96.IW', '96.QG'], 'contains': ['384.BN', '384.BO', '384.BQ', '384.CD', '384.CE', '384.CF', '384.DM', '384.HN', '384.HO', '384.HP'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [53952413035981411118158, 25903229691554491852799, 25903229681844523013167, 187922473375925652905521], 'label': '3072.bgb.192.HG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.MC', 'old_label': '192.gn2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.HG', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761121
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.X', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.D', '12.Q', '12.R'], 'contains': ['48.M', '48.N', '48.DU', '48.DW', '48.EA', '48.FJ', '48.FM', '48.HH', '48.HP'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 324406991811924875755576, 1313941673647, 53952035291802302422343, 378358649363678452761737], 'label': '3072.bgb.24.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.x1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.X', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184761122
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.HH', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.QH', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.HF', '96.IV', '96.QH'], 'contains': ['384.BT', '384.BU', '384.BW', '384.CD', '384.CE', '384.CG', '384.DI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79804308122845802507662, 25903229691554491852799, 25903229681844523013167, 187922473375925652905521], 'label': '3072.bgb.192.HH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GB', 'old_label': '192.go1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.HH', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761123
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.HI', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.QH', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.HG', '96.IW', '96.QH'], 'contains': ['384.BT', '384.BU', '384.BX', '384.CD', '384.CE', '384.CH', '384.DJ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229691554491852799, 25903229681844523013167, 187922473375925652905521, 79804308124159744181057], 'label': '3072.bgb.192.HI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GB', 'old_label': '192.gp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.HI', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761124
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.HJ', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.FR', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BE', '96.BG', '96.GI', '96.GO', '96.HI', '96.HJ', '96.QI'], 'contains': ['384.CI', '384.CK', '384.CN', '384.CW', '384.DB', '384.DO', '384.EQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229337376182892926, 122007701746409022, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.192.HJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.gq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.HJ', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761125
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.HK', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.GA', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BD', '96.BF', '96.GH', '96.GN', '96.HI', '96.HK', '96.QI'], 'contains': ['384.CJ', '384.CK', '384.CR', '384.CW', '384.DC', '384.DS', '384.FR'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [122007701746409022, 368207923870206, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.192.HK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.gr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.HK', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761126
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.HL', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.HL', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BD', '96.BG', '96.GK', '96.GP', '96.HH', '96.HI', '96.QJ'], 'contains': ['384.CI', '384.CQ', '384.CR', '384.DC', '384.DE', '384.EQ', '384.ER'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903107687970595565937, 1313941673647, 51091307562878992073, 51212962568394582352], 'label': '3072.bgb.192.HL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.gs1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.HL', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761127
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.HM', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.HM', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BE', '96.BF', '96.GJ', '96.GQ', '96.HH', '96.HI', '96.QJ'], 'contains': ['384.CJ', '384.CN', '384.CQ', '384.DB', '384.DE', '384.ER', '384.FR'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [122007701746409022, 1313941673647, 51091307562878992073, 51212962568394582352], 'label': '3072.bgb.192.HM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.gs2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.HM', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761128
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.HN', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.GK', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.CE', '96.CX', '96.GH', '96.GI', '96.IX', '96.IY', '96.RF'], 'contains': ['384.CK', '384.CP', '384.DR', '384.DW', '384.FI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [108118165248982343710201, 187922473375925652905521, 25903229683158464676480, 404210922196204071249966], 'label': '3072.bgb.192.HN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.gt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.HN', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761129
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.HO', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.E', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.CG', '96.CI', '96.HZ', '96.IB', '96.IZ', '96.JB', '96.QT'], 'contains': ['384.CL', '384.CO', '384.EI', '384.EK', '384.EY'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79804429416356250372480, 378358770650295628183080, 25852272837936812846761, 25903229683158464676480], 'label': '3072.bgb.192.HO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BO', 'old_label': '192.gu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.HO', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761130
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.HP', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.E', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.CH', '96.CI', '96.IX', '96.JC', '96.JK', '96.JM', '96.QU'], 'contains': ['384.CL', '384.CP', '384.EI', '384.EM', '384.EZ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [378358770650295628183080, 25852272837936812846761, 79804308125641822294440, 25903229683158464676480], 'label': '3072.bgb.192.HP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.DK', 'old_label': '192.gv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.HP', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761131
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.HQ', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.T', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.CG', '96.CJ', '96.IA', '96.IC', '96.JA', '96.JD', '96.QT'], 'contains': ['384.CM', '384.CO', '384.EJ', '384.EK', '384.FC'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79804429416356250372480, 378358770648994141276807, 25852272837936812846761, 25903229683158464676480], 'label': '3072.bgb.192.HQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BO', 'old_label': '192.gw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.HQ', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761132
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.Y', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.D', '12.P', '12.S'], 'contains': ['48.S', '48.T', '48.DU', '48.DX', '48.DZ', '48.FK', '48.FO', '48.HO', '48.HR'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 122002101738321960, 162070321828715682652927, 324406870523993839248121, 79804308125641822294440, 378358770650295628183080], 'label': '3072.bgb.24.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.y1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.Y', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184761133
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.HR', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.T', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.CH', '96.CJ', '96.IY', '96.JE', '96.JL', '96.JN', '96.QU'], 'contains': ['384.CM', '384.CP', '384.EJ', '384.EM', '384.FL'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [378358770648994141276807, 25852272837936812846761, 79804308125641822294440, 25903229683158464676480], 'label': '3072.bgb.192.HR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.DK', 'old_label': '192.gx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.HR', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761134
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.HS', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.IS', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BH', '96.BJ', '96.HH', '96.HJ', '96.IZ', '96.JA', '96.QW'], 'contains': ['384.CN', '384.CO', '384.EQ', '384.ES', '384.FB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107687970595565937, 2796019804937, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.HS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.gy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.HS', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761135
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.HT', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.HY', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BH', '96.BK', '96.HH', '96.HK', '96.JB', '96.JD', '96.QW'], 'contains': ['384.CO', '384.CR', '384.FB', '384.FD', '384.FR'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107687970595565937, 2796019804937, 1313941673647, 25852016759807766522832], 'label': '3072.bgb.192.HT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.gz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.HT', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761136
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.HU', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.HU', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.CT', '96.CU', '96.HZ', '96.IC', '96.JA', '96.JB', '96.QY'], 'contains': ['384.CO', '384.FE', '384.FF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79804429416356250372480, 270240484111912758504367, 404210922197505558871681, 25903229683158464676480], 'label': '3072.bgb.192.HU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BO', 'old_label': '192.ha1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.HU', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761137
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.HV', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.HV', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.CT', '96.CU', '96.IA', '96.IB', '96.IZ', '96.JD', '96.QY'], 'contains': ['384.CO', '384.FE', '384.FF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79804429416356250372480, 270240484111912758504367, 25903229683158464676480, 404210922196204071249966], 'label': '3072.bgb.192.HV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BO', 'old_label': '192.ha2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.HV', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761138
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.HW', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.HW', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.CS', '96.CV', '96.IX', '96.JE', '96.JL', '96.JM', '96.RC'], 'contains': ['384.CP', '384.FO', '384.FQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [54003503618341535825287, 25903229683158464676480, 133970560084911187416382, 378358649362364591657542], 'label': '3072.bgb.192.HW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.DK', 'old_label': '192.hb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.HW', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761139
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.HX', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.HX', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.CS', '96.CV', '96.IY', '96.JC', '96.JK', '96.JN', '96.RC'], 'contains': ['384.CP', '384.FO', '384.FQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [108169512287410083283217, 54003503618341535825287, 25903229683158464676480, 378358649363678452761737], 'label': '3072.bgb.192.HX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.DK', 'old_label': '192.hb2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.HX', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761140
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.HY', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.HT', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.CE', '96.CX', '96.GJ', '96.GK', '96.JC', '96.JE', '96.RG'], 'contains': ['384.CP', '384.CQ', '384.FI', '384.FK', '384.FS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922594664024732247801, 404210922197505558871681, 79804308125641822294440, 25903229683158464676480], 'label': '3072.bgb.192.HY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.hc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.HY', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761141
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.HZ', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.FL', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BF', '96.BG', '96.GN', '96.GO', '96.HH', '96.HL', '96.QI'], 'contains': ['384.CI', '384.CJ', '384.CN', '384.CR', '384.CS', '384.CW', '384.DN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229337376182892926, 25903107687970595565937, 1313941673647, 51212595674412385793], 'label': '3072.bgb.192.HZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.hd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.HZ', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761142
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.IA', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.IA', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.BG', '96.GQ', '96.HJ', '96.HL', '96.QJ'], 'contains': ['384.CI', '384.CN', '384.CV', '384.DE', '384.EU'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [122007701746409022, 25852138393689126932998, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.IA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.he1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.IA', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761143
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.Z', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.D', '12.Q', '12.S'], 'contains': ['48.U', '48.V', '48.DU', '48.DZ', '48.EA', '48.FP', '48.FQ', '48.HS', '48.HT'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108169512287410083283217, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 324406991811924875755576, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.24.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.z1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.Z', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184761144
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.IB', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.IV', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.BF', '96.GP', '96.HK', '96.HL', '96.QJ'], 'contains': ['384.CJ', '384.CR', '384.CV', '384.DE', '384.FV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107687970595565937, 25852138393689126932998, 1313941673647, 25852016759807766522832], 'label': '3072.bgb.192.IB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.hf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.IB', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761145
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.IC', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.C', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.CD', '96.CW', '96.HP', '96.HQ', '96.HR', '96.HS', '96.QK'], 'contains': ['384.CU', '384.DH', '384.FP'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [53952291032377091563446, 53952412691500576681559, 122004885304085057, 1313941673647], 'label': '3072.bgb.192.IC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BN', 'old_label': '192.hg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.IC', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761146
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.ID', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.BM', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.GL', '96.GM', '96.IR', '96.IS', '96.JF', '96.JO', '96.QL'], 'contains': ['384.CS', '384.DL', '384.DU', '384.HQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [53952413035981411118158, 187922473375925652905521, 25903229683158464676480, 378358905093235639407953], 'label': '3072.bgb.192.ID', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.hh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.ID', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761147
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.IE', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.IE', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.CX', '96.GT', '96.HJ', '96.HK', '96.RE'], 'contains': ['384.CK', '384.CO', '384.CV', '384.DP', '384.FS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [134021272931340477137406, 25903229683158464676480, 404210922196204071249966, 162121668868625366436606], 'label': '3072.bgb.192.IE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.hi1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.IE', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761148
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.IF', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.IF', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.CX', '96.GV', '96.GW', '96.HH', '96.ID', '96.JF', '96.RE'], 'contains': ['384.CO', '384.CQ', '384.CS', '384.DP', '384.DR'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922473375925652905521, 25903229683158464676480, 108118287251071627990321, 404210922196204071249966], 'label': '3072.bgb.192.IF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '192.hi2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.IF', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761149
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.IG', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.JH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.CE', '96.DD', '96.GU', '96.HI', '96.RE'], 'contains': ['384.CK', '384.CQ', '384.CT', '384.DQ', '384.FG'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229683158464676480, 108118287251071627990321, 404210922196204071249966, 162121668868625366436606], 'label': '3072.bgb.192.IG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.hj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.IG', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761150
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.IH', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.DP', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.GL', '96.GM', '96.HN', '96.HO', '96.ID', '96.IE', '96.QP'], 'contains': ['384.CS', '384.DT', '384.DV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25852138389591620222016, 1313941673647, 133970303635757521608262, 108118286902479131308678], 'label': '3072.bgb.192.IH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.hk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.IH', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761151
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.II', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.X', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.HB', '96.HC', '96.HN', '96.HO', '96.JF', '96.JO', '96.QR'], 'contains': ['384.CS', '384.DU', '384.DY', '384.HR'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [378358905094537127039998, 187922473375925652905521, 25903229683158464676480, 162070456272950954131199], 'label': '3072.bgb.192.II', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.hl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.II', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761152
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.IJ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.HD', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.CF', '96.CY', '96.HP', '96.HQ', '96.JG', '96.JH', '96.QS'], 'contains': ['384.CU', '384.EG', '384.FN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [404211043482821032924936, 79804308125641822294440, 134021394933610431760703, 25903229683158464676480], 'label': '3072.bgb.192.IJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '192.hm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.IJ', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761153
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.IK', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.O', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.CH', '96.CZ', '96.QT'], 'contains': ['384.CL', '384.CM', '384.CT', '384.EL', '384.EV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [378358770650295628183080, 54003382330230002441647, 25852272837936812846761, 25903229683158464676480], 'label': '3072.bgb.192.IK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.FI', 'old_label': '192.hn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.IK', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761154
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.BA', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.D', '12.E', '12.R', '12.S'], 'contains': ['48.A', '48.DU', '48.DY', '48.FD', '48.FR', '48.FY', '48.HU', '48.JZ', '48.KA'], 'core': '48.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79855520714221614566521, 25903229681844523013167, 53952412691500576681559, 79804308125641822294440, 122002101738321960, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.24.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ba1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BA', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184761155
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.IL', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.O', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.CG', '96.CZ', '96.JG', '96.JH', '96.JI', '96.JJ', '96.QU'], 'contains': ['384.CL', '384.CM', '384.CU', '384.EN', '384.EW'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [378358770650295628183080, 54003503618341535825287, 25852272837936812846761, 25903229683158464676480], 'label': '3072.bgb.192.IL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '192.ho1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.IL', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761156
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.IM', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.CK', '96.DA', '96.JK', '96.JL', '96.JM', '96.JN', '96.QV'], 'contains': ['384.CU', '384.EM', '384.FQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [54003503618341535825287, 25903229683158464676480, 53952035291802302422343, 378358649362364591657542], 'label': '3072.bgb.192.IM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.DK', 'old_label': '192.hp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.IM', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761157
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.IN', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.LS', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.BI', '96.BL', '96.HI', '96.HL', '96.QW'], 'contains': ['384.CN', '384.CR', '384.CT', '384.EO', '384.FH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229684640542817862, 122007701746409022, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.IN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.hq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.IN', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761158
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.IO', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.IO', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.CL', '96.DB', '96.JH', '96.JJ', '96.JK', '96.JM', '96.QX'], 'contains': ['384.CU', '384.EZ', '384.FO'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 187973308220359388001840, 79804308125641822294440, 25903229683158464676480], 'label': '3072.bgb.192.IO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '192.hr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.IO', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761159
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.IP', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.LW', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.CF', '96.CY', '96.HR', '96.HS', '96.JI', '96.JJ', '96.RA'], 'contains': ['384.CU', '384.FJ', '384.FN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [404210922197505558871681, 162121547575114918571536, 25903229683158464676480, 134021272934136496216343], 'label': '3072.bgb.192.IP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '192.hs1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.IP', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761160
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.IQ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.LY', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.CQ', '96.DB', '96.JG', '96.JI', '96.JL', '96.JN', '96.QX'], 'contains': ['384.CU', '384.FL', '384.FO'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770648994141276807, 162070321828715682652927, 79804308125641822294440, 25903229683158464676480], 'label': '3072.bgb.192.IQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '192.ht1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.IQ', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761161
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.IR', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.GJ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.CX', '96.DD', '96.GN', '96.GO', '96.JK', '96.JL', '96.RF'], 'contains': ['384.CK', '384.CP', '384.CS', '384.CU', '384.DW'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [108118165248982343710201, 187922473375925652905521, 404210922197505558871681, 25903229683158464676480], 'label': '3072.bgb.192.IR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.hu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.IR', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761162
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.IS', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.HS', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.CX', '96.DD', '96.GP', '96.GQ', '96.JM', '96.JN', '96.RG'], 'contains': ['384.CP', '384.CQ', '384.CU', '384.CV', '384.FK'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922594664024732247801, 79804308125641822294440, 25903229683158464676480, 404210922196204071249966], 'label': '3072.bgb.192.IS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.hv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.IS', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761163
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.IT', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '192.JL', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.DD', '96.GX', '96.HL', '96.IE', '96.JO', '96.RE'], 'contains': ['384.CS', '384.CT', '384.CV', '384.DQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [187922473375925652905521, 404210922197505558871681, 134021272931340477137406, 25903229683158464676480], 'label': '3072.bgb.192.IT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '192.hw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.IT', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761164
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.IU', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.FM', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BD', '96.BE', '96.GH', '96.GI', '96.HH', '96.HM', '96.QI'], 'contains': ['384.CW', '384.DB', '384.DC', '384.DN', '384.DR', '384.EQ', '384.FR'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229337376182892926, 122007701746409022, 1313941673647, 51212595674412385793], 'label': '3072.bgb.192.IU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.hx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.IU', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761165
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.BB', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.I', '12.P', '12.Q'], 'contains': ['48.DV', '48.DW', '48.DZ', '48.GV', '48.GY', '48.HJ', '48.IA'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 79855398717732338388456, 25903229681844523013167, 256460345499052777, 51212588579793007921, 122002101738321960, 1313941673647], 'label': '3072.bgb.24.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.bb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BB', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184761166
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.IV', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.IB', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.BE', '96.GK', '96.HJ', '96.HM', '96.QJ'], 'contains': ['384.DB', '384.DE', '384.EQ', '384.EU', '384.FS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107687970595565937, 25852138393689126932998, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.IV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.hy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.IV', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761167
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.IW', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.IW', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.BD', '96.GJ', '96.HK', '96.HM', '96.QJ'], 'contains': ['384.DC', '384.DE', '384.FR', '384.FS', '384.FV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [122007701746409022, 25852138393689126932998, 1313941673647, 25852016759807766522832], 'label': '3072.bgb.192.IW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.hz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.IW', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761168
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.IX', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.GH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.BM', '96.JP', '96.JQ', '96.JR', '96.SB'], 'contains': ['384.CZ', '384.DD', '384.DF', '384.EB', '384.FB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79855398716250260275073, 79855520714221614566521, 79855398717732338388456, 1313941673647], 'label': '3072.bgb.192.IX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BX', 'old_label': '192.ia1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.IX', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761169
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.IY', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.GH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.BN', '96.JS', '96.SB'], 'contains': ['384.CZ', '384.DD', '384.DG', '384.EC', '384.FH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [53952413035981411118158, 79855520714221614566521, 79855398717732338388456, 1313941673647], 'label': '3072.bgb.192.IY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BZ', 'old_label': '192.ib1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.IY', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761170
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.IZ', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.C', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.DL', '96.DM', '96.HP', '96.HR', '96.HV', '96.HX', '96.SD'], 'contains': ['384.DH', '384.ET', '384.FN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [53952291032377091563446, 25852138757799544092222, 25903107685154153232142, 1313941673647], 'label': '3072.bgb.192.IZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BN', 'old_label': '192.ic1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.IZ', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761171
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.JA', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.I', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.DN', '96.DO', '96.IF', '96.IG', '96.JP', '96.JQ', '96.SE'], 'contains': ['384.DF', '384.EY', '384.FE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79804429416356250372480, 378358770650295628183080, 324406991811924875755576, 25903229683158464676480], 'label': '3072.bgb.192.JA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BX', 'old_label': '192.id1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.JA', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761172
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.JB', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.I', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.DN', '96.DP', '96.IF', '96.IH', '96.JP', '96.JR', '96.SE'], 'contains': ['384.DF', '384.FC', '384.FE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79804429416356250372480, 378358770648994141276807, 324406991811924875755576, 25903229683158464676480], 'label': '3072.bgb.192.JB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BX', 'old_label': '192.ie1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.JB', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761173
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.JC', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.C', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.CD', '96.DS', '96.HV', '96.HW', '96.HX', '96.HY', '96.QK'], 'contains': ['384.DH', '384.FI', '384.FP'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79855520714221614566521, 53952412691500576681559, 122004885304085057, 1313941673647], 'label': '3072.bgb.192.JC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BN', 'old_label': '192.if1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.JC', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761174
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.JD', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.C', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.DL', '96.DQ', '96.HQ', '96.HS', '96.HW', '96.HY', '96.SD'], 'contains': ['384.DH', '384.FM', '384.FN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79855520714221614566521, 25903107685154153232142, 1313941673647, 51090958997032170942], 'label': '3072.bgb.192.JD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BN', 'old_label': '192.ig1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.JD', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761175
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.JE', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.BM', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.GL', '96.GR', '96.IR', '96.IT', '96.JX', '96.JY', '96.SL'], 'contains': ['384.DL', '384.DO', '384.DV', '384.HS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [162121669227129588479873, 1313941673647, 162070456274433112077942, 25852017102974698844878], 'label': '3072.bgb.192.JE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.ih1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.JE', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761176
    {'ambient': '3072.bgb', 'aut_centralizer_order': 1, 'aut_label': '4.G', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '3072.a1', 'complements': ['768.BK', '768.BL', '768.BS', '768.BT'], 'conjugacy_class_count': 1, 'contained_in': ['2.C', '2.E', '2.F'], 'contains': ['8.A', '12.CC', '16.J', '16.O'], 'core': '4.G', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [25903229681844523013167, 108118165248982343710201, 187922473375925652905521, 566444897749485959875336, 133970303627361494479417, 404159831259638948150382, 1313941673647, 134021529040297499210286, 162070456272950954131199], 'label': '3072.bgb.4.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': ['2.C', '2.E', '2.F'], 'normal_contains': ['8.A'], 'normalizer': '1.a1', 'old_label': '4.g1', 'projective_image': '3072.bgb', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.G', 'subgroup_fusion': None, 'weyl_group': '3072.bgb'}
  • id: 184761177
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.BC', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.F', '12.J', '12.P'], 'contains': ['48.DV', '48.DX', '48.EB', '48.FU', '48.GX', '48.GZ', '48.HW'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [242089752358354392177983, 25903229681844523013167, 122002101738321960, 1313941673647, 134021272934136496216343, 296041409911409376977422, 187922594661241166512703], 'label': '3072.bgb.24.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BC', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184761178
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.JF', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.BM', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.GR', '96.GS', '96.IT', '96.IU', '96.JF', '96.KA', '96.QL'], 'contains': ['384.DL', '384.DR', '384.DU'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [53952413035981411118158, 378358905094537127039998, 187922473375925652905521, 25903229683158464676480], 'label': '3072.bgb.192.JF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.ii1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.JF', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761179
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.JG', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.BM', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.GM', '96.GS', '96.IS', '96.IU', '96.JX', '96.JZ', '96.SL'], 'contains': ['384.DL', '384.DS', '384.DV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922473021741077083393, 1313941673647, 162070456274433112077942, 25852017102974698844878], 'label': '3072.bgb.192.JG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.ij1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.JG', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761180
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.JH', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.IG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.DW', '96.DY', '96.GT', '96.HH', '96.ST'], 'contains': ['384.DN', '384.DP', '384.ER', '384.ES', '384.FD'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229337376182892926, 51212594192254410823, 1313941673647, 51212595674412385793], 'label': '3072.bgb.192.JH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.ik1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.JH', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761181
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.JI', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.JI', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.DX', '96.GU', '96.HL', '96.HM', '96.ST'], 'contains': ['384.DN', '384.DQ', '384.EO', '384.EU', '384.FV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229337376182892926, 1313941673647, 51212595674412385793, 25852017101492540879976], 'label': '3072.bgb.192.JI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.il1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.JI', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761182
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.JJ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.JJ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.DX', '96.GX', '96.GY', '96.HI', '96.IJ', '96.JX', '96.ST'], 'contains': ['384.DO', '384.DQ', '384.DS', '384.EO', '384.ER'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229337376182892926, 51212594192254410823, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.192.JJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '192.il2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.JJ', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761183
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.JK', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.DQ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.GL', '96.GR', '96.HN', '96.HT', '96.IJ', '96.IK', '96.SR'], 'contains': ['384.DO', '384.DT', '384.DU'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25852138389591620222016, 1313941673647, 133970303635757521608262, 51212962568394582352], 'label': '3072.bgb.192.JK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.im1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.JK', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761184
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.JL', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '192.IT', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.DY', '96.GV', '96.HJ', '96.IK', '96.JY', '96.ST'], 'contains': ['384.DO', '384.DP', '384.ES', '384.EU'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229337376182892926, 1313941673647, 25852017101492540879976, 25852017102974698844878], 'label': '3072.bgb.192.JL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '192.in1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.JL', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761185
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.JM', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '192.JP', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.DW', '96.GW', '96.HK', '96.IL', '96.JZ', '96.ST'], 'contains': ['384.DP', '384.DS', '384.FD', '384.FV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [368207923870206, 1313941673647, 25852017101492540879976, 25852017102974698844878], 'label': '3072.bgb.192.JM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '192.io1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.JM', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761186
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.JN', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.JR', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.GZ', '96.IK', '96.IL', '96.JF', '96.SW'], 'contains': ['384.DP', '384.DU'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922473375925652905521, 25903229683158464676480, 108118287251071627990321, 378358905093235639407953], 'label': '3072.bgb.192.JN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.ip1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.JN', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761187
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.JO', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.JO', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.GZ', '96.ID', '96.JY', '96.JZ', '96.SX'], 'contains': ['384.DP', '384.DV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [162121669227129588479873, 1313941673647, 25852017101492540879976, 25852017102974698844878], 'label': '3072.bgb.192.JO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.iq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.JO', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761188
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.BD', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.6536092', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.F', '12.G', '12.L'], 'contains': ['48.DV', '48.EC', '48.FV', '48.HA', '48.HD'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 404210787739267985320182, 122002101738321960, 1313941673647, 134021272934136496216343, 187922594661241166512703, 324355901222623977942343], 'label': '3072.bgb.24.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.bd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BD', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 184761189
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.JP', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '192.JM', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.CE', '96.GY', '96.HM', '96.IM', '96.KA', '96.RE'], 'contains': ['384.DQ', '384.DR', '384.FG', '384.FS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [187922473375925652905521, 134021272931340477137406, 25903229683158464676480, 404210922196204071249966], 'label': '3072.bgb.192.JP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '192.ir1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.JP', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761190
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.JQ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.JQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.HA', '96.IJ', '96.JO', '96.KA', '96.SW'], 'contains': ['384.DQ', '384.DU'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358905094537127039998, 187922473375925652905521, 134021272931340477137406, 25903229683158464676480], 'label': '3072.bgb.192.JQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.is1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.JQ', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761191
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.JR', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.JN', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.HA', '96.IE', '96.IM', '96.JX', '96.SX'], 'contains': ['384.DQ', '384.DV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922473021741077083393, 51212594192254410823, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.192.JR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.it1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.JR', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761192
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.JS', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.DP', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.GR', '96.GS', '96.HT', '96.HU', '96.ID', '96.IM', '96.QP'], 'contains': ['384.DR', '384.DT', '384.DV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [108169256549631273667337, 25852138389591620222016, 1313941673647, 108118286902479131308678], 'label': '3072.bgb.192.JS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.iu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.JS', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761193
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.JT', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.DQ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.GM', '96.GS', '96.HO', '96.HU', '96.IJ', '96.IL', '96.SR'], 'contains': ['384.DS', '384.DT', '384.DU'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [108169256549631273667337, 25852138389591620222016, 1313941673647, 25852016759807766522832], 'label': '3072.bgb.192.JT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.iv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.JT', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761194
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.JU', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.NR', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.IV', '96.JU', '96.JV', '96.JW', '96.TC'], 'contains': ['384.DI', '384.DM', '384.DX', '384.EB', '384.EH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804308122845802507662, 108118165248982343710201, 25903229681844523013167, 25852017102974698844878], 'label': '3072.bgb.192.JU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GO', 'old_label': '192.iw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.JU', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761195
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.JV', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.NR', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.IW', '96.JT', '96.TC'], 'contains': ['384.DJ', '384.DM', '384.DX', '384.EC', '384.EH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 79804308124159744181057, 25852017102974698844878], 'label': '3072.bgb.192.JV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GO', 'old_label': '192.ix1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.JV', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761196
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.JW', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.FY', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.DU', '96.DV', '96.IX', '96.IY', '96.JK', '96.JL', '96.TD'], 'contains': ['384.DW', '384.EM', '384.FO'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922473375925652905521, 134021394930826866723126, 25903229683158464676480, 53952035291802302422343], 'label': '3072.bgb.192.JW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.DK', 'old_label': '192.iy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.JW', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761197
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.JX', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.HC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.DW', '96.DX', '96.GH', '96.GN', '96.TE'], 'contains': ['384.DN', '384.DS', '384.DW', '384.EP', '384.FM'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25852138757799544092222, 25852138389591620222016, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.192.JX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.iz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.JX', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761198
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.JY', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.GM', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.DX', '96.DY', '96.GI', '96.GO', '96.TE'], 'contains': ['384.DN', '384.DO', '384.DW', '384.EP', '384.ET'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25852138389591620222016, 1313941673647, 25852017102974698844878, 51090958997032170942], 'label': '3072.bgb.192.JY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.ja1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.JY', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761199
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.BE', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.G', '12.J', '12.Q'], 'contains': ['48.DV', '48.EA', '48.HB', '48.HC', '48.IE'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229681844523013167, 122002101738321960, 324406991811924875755576, 1313941673647, 134021272934136496216343, 378358649363678452761737, 187922594661241166512703], 'label': '3072.bgb.24.BE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.be1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BE', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184761200
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.JZ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.CT', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.DZ', '96.EA', '96.IX', '96.JK', '96.TF'], 'contains': ['384.DW', '384.EZ', '384.FQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922473375925652905521, 134021394930826866723126, 25903229683158464676480, 378358649362364591657542], 'label': '3072.bgb.192.JZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.DK', 'old_label': '192.jb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.JZ', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761201
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.KA', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '768.K', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.JT', '96.JU', '96.TG'], 'contains': ['384.DX', '384.FA', '384.FU'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [133970303627361494479417, 25903229683158464676480, 25852017102974698844878, 242089752359655799966096], 'label': '3072.bgb.192.KA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.OC', 'old_label': '192.jc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.KA', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761202
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.KB', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.FG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.DZ', '96.ED', '96.IY', '96.JL', '96.TF'], 'contains': ['384.DW', '384.FL', '384.FQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922473375925652905521, 134021394930826866723126, 25903229683158464676480, 378358649363678452761737], 'label': '3072.bgb.192.KB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.DK', 'old_label': '192.jd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.KB', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761203
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.KC', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '768.K', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.JT', '96.JV', '96.TG'], 'contains': ['384.DX', '384.FT', '384.FU'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [242089752358354392177983, 133970303627361494479417, 25903229683158464676480, 25852017102974698844878], 'label': '3072.bgb.192.KC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.OC', 'old_label': '192.je1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.KC', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761204
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.KD', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.NQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.HF', '96.JF', '96.JY', '96.JZ', '96.TO'], 'contains': ['384.DI', '384.DK', '384.DL', '384.DP', '384.DY'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922473375925652905521, 25903229683158464676480, 108118287251071627990321, 162070456272950954131199], 'label': '3072.bgb.192.KD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.jf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.KD', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761205
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.KE', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.NQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.HG', '96.JO', '96.JX', '96.KA', '96.TO'], 'contains': ['384.DJ', '384.DK', '384.DL', '384.DQ', '384.DY'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922473375925652905521, 134021272931340477137406, 25903229683158464676480, 162070456272950954131199], 'label': '3072.bgb.192.KE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.jg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.KE', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761206
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.KF', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.X', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.HB', '96.HD', '96.HN', '96.HT', '96.JX', '96.JY', '96.TP'], 'contains': ['384.DO', '384.DV', '384.DY', '384.HT'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922473375925652905521, 162121669227129588479873, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.192.KF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.jh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.KF', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761207
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.KG', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.X', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.HD', '96.HE', '96.HT', '96.HU', '96.JF', '96.KA', '96.QR'], 'contains': ['384.DR', '384.DU', '384.DY'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922473375925652905521, 25903229683158464676480, 378358905093235639407953, 162070456272950954131199], 'label': '3072.bgb.192.KG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.ji1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.KG', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761208
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.KH', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.X', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.HC', '96.HE', '96.HO', '96.HU', '96.JX', '96.JZ', '96.TP'], 'contains': ['384.DS', '384.DV', '384.DY'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922473021741077083393, 187922473375925652905521, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.192.KH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '192.jj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.KH', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761209
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.KI', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.EC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.EJ', '96.EL', '96.IF', '96.JP', '96.TU'], 'contains': ['384.DZ', '384.EB', '384.EX', '384.EY', '384.FC'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804429416356250372480, 25903229683158464676480, 134021272934136496216343, 216288705272228144236816], 'label': '3072.bgb.192.KI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BX', 'old_label': '192.jk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.KI', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761210
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.BF', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.H', '12.P', '12.R'], 'contains': ['48.DW', '48.DX', '48.DY', '48.HI', '48.HK', '48.HV', '48.IB'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 324406870523993839248121, 53952035291802302422343], 'label': '3072.bgb.24.BF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.bf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BF', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184761211
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.KJ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.KJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.EK', '96.IN', '96.TU'], 'contains': ['384.EA', '384.EC', '384.ED', '384.EV', '384.EX'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [54003382330230002441647, 25903229683158464676480, 134021272934136496216343, 216288705272228144236816], 'label': '3072.bgb.192.KJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CD', 'old_label': '192.jl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.KJ', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761212
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.KK', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.KK', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.EK', '96.JT', '96.TU'], 'contains': ['384.DZ', '384.EC', '384.EV', '384.FA', '384.FT'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [108118287253867647069496, 54003382330230002441647, 25903229683158464676480, 216288705272228144236816], 'label': '3072.bgb.192.KK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.EH', 'old_label': '192.jl2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.KK', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761213
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.KL', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '384.EC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.IN', '96.IO', '96.TS'], 'contains': ['384.EA', '384.EE', '384.EF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [378358770650295628183080, 162121668865829346659896, 25903229683158464676480, 242089752368057879612857], 'label': '3072.bgb.192.KL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.LQ', 'old_label': '192.jm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.KL', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761214
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.KM', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '384.EC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.EL', '96.IG', '96.IO', '96.JQ', '96.JU', '96.TU'], 'contains': ['384.EA', '384.EB', '384.EY', '384.FA'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804429416356250372480, 108118287253867647069496, 25903229683158464676480, 216288705272228144236816], 'label': '3072.bgb.192.KM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BA', 'old_label': '192.jn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.KM', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 184761215
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.KN', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '384.EC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.EJ', '96.IH', '96.IP', '96.JR', '96.JV', '96.TU'], 'contains': ['384.EB', '384.ED', '384.FC', '384.FT'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804429416356250372480, 108118287253867647069496, 216288705273529552035263, 25903229683158464676480], 'label': '3072.bgb.192.KN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BA', 'old_label': '192.jo1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.KN', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 184761216
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.KO', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.EC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.II', '96.IO', '96.IP', '96.JW', '96.TW'], 'contains': ['384.EB', '384.EF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79855398716250260275073, 79855398717732338388456, 162121291492681005016326, 1313941673647], 'label': '3072.bgb.192.KO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GO', 'old_label': '192.jp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.KO', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761217
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.KP', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.KP', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.EP', '96.IF', '96.JQ', '96.JR', '96.TX'], 'contains': ['384.EB', '384.FE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [53952413035981411118158, 53952413037463489231303, 79855142625594763233847, 1313941673647], 'label': '3072.bgb.192.KP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BX', 'old_label': '192.jq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.KP', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761218
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.KQ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.KQ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.EP', '96.IG', '96.IH', '96.IQ', '96.JP', '96.JW', '96.TX'], 'contains': ['384.EB', '384.FE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79855398716250260275073, 79855398717732338388456, 53952156946639855024567, 1313941673647], 'label': '3072.bgb.192.KQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BA', 'old_label': '192.jq2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.KQ', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761219
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.KR', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.KR', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.II', '96.IQ', '96.JU', '96.JV', '96.TY'], 'contains': ['384.EB', '384.FU'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804429416356250372480, 108118287253867647069496, 242140721661025660593358, 25903229683158464676480], 'label': '3072.bgb.192.KR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GO', 'old_label': '192.jr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.KR', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761220
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.KS', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.KS', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.IN', '96.JS', '96.TW'], 'contains': ['384.EC', '384.EF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [53952413037463489231303, 79855398716250260275073, 187922338577505845884806, 1313941673647], 'label': '3072.bgb.192.KS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GI', 'old_label': '192.js1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.KS', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761221
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.BG', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.H', '12.Q', '12.R'], 'contains': ['48.DW', '48.DY', '48.EA', '48.HL', '48.HM', '48.IC', '48.ID'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 122002101738321960, 324406991811924875755576, 79804308125641822294440, 378358649363678452761737, 25852272837936812846761], 'label': '3072.bgb.24.BG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.bg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BG', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184761222
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.KT', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.EB', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.JS', '96.JT', '96.TY'], 'contains': ['384.EC', '384.FU'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [108118287253867647069496, 242140721662339602266753, 54003382330230002441647, 25903229683158464676480], 'label': '3072.bgb.192.KT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.HF', 'old_label': '192.jt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.KT', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761223
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.KU', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '384.EC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.IN', '96.IP', '96.TS'], 'contains': ['384.ED', '384.EE', '384.EF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [378358770648994141276807, 162121668865829346659896, 25903229683158464676480, 242089752368057879612857], 'label': '3072.bgb.192.KU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.LQ', 'old_label': '192.ju1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.KU', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761224
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.KV', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.GE', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.EF', '96.EG', '96.JG', '96.JH', '96.KB', '96.KC', '96.UB'], 'contains': ['384.EG', '384.EN', '384.FO'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79804308125641822294440, 134021394933610431760703, 25903229683158464676480, 53952035291802302422343], 'label': '3072.bgb.192.KV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '192.jv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.KV', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761225
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.KW', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.CH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.EH', '96.EI', '96.HP', '96.HV', '96.UC'], 'contains': ['384.EG', '384.ET', '384.FP'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25852138757799544092222, 25903107685154153232142, 1313941673647, 53952291036675691857216], 'label': '3072.bgb.192.KW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BN', 'old_label': '192.jw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.KW', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761226
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.KX', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.EV', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.EJ', '96.EK', '96.JG', '96.KB', '96.UE'], 'contains': ['384.DZ', '384.ED', '384.EG', '384.EW', '384.FL'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770648994141276807, 79804308125641822294440, 134021394933610431760703, 25903229683158464676480], 'label': '3072.bgb.192.KX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '192.jx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.KX', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761227
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.KY', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '768.K', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.JT', '96.JU', '96.UD'], 'contains': ['384.EH', '384.FA', '384.FU'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [108118287253867647069496, 242140721661025660593358, 25903229683158464676480, 162070456275746973182137], 'label': '3072.bgb.192.KY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.OC', 'old_label': '192.jy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.KY', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761228
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.KZ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.EV', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.EK', '96.EL', '96.JH', '96.KC', '96.UE'], 'contains': ['384.DZ', '384.EA', '384.EG', '384.EW', '384.EZ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 79804308125641822294440, 134021394933610431760703, 25903229683158464676480], 'label': '3072.bgb.192.KZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '192.jz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.KZ', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761229
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.LA', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.HE', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.CF', '96.EQ', '96.HV', '96.HW', '96.KB', '96.KC', '96.QS'], 'contains': ['384.EG', '384.FI', '384.FN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [404211043484134973872583, 79804308125641822294440, 134021394933610431760703, 25903229683158464676480], 'label': '3072.bgb.192.LA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '192.ka1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.LA', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761230
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.LB', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.CH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.EH', '96.EO', '96.HQ', '96.HW', '96.UC'], 'contains': ['384.EG', '384.FM', '384.FP'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107685154153232142, 1313941673647, 53952291036675691857216, 51090958997032170942], 'label': '3072.bgb.192.LB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BN', 'old_label': '192.kb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.LB', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761231
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.LC', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '768.K', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.JT', '96.JV', '96.UD'], 'contains': ['384.EH', '384.FT', '384.FU'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [108118287253867647069496, 242140721662339602266753, 25903229683158464676480, 162070456275746973182137], 'label': '3072.bgb.192.LC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.OC', 'old_label': '192.kc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.LC', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761232
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.BH', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.H', '12.P', '12.S'], 'contains': ['48.DX', '48.DY', '48.DZ', '48.HX', '48.HY', '48.IF', '48.IG'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [378358770650295628183080, 108169512287410083283217, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 324406870523993839248121], 'label': '3072.bgb.24.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.bh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BH', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184761233
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.LD', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.ER', '96.EU', '96.HZ', '96.IA', '96.IZ', '96.JA', '96.UK'], 'contains': ['384.EK', '384.ES', '384.FE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79855142625594763233847, 2796019804937, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.192.LD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BO', 'old_label': '192.kd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.LD', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761234
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.LE', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.U', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.CH', '96.EV', '96.QT'], 'contains': ['384.EI', '384.EJ', '384.EL', '384.EV', '384.FG'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [378358770648994141276807, 54003382330230002441647, 25852272837936812846761, 25903229683158464676480], 'label': '3072.bgb.192.LE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.FI', 'old_label': '192.ke1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.LE', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761235
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.LF', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.U', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.CG', '96.EV', '96.KB', '96.KC', '96.KD', '96.KE', '96.QU'], 'contains': ['384.EI', '384.EJ', '384.EN', '384.EW', '384.FI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [378358770648994141276807, 54003503618341535825287, 25852272837936812846761, 25903229683158464676480], 'label': '3072.bgb.192.LF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '192.kf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.LF', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761236
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.LG', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.N', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.EW', '96.EX', '96.JH', '96.JJ', '96.KC', '96.KE', '96.UL'], 'contains': ['384.EN', '384.EZ', '384.FN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [378358770650295628183080, 79804308125641822294440, 25903229683158464676480, 53952035291802302422343], 'label': '3072.bgb.192.LG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '192.kg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.LG', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761237
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.LH', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.FY', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BO', '96.BP', '96.IZ', '96.JA', '96.JB', '96.JD', '96.UM'], 'contains': ['384.EK', '384.FB', '384.FF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79804429416356250372480, 108169377837562135992360, 25903229683158464676480, 53952035291802302422343], 'label': '3072.bgb.192.LH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BO', 'old_label': '192.kh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.LH', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761238
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.LI', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.ER', '96.FA', '96.IB', '96.IC', '96.JB', '96.JD', '96.UK'], 'contains': ['384.EK', '384.FD', '384.FE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79855142625594763233847, 2796019804937, 1313941673647, 79855264262271969233416], 'label': '3072.bgb.192.LI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BO', 'old_label': '192.ki1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.LI', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761239
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.LJ', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.CK', '96.FC', '96.IX', '96.IY', '96.JC', '96.JE', '96.QV'], 'contains': ['384.EM', '384.FI', '384.FQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [54003503618341535825287, 25903229683158464676480, 53952035291802302422343, 378358649363678452761737], 'label': '3072.bgb.192.LJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.DK', 'old_label': '192.kj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.LJ', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761240
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.LK', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.GE', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.EF', '96.EG', '96.JI', '96.JJ', '96.KD', '96.KE', '96.UO'], 'contains': ['384.EN', '384.FJ', '384.FO'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79855398717732338388456, 256460345499052777, 1313941673647, 79855520715724195809353], 'label': '3072.bgb.192.LK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '192.kk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.LK', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761241
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.LL', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.FY', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.DU', '96.DV', '96.JC', '96.JE', '96.JM', '96.JN', '96.UP'], 'contains': ['384.EM', '384.FK', '384.FO'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922594664024732247801, 108169512287410083283217, 54003503618341535825287, 25903229683158464676480], 'label': '3072.bgb.192.LL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.DK', 'old_label': '192.kl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.LL', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761242
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.LM', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.N', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.EW', '96.EY', '96.JG', '96.JI', '96.KB', '96.KD', '96.UL'], 'contains': ['384.EN', '384.FL', '384.FN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [378358770648994141276807, 79804308125641822294440, 25903229683158464676480, 53952035291802302422343], 'label': '3072.bgb.192.LM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '192.km1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.LM', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761243
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.BI', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.H', '12.Q', '12.S'], 'contains': ['48.DY', '48.DZ', '48.EA', '48.IH', '48.II', '48.IJ', '48.IK'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 122002101738321960, 162070321828715682652927, 324406991811924875755576, 79804308125641822294440, 378358649363678452761737], 'label': '3072.bgb.24.BI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.bi1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BI', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184761244
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.LN', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.LO', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.BI', '96.BQ', '96.HI', '96.HM', '96.QW'], 'contains': ['384.EO', '384.EQ', '384.FG', '384.FH', '384.FR'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229684640542817862, 25903107687970595565937, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.LN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.kn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.LN', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761245
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.LO', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.LN', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.DW', '96.DX', '96.GJ', '96.GP', '96.UY'], 'contains': ['384.EP', '384.ER', '384.FK', '384.FM', '384.FV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107685154153232142, 1313941673647, 25852017101492540879976, 51090958997032170942], 'label': '3072.bgb.192.LO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.ko1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.LO', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761246
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.LP', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.CT', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.FF', '96.FK', '96.HZ', '96.IZ', '96.UT'], 'contains': ['384.ES', '384.EY', '384.FF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804429416356250372480, 378358770650295628183080, 216288448821592360017966, 25903229683158464676480], 'label': '3072.bgb.192.LP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BO', 'old_label': '192.kp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.LP', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761247
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.LQ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.FG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.FI', '96.FK', '96.IA', '96.JA', '96.UT'], 'contains': ['384.ES', '384.FC', '384.FF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804429416356250372480, 378358770648994141276807, 216288448821592360017966, 25903229683158464676480], 'label': '3072.bgb.192.LQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BO', 'old_label': '192.kq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.LQ', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761248
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.LR', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.FH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.EH', '96.EI', '96.HR', '96.HX', '96.UV'], 'contains': ['384.ET', '384.FJ', '384.FP'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79855398717732338388456, 53952412691500576681559, 1313941673647, 79855520715724195809353], 'label': '3072.bgb.192.LR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BN', 'old_label': '192.kr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.LR', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761249
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.LS', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.IN', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.DX', '96.DY', '96.GK', '96.GQ', '96.UY'], 'contains': ['384.EP', '384.ER', '384.ET', '384.EU', '384.FK'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25852138757799544092222, 25903107685154153232142, 1313941673647, 25852017101492540879976], 'label': '3072.bgb.192.LS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.ks1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.LS', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761250
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.LT', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.EV', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.EJ', '96.EK', '96.JI', '96.KD', '96.VG'], 'contains': ['384.EW', '384.EX', '384.FJ', '384.FL', '384.FT'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229683158464676480, 134021272934136496216343, 187922594661241166512703, 242089752359655799966096], 'label': '3072.bgb.192.LT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '192.kt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.LT', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761251
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.LU', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.LU', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.FS', '96.FU', '96.JG', '96.JJ', '96.KC', '96.KD', '96.VC'], 'contains': ['384.EW', '384.FN', '384.FO'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [378358770650295628183080, 108169512287410083283217, 54003503618341535825287, 25903229683158464676480], 'label': '3072.bgb.192.LU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '192.ku1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.LU', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761252
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.LV', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.LV', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.FS', '96.FU', '96.JH', '96.JI', '96.KB', '96.KE', '96.VC'], 'contains': ['384.EW', '384.FN', '384.FO'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [378358770648994141276807, 54003503618341535825287, 25903229683158464676480, 133970560084911187416382], 'label': '3072.bgb.192.LV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '192.ku2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.LV', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761253
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.LW', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.IP', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BR', '96.BS', '96.IZ', '96.JB', '96.JP', '96.JQ', '96.UZ'], 'contains': ['384.EY', '384.FB', '384.FE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804429416356250372480, 378358770650295628183080, 270240484111912758504367, 25903229683158464676480], 'label': '3072.bgb.192.LW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '192.kv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.LW', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761254
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.BJ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.F', '12.J', '12.R', '12.S'], 'contains': ['48.A', '48.DX', '48.EA', '48.FZ', '48.GA', '48.HZ', '48.IL'], 'core': '48.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 378307558065813088567696, 79804308125641822294440, 122002101738321960, 1313941673647, 79804429413572684637382, 378358649363678452761737], 'label': '3072.bgb.24.BJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.bj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BJ', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184761255
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.LX', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.CT', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.FF', '96.FR', '96.IB', '96.JB', '96.UT'], 'contains': ['384.EY', '384.FD', '384.FF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804429416356250372480, 378358770650295628183080, 216288448822893847639681, 25903229683158464676480], 'label': '3072.bgb.192.LX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BO', 'old_label': '192.kw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.LX', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761256
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.LY', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.IQ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.CL', '96.FT', '96.IX', '96.JC', '96.KC', '96.KE', '96.QX'], 'contains': ['384.EZ', '384.FI', '384.FO'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 162070321828715682652927, 79804308125641822294440, 25903229683158464676480], 'label': '3072.bgb.192.LY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '192.kx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.LY', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761257
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.LZ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.CT', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.DZ', '96.EA', '96.JC', '96.JM', '96.VB'], 'contains': ['384.EZ', '384.FK', '384.FQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922594664024732247801, 378358770650295628183080, 79804308125641822294440, 25903229683158464676480], 'label': '3072.bgb.192.LZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.DK', 'old_label': '192.ky1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.LZ', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761258
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.MA', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.EV', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.EK', '96.EL', '96.JJ', '96.KE', '96.VG'], 'contains': ['384.EW', '384.EX', '384.EZ', '384.FA', '384.FJ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [242089752358354392177983, 25903229683158464676480, 134021272934136496216343, 187922594661241166512703], 'label': '3072.bgb.192.MA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '192.kz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.MA', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761259
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.MB', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.MD', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.BR', '96.BV', '96.JA', '96.JD', '96.JP', '96.JR', '96.UZ'], 'contains': ['384.FB', '384.FC', '384.FE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804429416356250372480, 378358770648994141276807, 270240484111912758504367, 25903229683158464676480], 'label': '3072.bgb.192.MB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '192.la1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.MB', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761260
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.MC', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.FG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.FI', '96.FR', '96.IC', '96.JD', '96.UT'], 'contains': ['384.FC', '384.FD', '384.FF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804429416356250372480, 378358770648994141276807, 216288448822893847639681, 25903229683158464676480], 'label': '3072.bgb.192.MC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BO', 'old_label': '192.lb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.MC', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761261
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.MD', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.MB', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.CF', '96.EQ', '96.HX', '96.HY', '96.KD', '96.KE', '96.RA'], 'contains': ['384.FI', '384.FJ', '384.FN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [162121547575114918571536, 25903229683158464676480, 134021272934136496216343, 404210922196204071249966], 'label': '3072.bgb.192.MD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '192.lc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.MD', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761262
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.ME', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.ME', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.CQ', '96.FT', '96.IY', '96.JE', '96.KB', '96.KD', '96.QX'], 'contains': ['384.FI', '384.FL', '384.FO'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770648994141276807, 187973308220359388001840, 79804308125641822294440, 25903229683158464676480], 'label': '3072.bgb.192.ME', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '192.ld1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.ME', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761263
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.MF', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.FH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.EH', '96.EO', '96.HS', '96.HY', '96.UV'], 'contains': ['384.FJ', '384.FM', '384.FP'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79855398717732338388456, 79855399081842795124439, 1313941673647, 79855520715724195809353], 'label': '3072.bgb.192.MF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BN', 'old_label': '192.le1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.MF', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761264
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.MG', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.FG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.DZ', '96.ED', '96.JE', '96.JN', '96.VB'], 'contains': ['384.FK', '384.FL', '384.FQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922594664024732247801, 378358770648994141276807, 79804308125641822294440, 25903229683158464676480], 'label': '3072.bgb.192.MG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.DK', 'old_label': '192.lf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.MG', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761265
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.BK', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.6407063', 'aut_weyl_index': 12, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.I', '12.M', '12.S'], 'contains': ['48.A', '48.DZ', '48.GB', '48.IM', '48.IN'], 'core': '48.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118421696801471190456, 79855520714221614566521, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.24.BK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BK', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 184761266
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.MH', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.NP', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KF', '96.KL', '96.KM', '96.KN', '96.KO', '96.KP', '96.KQ', '96.KR', '96.KS', '96.KT'], 'contains': ['384.A', '384.C', '384.FX', '384.GJ'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 187973685961890096441600, 122002101738321960, 1313941673647], 'label': '3072.bgb.192.MH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '192.lg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.MH', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761267
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.MI', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.B', '96.KG', '96.KL', '96.KU', '96.KV', '96.KW', '96.KX', '96.KY'], 'contains': ['384.A', '384.D', '384.E', '384.T', '384.FY'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 122002101738321960, 1313941673647, 404210922196204071249966], 'label': '3072.bgb.192.MI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.lh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.MI', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761268
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.MJ', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '192.MJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KH', '96.KM', '96.KN', '96.KU', '96.KZ', '96.LA', '96.LB', '96.LC', '96.LD'], 'contains': ['384.A', '384.F', '384.G', '384.FZ'], 'core': '384.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [79855520714221614566521, 25903229681844523013167, 122002101738321960, 1313941673647], 'label': '3072.bgb.192.MJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '192.li1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.MJ', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184761269
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.MK', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.MW', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KF', '96.KM', '96.KO', '96.KR', '96.KX', '96.KZ', '96.LE', '96.LF', '96.LG', '96.LH', '96.LI', '96.LJ', '96.LK', '96.LL', '96.LM'], 'contains': ['384.A', '384.H', '384.GA', '384.GI'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647], 'label': '3072.bgb.192.MK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '192.lj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.MK', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184761270
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.ML', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.OK', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KI', '96.KN', '96.KP', '96.KS', '96.LA', '96.LE', '96.LF', '96.LK', '96.LN', '96.LO', '96.LP', '96.LQ', '96.LR', '96.LS', '96.LT'], 'contains': ['384.A', '384.I', '384.GB', '384.GH'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79855398717732338388456, 25903229681844523013167, 122002101738321960, 1313941673647], 'label': '3072.bgb.192.ML', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '192.lk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.ML', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184761271
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.MM', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '192.MM', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.C', '96.KJ', '96.KV', '96.LB', '96.LU', '96.LV'], 'contains': ['384.A', '384.J', '384.K', '384.GC'], 'core': '384.A', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [25903229681844523013167, 122002101738321960, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.192.MM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.H', 'old_label': '192.ll1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.MM', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 184761272
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.MN', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.H', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.D', '96.KG', '96.KL', '96.KU', '96.LG', '96.LU', '96.LW', '96.LX'], 'contains': ['384.A', '384.L', '384.M', '384.V', '384.GD'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 122002101738321960, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.MN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.lm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.MN', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761273
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.MO', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.CK', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.E', '96.KK', '96.KV', '96.LC', '96.LN', '96.LW', '96.LY', '96.LZ'], 'contains': ['384.A', '384.N', '384.O', '384.U', '384.GE'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 122002101738321960, 1313941673647], 'label': '3072.bgb.192.MO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.P', 'old_label': '192.ln1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.MO', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761274
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '192.MP', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '48.C', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.A', '96.KH', '96.KQ', '96.KT', '96.KY', '96.LD', '96.LE', '96.LL', '96.LS', '96.LV', '96.LX', '96.LZ', '96.MA', '96.MB', '96.MC', '96.MD', '96.ME', '96.MF', '96.MG', '96.MH', '96.MI'], 'contains': ['384.A', '384.P', '384.Q', '384.GF', '384.GG'], 'core': '384.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647], 'label': '3072.bgb.192.MP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '192.lo1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.MP', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761275
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '192.MQ', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 512, 'centralizer': '48.C', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.F', '96.KJ', '96.KW', '96.LB', '96.LW', '96.MA'], 'contains': ['384.A', '384.R', '384.S'], 'core': '384.A', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [25903229681844523013167, 122002101738321960, 1313941673647, 25903364135789722998960], 'label': '3072.bgb.192.MQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.H', 'old_label': '192.lp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.MQ', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 184761276
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.BL', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.G', '12.F'], 'contains': ['48.EB', '48.EC', '48.ED', '48.GT', '48.GU', '48.HE', '48.HF'], 'core': '192.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 296092500497899884979223, 25903229681844523013167, 122002101738321960, 1313941673647, 134021272934136496216343, 296041409911409376977422], 'label': '3072.bgb.24.BL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.F', 'old_label': '24.bl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BL', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761277
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.MR', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.QC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KI', '96.KO', '96.KP', '96.KQ', '96.KZ', '96.LA', '96.LH', '96.LO', '96.LY', '96.MB'], 'contains': ['384.A', '384.GK'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 122002101738321960, 1313941673647, 79804429421968711780537], 'label': '3072.bgb.192.MR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '192.lq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.MR', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184761278
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.MS', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.CX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.G', '96.KK', '96.KW', '96.LC', '96.LP', '96.LU', '96.LY', '96.MC'], 'contains': ['384.A', '384.W'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [51347406816160329727, 25903229681844523013167, 122002101738321960, 1313941673647], 'label': '3072.bgb.192.MS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.P', 'old_label': '192.lr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.MS', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761279
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.MT', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.NB', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KF', '96.MJ', '96.ML', '96.MM', '96.MN', '96.MR', '96.MS', '96.MT', '96.MU', '96.MV', '96.MY', '96.MZ', '96.NB'], 'contains': ['384.X', '384.Y', '384.FW', '384.FX', '384.GA'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 1313941673647], 'label': '3072.bgb.192.MT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '192.ls1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.MT', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761280
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.MU', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.NA', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KF', '96.MK', '96.MO', '96.MP', '96.MQ', '96.MW', '96.MX', '96.MY', '96.MZ', '96.NA'], 'contains': ['384.Z', '384.FW', '384.FX', '384.GI'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [187922594664024732247801, 25903229681844523013167, 187973685961890096441600, 1313941673647], 'label': '3072.bgb.192.MU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '192.lt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.MU', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761281
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.MV', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.C', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['64.H', '96.KG', '96.MJ', '96.MK', '96.NC', '96.ND', '96.NE', '96.NF'], 'contains': ['384.BA', '384.BB', '384.BH', '384.BI', '384.FW', '384.FY', '384.GD'], 'core': '768.A', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229681844523013167, 51212588579793007921, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.MV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.lu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.MV', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761282
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '192.MW', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.KR', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KH', '96.ML', '96.MP', '96.MY', '96.NC', '96.NG', '96.NH', '96.NJ', '96.NM', '96.NP'], 'contains': ['384.BC', '384.BD', '384.FW', '384.FZ', '384.GF'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79804429416356250372480, 25903229681844523013167, 51212588579793007921, 1313941673647], 'label': '3072.bgb.192.MW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '192.lv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.MW', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761283
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.MX', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.MH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KH', '96.MM', '96.MN', '96.MO', '96.MQ', '96.ND', '96.NI', '96.NK', '96.NL', '96.NN', '96.NO', '96.NP', '96.NQ'], 'contains': ['384.BE', '384.FW', '384.FZ', '384.GG'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 51212588579793007921, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.192.MX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '192.lw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.MX', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184761284
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.MY', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.MU', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KF', '96.MN', '96.MV', '96.NA', '96.NE', '96.NG', '96.NH', '96.NI', '96.NR', '96.NS', '96.NT', '96.NU', '96.NV'], 'contains': ['384.BF', '384.FW', '384.GA', '384.GJ'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 51212588579793007921, 1313941673647], 'label': '3072.bgb.192.MY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '192.lx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.MY', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184761285
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.MZ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '192.NQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KI', '96.ML', '96.MO', '96.MR', '96.MW', '96.MZ', '96.NG', '96.NJ', '96.NK', '96.NL', '96.NR', '96.NS', '96.NW', '96.NX'], 'contains': ['384.BG', '384.FW', '384.GB', '384.GK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855520719821622658496, 25903229681844523013167, 51212588579793007921, 1313941673647], 'label': '3072.bgb.192.MZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.ly1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.MZ', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761286
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.NA', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '192.NO', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KI', '96.MM', '96.MP', '96.MS', '96.MV', '96.MW', '96.MX', '96.NI', '96.NJ', '96.NM', '96.NN', '96.NT', '96.NW', '96.NX', '96.NY'], 'contains': ['384.FW', '384.GH', '384.GK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855398717732338388456, 25903229681844523013167, 1313941673647, 79804429421968711780537], 'label': '3072.bgb.192.NA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.lz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.NA', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761287
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '4.H', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '768.1089093', 'aut_weyl_index': 8, 'centralizer': '1536.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['8.D', '8.E', '8.F', '8.H', '8.I', '8.J', '8.K', '12.R', '16.C'], 'core': '24.A', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [79855142625594763233847, 25903229681844523013167, 566444897749485959875336, 404159831259638948150382, 79804308125641822294440, 1313941673647, 79804429413572684637382, 53952035291802302422343, 378358649363678452761737], 'label': '3072.bgb.4.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.H', 'old_label': '4.h1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.H', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 184761402
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.QZ', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '384.BM', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.IR'], 'contains': ['384.HG', '384.HH', '384.HJ', '384.HK', '384.HP', '384.HQ', '384.HS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [162121669227129588479873, 187973685961890096441600, 162070456274433112077942, 25852017102974698844878], 'label': '3072.bgb.192.QZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.IR', 'old_label': '192.ps2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.QZ', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761288
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.BM', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.N'], 'contains': ['48.EE', '48.EG', '48.EH', '48.FF', '48.FG', '48.GD', '48.GR', '48.KL', '48.KM', '48.MF', '48.MG'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 162121669227129588479873, 122002101738321960, 1313941673647, 187922594658424724202816, 162070456272950954131199], 'label': '3072.bgb.24.BM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '24.bm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BM', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 184761289
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.NB', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.NB', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KF', '96.MQ', '96.MT', '96.MX', '96.NF', '96.NH', '96.NK', '96.NM', '96.NR', '96.NW'], 'contains': ['384.BJ', '384.FW', '384.GI', '384.GJ'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [187922594664024732247801, 25903229681844523013167, 51212588579793007921, 1313941673647], 'label': '3072.bgb.192.NB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '192.ma1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.NB', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184761290
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.NC', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.ED', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.KL', '96.MJ', '96.MK', '96.NZ', '96.OA', '96.OB', '96.PN'], 'contains': ['384.BK', '384.BL', '384.BV', '384.BZ', '384.FX', '384.FY', '384.GD'], 'core': '768.A', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229691554491852799, 25903229681844523013167, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.NC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.mb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.NC', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761291
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.ND', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.QG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KM', '96.MN', '96.MY', '96.NZ', '96.OD', '96.OF', '96.OI', '96.OJ', '96.OK', '96.OS', '96.OT', '96.PQ', '96.QG'], 'contains': ['384.BM', '384.BN', '384.FX', '384.FZ', '384.GA'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187973685961890096441600, 1313941673647], 'label': '3072.bgb.192.ND', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '192.mc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.ND', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761292
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.NE', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.QG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KN', '96.ML', '96.MO', '96.OC', '96.OE', '96.OL', '96.ON', '96.OO', '96.OS', '96.OU', '96.OV', '96.PO', '96.PS', '96.PT', '96.QG'], 'contains': ['384.BO', '384.BP', '384.BQ', '384.FX', '384.FZ', '384.GB'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855520714221614566521, 79855520719821622658496, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.192.NE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.md1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.NE', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761293
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.NF', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.PR', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KN', '96.MM', '96.MP', '96.OG', '96.OM', '96.OP', '96.OR', '96.OT', '96.OW', '96.OX', '96.PP', '96.PQ', '96.PR', '96.PS', '96.PT'], 'contains': ['384.BR', '384.FX', '384.FZ', '384.GH'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229691554491852799, 79855398717732338388456, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.192.NF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.me1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.NF', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761294
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.NG', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.PP', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KM', '96.MQ', '96.MY', '96.OA', '96.OH', '96.OQ', '96.OU', '96.OW', '96.PO', '96.PR'], 'contains': ['384.BS', '384.FX', '384.FZ', '384.GI'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [187922594664024732247801, 79855520714221614566521, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.192.NG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '192.mf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.NG', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761295
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.NH', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.QH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KO', '96.MV', '96.MZ', '96.OC', '96.OE', '96.OG', '96.OH', '96.OK', '96.OY', '96.OZ', '96.PA', '96.PB', '96.PQ', '96.PX', '96.QH'], 'contains': ['384.BT', '384.FX', '384.GA', '384.GK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229691554491852799, 108118165248982343710201, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.192.NH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.mg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.NH', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761296
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.NI', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.QH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KP', '96.MR', '96.MW', '96.OD', '96.OE', '96.OM', '96.OO', '96.OY', '96.PC', '96.PD', '96.PE', '96.PO', '96.PS', '96.QB', '96.QH'], 'contains': ['384.BU', '384.FX', '384.GB', '384.GK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855520719821622658496, 25903229681844523013167, 1313941673647, 187922594658424724202816], 'label': '3072.bgb.192.NI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.mh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.NI', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761297
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '192.NJ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '48.MB', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KQ', '96.ML', '96.MP', '96.OS', '96.OW', '96.OY', '96.OZ', '96.PC', '96.PF', '96.PG', '96.PH', '96.PV', '96.PZ', '96.QF', '96.QH'], 'contains': ['384.BW', '384.BX', '384.FX', '384.GF', '384.GK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804429416356250372480, 25903229681844523013167, 1313941673647, 79804429421968711780537], 'label': '3072.bgb.192.NJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.mi1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.NJ', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761298
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.NK', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.PH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KT', '96.MN', '96.MQ', '96.OB', '96.OV', '96.OX', '96.PA', '96.PD', '96.PH', '96.PK', '96.PL', '96.PW', '96.QA'], 'contains': ['384.BY', '384.FX', '384.GG', '384.GJ'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 187973685961890096441600, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.192.NK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '192.mj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.NK', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761299
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.BN', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.E', '12.T', '12.U'], 'contains': ['48.Y', '48.Z', '48.BM', '48.BP', '48.EL', '48.EO', '48.EY', '48.FD', '48.FH', '48.FY', '48.GW', '48.KN', '48.KO'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 79855520714221614566521, 79855398717732338388456, 25903229681844523013167, 53952412691500576681559, 122002101738321960, 1313941673647], 'label': '3072.bgb.24.BN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.bn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BN', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184761300
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.NL', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.QF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KQ', '96.MM', '96.MO', '96.OT', '96.OU', '96.PB', '96.PE', '96.PI', '96.PJ', '96.PL', '96.PW', '96.PX', '96.QA', '96.QB', '96.QF'], 'contains': ['384.FX', '384.GG', '384.GK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229691554491852799, 25903229681844523013167, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.192.NL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.mk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.NL', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761301
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.NM', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.OW', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KS', '96.MV', '96.MX', '96.OF', '96.OL', '96.OO', '96.OR', '96.PA', '96.PC', '96.PF', '96.PI', '96.PP', '96.PR', '96.PW', '96.QE'], 'contains': ['384.FX', '384.GH', '384.GJ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855398717732338388456, 25903229681844523013167, 187973685961890096441600, 1313941673647], 'label': '3072.bgb.192.NM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.ml1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.NM', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761302
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.NN', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.PZ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KP', '96.MS', '96.MW', '96.OG', '96.ON', '96.OQ', '96.OR', '96.PB', '96.PG', '96.PI', '96.PQ', '96.PS', '96.PW', '96.PZ', '96.QE'], 'contains': ['384.CA', '384.FX', '384.GH', '384.GK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855398717732338388456, 25903229681844523013167, 1313941673647, 133970303635757521608262], 'label': '3072.bgb.192.NN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.mm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.NN', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761567
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '384.FH', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.PN', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.V', '192.FD', '192.IN', '192.IY', '192.LN', '192.PY'], 'contains': ['768.Q', '768.V'], 'core': '3072.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [54003382330230002441647, 108169377837562135992360, 25903229683158464676480], 'label': '3072.bgb.384.FH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.C', 'old_label': '384.ew1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.FH', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761303
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.NO', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.MP', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KR', '96.MT', '96.NA', '96.OC', '96.OD', '96.OL', '96.OP', '96.OQ', '96.OZ', '96.PD', '96.PF', '96.PJ', '96.PR', '96.QA', '96.QE'], 'contains': ['384.FX', '384.GI', '384.GJ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [187922594664024732247801, 25903229691554491852799, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.192.NO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.mn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.NO', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761304
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.NP', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.PV', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KO', '96.MX', '96.MZ', '96.OH', '96.OI', '96.OM', '96.ON', '96.OP', '96.PE', '96.PG', '96.PJ', '96.PO', '96.PV', '96.QA', '96.QE'], 'contains': ['384.CB', '384.FX', '384.GI', '384.GK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [187922594664024732247801, 25903229681844523013167, 1313941673647, 79804429421968711780537], 'label': '3072.bgb.192.NP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.mo1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.NP', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761305
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '192.NQ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '48.JW', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KR', '96.NA', '96.NB', '96.PM', '96.PO', '96.PP', '96.PQ', '96.PU', '96.PV', '96.PW', '96.PX', '96.QG', '96.QH'], 'contains': ['384.CC', '384.CD', '384.FX', '384.GA'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229691554491852799, 25903229681844523013167, 187922473375925652905521, 1313941673647], 'label': '3072.bgb.192.NQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '192.mp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.NQ', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761306
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '192.NR', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '48.MC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KS', '96.MZ', '96.PR', '96.PS', '96.PY', '96.PZ', '96.QA', '96.QB', '96.QG', '96.QH'], 'contains': ['384.CE', '384.CF', '384.FX', '384.GB'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79855520719821622658496, 25903229681844523013167, 187973685961890096441600, 1313941673647], 'label': '3072.bgb.192.NR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '192.mq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.NR', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761307
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '192.NS', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '48.MD', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KT', '96.MY', '96.PN', '96.PT', '96.QC', '96.QD', '96.QE', '96.QF', '96.QH'], 'contains': ['384.CG', '384.CH', '384.FX', '384.GF'], 'core': '768.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [79804429416356250372480, 25903229681844523013167, 187973685961890096441600, 1313941673647], 'label': '3072.bgb.192.NS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '192.mr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.NS', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761308
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.NT', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.R', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.KU', '96.NC', '96.ND', '96.NZ', '96.OA', '96.QI', '96.QJ'], 'contains': ['384.CI', '384.CJ', '384.DB', '384.DC', '384.FY', '384.FZ', '384.GD'], 'core': '768.A', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25852138386775177898303, 25903229681844523013167, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.NT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.ms1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.NT', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761309
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.NU', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '384.J', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['64.I', '96.KV', '96.QT', '96.QU'], 'contains': ['384.CL', '384.CM', '384.EI', '384.EJ', '384.FY', '384.GC', '384.GE'], 'core': '768.A', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 25852272837936812846761, 1313941673647], 'label': '3072.bgb.192.NU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.FI', 'old_label': '192.mt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.NU', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761310
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.BO', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.D', '12.T', '12.V'], 'contains': ['48.BA', '48.BB', '48.BC', '48.BE', '48.EL', '48.EU', '48.EV', '48.FI', '48.FQ', '48.HH', '48.HO', '48.KZ', '48.MJ'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [378358770650295628183080, 270240484111912758504367, 25903229681844523013167, 25852272837936812846761, 79804308125641822294440, 122002101738321960, 1313941673647], 'label': '3072.bgb.24.BO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.bo1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BO', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184761311
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.NV', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.EE', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.KL', '96.NE', '96.NF', '96.OB', '96.QI', '96.QJ', '96.QW'], 'contains': ['384.CN', '384.CR', '384.EQ', '384.FR', '384.FY', '384.GD', '384.GJ'], 'core': '768.A', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903107687970595565937, 25903229681844523013167, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.NV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.mu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.NV', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761312
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.NW', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.EL', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.KX', '96.MJ', '96.NE', '96.NZ', '96.PM', '96.QI', '96.QL', '96.QM', '96.QN', '96.QO', '96.QP', '96.QQ', '96.QR', '96.RE', '96.RF'], 'contains': ['384.CK', '384.CS', '384.DR', '384.FY', '384.GA'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 1313941673647, 404210922196204071249966], 'label': '3072.bgb.192.NW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '192.mv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.NW', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761313
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.NX', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.EB', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KY', '96.NC', '96.PN', '96.QT', '96.QW', '96.QY', '96.RE'], 'contains': ['384.CO', '384.CT', '384.FG', '384.FY', '384.GF'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804429416356250372480, 25903229681844523013167, 1313941673647, 404210922196204071249966], 'label': '3072.bgb.192.NX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.mw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.NX', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761314
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.NY', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.BT', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.KY', '96.ND', '96.OB', '96.QK', '96.QS', '96.QU', '96.QV', '96.QX', '96.QZ', '96.RA', '96.RB', '96.RC', '96.RD', '96.RF', '96.RG'], 'contains': ['384.CP', '384.CU', '384.FI', '384.FY', '384.GG'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 1313941673647, 404210922196204071249966], 'label': '3072.bgb.192.NY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '192.mx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.NY', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761315
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.NZ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.FC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KX', '96.MK', '96.NF', '96.OA', '96.QJ', '96.RE', '96.RG'], 'contains': ['384.CQ', '384.CV', '384.FS', '384.FY', '384.GI'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922594664024732247801, 25903229681844523013167, 1313941673647, 404210922196204071249966], 'label': '3072.bgb.192.NZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.my1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.NZ', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761316
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.OA', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.NG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KM', '96.MN', '96.NH', '96.OC', '96.PP', '96.QI', '96.RL', '96.RO', '96.RP', '96.RQ', '96.RS', '96.RX', '96.RZ'], 'contains': ['384.CW', '384.FZ', '384.GA', '384.GJ'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79855520714221614566521, 25903229681844523013167, 187922473375925652905521, 1313941673647], 'label': '3072.bgb.192.OA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '192.mz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.OA', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184761317
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.OB', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '192.NQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KZ', '96.ML', '96.NI', '96.OG', '96.OK', '96.OT', '96.PO', '96.RI', '96.RK', '96.RN', '96.RQ', '96.RR', '96.RX', '96.RY', '96.SA'], 'contains': ['384.CX', '384.FZ', '384.GA', '384.GK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 1313941673647, 133970303635757521608262], 'label': '3072.bgb.192.OB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.na1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.OB', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761318
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.OC', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '192.NR', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KZ', '96.MM', '96.NG', '96.OE', '96.OH', '96.OS', '96.PQ', '96.RH', '96.RJ', '96.RM', '96.RR', '96.RS', '96.RY', '96.RZ', '96.SA'], 'contains': ['384.CY', '384.FZ', '384.GA', '384.GK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 1313941673647, 133970303635757521608262], 'label': '3072.bgb.192.OC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.na2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.OC', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761319
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.OD', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '192.NF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KN', '96.NG', '96.NK', '96.OD', '96.OO', '96.OV', '96.PR', '96.RH', '96.RK', '96.RL', '96.RU', '96.RV', '96.RX', '96.SB', '96.SC'], 'contains': ['384.CZ', '384.FZ', '384.GB', '384.GJ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107687970595565937, 79855520719821622658496, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.192.OD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.nb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.OD', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761320
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.OE', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '192.NR', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LA', '96.NJ', '96.NL', '96.OE', '96.OM', '96.OS', '96.OU', '96.PS', '96.RI', '96.RJ', '96.RK', '96.RT', '96.RV', '96.RX', '96.SC'], 'contains': ['384.DA', '384.FZ', '384.GB', '384.GK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [54003503622459465078359, 79855520719821622658496, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.192.OE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.nc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.OE', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761321
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.BP', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.D', '12.U', '12.V'], 'contains': ['48.BD', '48.BF', '48.EL', '48.EU', '48.EX', '48.FJ', '48.FO', '48.HG', '48.HT'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 53952035291802302422343, 378358649363678452761737, 296041409911409376977422], 'label': '3072.bgb.24.BP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.bp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BP', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184761322
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.OF', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '192.OF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KN', '96.NI', '96.NM', '96.OF', '96.OL', '96.OQ', '96.OR', '96.OX', '96.RM', '96.RQ', '96.RT', '96.RV', '96.RZ', '96.SB', '96.SF'], 'contains': ['384.DD', '384.FZ', '384.GH', '384.GJ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855520714221614566521, 79855398717732338388456, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.192.OF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.nd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.OF', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761323
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.OG', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '192.NM', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LA', '96.NJ', '96.NN', '96.OG', '96.ON', '96.OO', '96.OR', '96.OT', '96.OW', '96.RM', '96.RR', '96.RU', '96.RW', '96.RZ', '96.SF'], 'contains': ['384.FZ', '384.GH', '384.GK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25852138386775177898303, 79855398717732338388456, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.192.OG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.ne1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.OG', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761324
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.OH', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.OH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KM', '96.MQ', '96.NH', '96.OL', '96.OP', '96.QJ', '96.RH', '96.RN', '96.SC', '96.SF'], 'contains': ['384.DE', '384.FZ', '384.GI', '384.GJ'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [187922594664024732247801, 25903229681844523013167, 108169377837562135992360, 1313941673647], 'label': '3072.bgb.192.OH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '192.nf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.OH', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184761325
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.OI', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '192.NM', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KZ', '96.MO', '96.NM', '96.OC', '96.OI', '96.OM', '96.OQ', '96.OW', '96.RJ', '96.RN', '96.RU', '96.RW', '96.RY', '96.SC', '96.SG'], 'contains': ['384.FZ', '384.GI', '384.GK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [187922594664024732247801, 25903229681844523013167, 1313941673647, 133970303635757521608262], 'label': '3072.bgb.192.OI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.ng1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.OI', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761326
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.OJ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '192.NO', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KZ', '96.MP', '96.NK', '96.OD', '96.OH', '96.ON', '96.OP', '96.OU', '96.RI', '96.RO', '96.RT', '96.RW', '96.RY', '96.SF', '96.SG'], 'contains': ['384.FZ', '384.GI', '384.GK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [187922594664024732247801, 25903229681844523013167, 79855398709336311235223, 1313941673647], 'label': '3072.bgb.192.OJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.ng2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.OJ', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761327
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '192.OK', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.KS', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LD', '96.NP', '96.OS', '96.OW', '96.PT', '96.RX', '96.RY', '96.SB', '96.SE', '96.SF'], 'contains': ['384.DF', '384.DG', '384.FZ', '384.GF'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79804429416356250372480, 25903229681844523013167, 79855398709336311235223, 1313941673647], 'label': '3072.bgb.192.OK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '192.nh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.OK', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761328
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.OL', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.MH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LD', '96.NP', '96.NQ', '96.OT', '96.OU', '96.OV', '96.OX', '96.QK', '96.RZ', '96.SA', '96.SC', '96.SD', '96.SG'], 'contains': ['384.DH', '384.FZ', '384.GG'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79855398709336311235223, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.192.OL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '192.ni1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.OL', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184761329
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '192.OM', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.QH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LE', '96.ML', '96.NG', '96.OS', '96.OY', '96.QH', '96.RX', '96.SH', '96.SI', '96.SJ', '96.SM', '96.SZ', '96.TA', '96.TC', '96.TO'], 'contains': ['384.DI', '384.DJ', '384.GA', '384.GB', '384.GF'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804308122845802507662, 25903229681844523013167, 187922473375925652905521, 1313941673647], 'label': '3072.bgb.192.OM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.nj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.OM', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761330
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.ON', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '192.NQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LK', '96.MZ', '96.NR', '96.OC', '96.OD', '96.PO', '96.RH', '96.RI', '96.RJ', '96.SK', '96.SM', '96.SN', '96.SZ', '96.TB', '96.TO'], 'contains': ['384.DK', '384.GA', '384.GB', '384.GI'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [133970182339249961095537, 25903229681844523013167, 187922473375925652905521, 1313941673647], 'label': '3072.bgb.192.ON', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.nk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.ON', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761331
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.OO', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.QG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LF', '96.MR', '96.NS', '96.OE', '96.QG', '96.QL', '96.RK', '96.RL', '96.SL', '96.SN', '96.TB', '96.TC', '96.TO'], 'contains': ['384.DL', '384.DM', '384.GA', '384.GB'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952413035981411118158, 25903229681844523013167, 187922473375925652905521, 1313941673647], 'label': '3072.bgb.192.OO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '192.nl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.OO', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761332
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.BQ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.D', '12.T', '12.W'], 'contains': ['48.BI', '48.BJ', '48.BK', '48.BL', '48.EL', '48.EV', '48.EW', '48.FK', '48.FM', '48.HN', '48.HS'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [378358770650295628183080, 270240484111912758504367, 25903229681844523013167, 162070321828715682652927, 79804308125641822294440, 122002101738321960, 1313941673647], 'label': '3072.bgb.24.BQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.bq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BQ', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761333
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.OP', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.EM', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.LG', '96.MJ', '96.NE', '96.NZ', '96.PU', '96.QI', '96.SL', '96.SO', '96.SP', '96.SQ', '96.SR', '96.SS', '96.ST', '96.TE', '96.TP'], 'contains': ['384.DN', '384.DO', '384.DS', '384.GA', '384.GD'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229337376182892926, 25903229681844523013167, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.192.OP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '192.nm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.OP', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761602
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.GN', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.MI', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.I', '192.J', '192.QT'], 'contains': ['768.Z', '768.BC', '768.BH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903107682370587468807, 51212588579793007921, 53952035291802302422343], 'label': '3072.bgb.384.GN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.DT', 'old_label': '384.gc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.GN', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761334
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '192.OQ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.PV', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LL', '96.MY', '96.NH', '96.OZ', '96.PV', '96.RE', '96.RY', '96.SJ', '96.ST', '96.SU', '96.SV', '96.SW', '96.SX', '96.SZ', '96.TO'], 'contains': ['384.DP', '384.DQ', '384.GA', '384.GF', '384.GI'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 1313941673647, 108118287251071627990321], 'label': '3072.bgb.192.OQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '192.nn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.OQ', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761335
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.OR', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '192.NJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LE', '96.MM', '96.NI', '96.OT', '96.PA', '96.PB', '96.PW', '96.RZ', '96.SJ', '96.SK', '96.SN', '96.SY', '96.TH', '96.TN', '96.TQ'], 'contains': ['384.GA', '384.GG', '384.GH'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.192.OR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.no1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.OR', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761336
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.OS', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.NG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LF', '96.MS', '96.NT', '96.OF', '96.OG', '96.PP', '96.QM', '96.RM', '96.SM', '96.SO', '96.SU', '96.TH', '96.TQ'], 'contains': ['384.GA', '384.GH'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 79855398717732338388456, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.192.OS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '192.np1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.OS', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184761337
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.OT', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.MU', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LM', '96.MT', '96.NA', '96.OH', '96.OI', '96.QN', '96.RN', '96.RO', '96.SK', '96.SP', '96.SU', '96.SZ', '96.TB'], 'contains': ['384.GA', '384.GI'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [162070578272437343706839, 25903229681844523013167, 187922473375925652905521, 1313941673647], 'label': '3072.bgb.192.OT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '192.nq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.OT', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184761338
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.OU', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '192.NJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KO', '96.MV', '96.NR', '96.OD', '96.OZ', '96.PW', '96.RK', '96.RM', '96.RN', '96.RQ', '96.RS', '96.SH', '96.SI', '96.SY', '96.TI'], 'contains': ['384.GA', '384.GJ', '384.GK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 1313941673647, 79804429421968711780537], 'label': '3072.bgb.192.OU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.nr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.OU', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761339
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.OV', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.MW', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KR', '96.MT', '96.NV', '96.OF', '96.PA', '96.QO', '96.RH', '96.RL', '96.RQ', '96.SI', '96.SQ', '96.SV', '96.TI'], 'contains': ['384.GA', '384.GJ'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 1313941673647, 134021272925740469097576], 'label': '3072.bgb.192.OV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '192.ns1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.OV', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184761340
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '192.OW', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.PV', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LH', '96.MR', '96.NT', '96.OK', '96.PB', '96.PV', '96.QP', '96.RJ', '96.RO', '96.RR', '96.SH', '96.SR', '96.TI'], 'contains': ['384.DT', '384.GA', '384.GK'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 1313941673647, 79804429421968711780537], 'label': '3072.bgb.192.OW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '192.nt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.OW', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761341
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.OX', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.NS', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LH', '96.MS', '96.NS', '96.OI', '96.OY', '96.PX', '96.QQ', '96.RI', '96.RR', '96.RS', '96.SS', '96.SV', '96.SY'], 'contains': ['384.GA', '384.GK'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 1313941673647, 134021394929311911342598], 'label': '3072.bgb.192.OX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '192.nt2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.OX', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184761342
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.OY', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.EM', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.LI', '96.MU', '96.NU', '96.OJ', '96.PU', '96.QL', '96.QM', '96.QN', '96.QR', '96.RP', '96.SQ', '96.SR', '96.SS', '96.SW', '96.TJ'], 'contains': ['384.DU', '384.GA'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 1313941673647, 378358905093235639407953], 'label': '3072.bgb.192.OY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '192.nu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.OY', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761343
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.BR', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.D', '12.U', '12.W'], 'contains': ['48.BG', '48.BH', '48.EL', '48.EW', '48.EX', '48.FL', '48.FP', '48.HP', '48.HR'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108169512287410083283217, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 378358649363678452761737, 296041409911409376977422], 'label': '3072.bgb.24.BR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.br1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BR', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761344
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.OZ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.EL', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.LJ', '96.MU', '96.NU', '96.OJ', '96.PM', '96.QO', '96.QP', '96.QQ', '96.RP', '96.SL', '96.SO', '96.SP', '96.SX', '96.TK', '96.TP'], 'contains': ['384.DV', '384.GA'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 162121669227129588479873, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.192.OZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '192.nv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.OZ', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761345
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.PA', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '192.NS', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LL', '96.MN', '96.PX', '96.RF', '96.SA', '96.TA', '96.TB', '96.TD', '96.TE', '96.TF', '96.TI', '96.TJ', '96.TK', '96.TL', '96.TM', '96.TN', '96.TQ'], 'contains': ['384.DW', '384.GA', '384.GG'], 'core': '768.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647], 'label': '3072.bgb.192.PA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '192.nw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.PA', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184761346
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.PB', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.NR', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LK', '96.MV', '96.PQ', '96.RQ', '96.RR', '96.SZ', '96.TC', '96.TG', '96.TH', '96.TQ'], 'contains': ['384.DX', '384.GA', '384.GH'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.192.PB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '192.nx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.PB', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184761347
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.PC', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.195', 'aut_weyl_index': 64, 'centralizer': '96.NB', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.J', '96.LM', '96.NB', '96.NV', '96.OK', '96.QR', '96.RS', '96.TO', '96.TP', '96.TQ'], 'contains': ['384.DY', '384.GA'], 'core': '768.A', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.192.PC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '192.ny1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.PC', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 184761348
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.PD', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.EC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LN', '96.PY', '96.TR', '96.TS', '96.TT', '96.TU', '96.UE'], 'contains': ['384.DZ', '384.EA', '384.ED', '384.GB', '384.GE'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 134021394933610431760703, 1313941673647], 'label': '3072.bgb.192.PD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CD', 'old_label': '192.nz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.PD', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761349
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '192.PE', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.PZ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LS', '96.NJ', '96.PC', '96.PT', '96.PZ', '96.SB', '96.SJ', '96.SM', '96.TC', '96.TU', '96.TV', '96.TW', '96.TX', '96.TY', '96.TZ'], 'contains': ['384.EB', '384.EC', '384.GB', '384.GF', '384.GH'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952413035981411118158, 79855398717732338388456, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.192.PE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '192.oa1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.PE', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761350
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.PF', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '192.NJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LE', '96.MO', '96.NK', '96.OU', '96.PD', '96.PE', '96.QA', '96.SC', '96.SJ', '96.SK', '96.SN', '96.TB', '96.UA', '96.UF', '96.UJ'], 'contains': ['384.GB', '384.GG', '384.GI'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [133970182339249961095537, 25903229681844523013167, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.192.PF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.ob1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.PF', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761351
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.PG', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '192.NF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LF', '96.MW', '96.NW', '96.OL', '96.OM', '96.ON', '96.PR', '96.RT', '96.RU', '96.SK', '96.SM', '96.SN', '96.SZ', '96.TZ', '96.UF'], 'contains': ['384.GB', '384.GH', '384.GI'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855398717732338388456, 25903229681844523013167, 1313941673647, 108118287251071627990321], 'label': '3072.bgb.192.PG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.oc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.PG', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761352
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.PH', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '192.NJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KP', '96.NS', '96.NW', '96.OC', '96.OO', '96.PC', '96.QA', '96.RH', '96.RK', '96.RT', '96.RV', '96.SH', '96.SI', '96.UA', '96.UG'], 'contains': ['384.GB', '384.GJ', '384.GK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855520719821622658496, 25903229681844523013167, 108169377837562135992360, 1313941673647], 'label': '3072.bgb.192.PH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.od1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.PH', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761353
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.PI', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.OK', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KS', '96.NR', '96.OL', '96.PD', '96.RL', '96.RV', '96.SI', '96.TR', '96.TV', '96.UG'], 'contains': ['384.GB', '384.GJ'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79855520719821622658496, 25903229681844523013167, 1313941673647, 134021272925740469097576], 'label': '3072.bgb.192.PI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '192.oe1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.PI', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184761354
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.BS', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.E', '12.V', '12.W'], 'contains': ['48.EL', '48.EY', '48.EZ', '48.FN', '48.FR', '48.HQ', '48.HU', '48.KP', '48.KQ'], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229691554491852799, 25903229681844523013167, 53952412691500576681559, 79804308125641822294440, 122002101738321960, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.24.BS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.bs1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BS', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761355
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '192.PJ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.PZ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LO', '96.NX', '96.OE', '96.PE', '96.PZ', '96.RI', '96.RU', '96.SH', '96.TS', '96.UG'], 'contains': ['384.EE', '384.GB', '384.GK'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79855520719821622658496, 25903229681844523013167, 1313941673647, 134021394929311911342598], 'label': '3072.bgb.192.PJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '192.of1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.PJ', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761356
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.PK', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.NS', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LO', '96.NX', '96.ON', '96.OY', '96.QB', '96.RJ', '96.RK', '96.TT', '96.TV', '96.UA'], 'contains': ['384.GB', '384.GK'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [187973563959620141846542, 79855520719821622658496, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.192.PK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '192.of2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.PK', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184761357
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.PL', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.EC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LQ', '96.PY', '96.TR', '96.TS', '96.TT', '96.TW', '96.UH'], 'contains': ['384.EF', '384.GB'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79855520719821622658496, 25903229681844523013167, 1313941673647, 134021529040297499210286], 'label': '3072.bgb.192.PL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CD', 'old_label': '192.og1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.PL', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761358
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.PM', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '192.NS', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LS', '96.NL', '96.OV', '96.QB', '96.QS', '96.SN', '96.TA', '96.UB', '96.UC', '96.UE', '96.UG', '96.UH', '96.UI', '96.UJ'], 'contains': ['384.EG', '384.GB', '384.GG'], 'core': '768.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 134021394933610431760703, 1313941673647], 'label': '3072.bgb.192.PM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '192.oh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.PM', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184761359
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.PN', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.NR', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LT', '96.NX', '96.OO', '96.PS', '96.RV', '96.SM', '96.SN', '96.TC', '96.UD', '96.UF'], 'contains': ['384.EH', '384.GB', '384.GH'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [187922473373129633118743, 79855398717732338388456, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.192.PN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '192.oi1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.PN', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184761360
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.PO', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LV', '96.QC', '96.QT', '96.UK', '96.UM', '96.UN', '96.UR'], 'contains': ['384.EK', '384.EL', '384.GC', '384.GF'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804429416356250372480, 25903229681844523013167, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.192.PO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.V', 'old_label': '192.oj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.PO', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 184761361
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.PP', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LV', '96.QU', '96.QV', '96.TD', '96.UB', '96.UL', '96.UO', '96.UP', '96.UQ', '96.UR', '96.US'], 'contains': ['384.EM', '384.EN', '384.GC', '384.GG'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.192.PP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '192.ok1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.PP', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 184761362
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.PQ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.BX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LX', '96.NC', '96.PN', '96.QW', '96.ST', '96.UK', '96.UT'], 'contains': ['384.EO', '384.ES', '384.FD', '384.GD', '384.GF'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229684640542817862, 25903229681844523013167, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.PQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '192.ol1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.PQ', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761363
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.PR', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.V', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LX', '96.ND', '96.OB', '96.SD', '96.TE', '96.UC', '96.UU', '96.UV', '96.UW', '96.UX', '96.UY'], 'contains': ['384.EP', '384.ET', '384.FM', '384.GD', '384.GG'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 25903107685154153232142, 1313941673647, 51090958997032170942], 'label': '3072.bgb.192.PR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '192.om1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.PR', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761364
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.PS', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.FD', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LG', '96.MK', '96.NF', '96.OA', '96.QJ', '96.ST', '96.UY'], 'contains': ['384.ER', '384.EU', '384.FV', '384.GD', '384.GI'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25852138393689126932998, 25903229681844523013167, 1313941673647, 51212962568394582352], 'label': '3072.bgb.192.PS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '192.on1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.PS', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761365
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.BT', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.53387', 'aut_weyl_index': 24, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.N', '12.X', '12.Z'], 'contains': ['48.EK', '48.EQ', '48.FF', '48.FS', '48.GO', '48.LA', '48.LB', '48.MT', '48.MX'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [162070577934876685646657, 25903229681844523013167, 187973685961890096441600, 25852138389591620222016, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.24.BT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.bt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BT', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761366
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.PT', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.CB', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LZ', '96.QD', '96.QT', '96.SE', '96.TU', '96.UT', '96.UZ'], 'contains': ['384.EV', '384.EY', '384.FC', '384.GE', '384.GF'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804429416356250372480, 378358770650295628183080, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.192.PT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '192.oo1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.PT', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761367
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.PU', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.DO', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LZ', '96.QU', '96.QX', '96.TF', '96.UE', '96.UL', '96.VA', '96.VB', '96.VC', '96.VD', '96.VG'], 'contains': ['384.EW', '384.EZ', '384.FL', '384.GE', '384.GG'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.192.PU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '192.op1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.PU', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761368
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.PV', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.EC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LN', '96.TG', '96.TU', '96.UD', '96.VE', '96.VF', '96.VG'], 'contains': ['384.EX', '384.FA', '384.FT', '384.GE', '384.GH'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 134021272934136496216343, 216288705272228144236816], 'label': '3072.bgb.192.PV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.EH', 'old_label': '192.oq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.PV', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761369
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '192.PW', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.PF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LE', '96.MP', '96.NM', '96.OW', '96.PF', '96.PG', '96.QE', '96.SF', '96.SJ', '96.SM', '96.SU', '96.SZ', '96.TZ', '96.VH', '96.VI'], 'contains': ['384.GF', '384.GH', '384.GI'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855398717732338388456, 25903229681844523013167, 1313941673647, 25852017101492540879976], 'label': '3072.bgb.192.PW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.or1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.PW', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761370
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '192.PX', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.PH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KQ', '96.NG', '96.NM', '96.OZ', '96.PC', '96.PH', '96.QE', '96.RX', '96.SF', '96.SH', '96.SI', '96.SV', '96.TV', '96.VH', '96.VJ'], 'contains': ['384.GF', '384.GJ', '384.GK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804429416356250372480, 25903229681844523013167, 1313941673647, 134021272925740469097576], 'label': '3072.bgb.192.PX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.os1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.PX', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761371
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '192.PY', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '96.VI', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KT', '96.NH', '96.PF', '96.QW', '96.SB', '96.SI', '96.UM', '96.UZ', '96.VJ'], 'contains': ['384.FB', '384.FH', '384.GF', '384.GJ'], 'core': '768.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [79804429416356250372480, 25903229681844523013167, 108169377837562135992360, 1313941673647], 'label': '3072.bgb.192.PY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '192.ot1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.PY', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 184761372
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '192.PZ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.QF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.MB', '96.NJ', '96.OY', '96.PG', '96.QF', '96.RY', '96.SH', '96.UN', '96.VH', '96.VJ'], 'contains': ['384.GF', '384.GK'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79804429416356250372480, 25903229681844523013167, 1313941673647, 133970303635757521608262], 'label': '3072.bgb.192.PZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '192.ou1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.PZ', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761373
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.QA', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.EM', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.MF', '96.QD', '96.QY', '96.SE', '96.TX', '96.UK', '96.UZ'], 'contains': ['384.FE', '384.GF'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855142625594763233847, 25903229684640542817862, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.192.QA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '192.ov1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.QA', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761374
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.QB', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.QB', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.MI', '96.QC', '96.QY', '96.UM', '96.UN', '96.UT', '96.VL'], 'contains': ['384.FF', '384.GF'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804429416356250372480, 25903229681844523013167, 1313941673647, 134021529384772106263086], 'label': '3072.bgb.192.QB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.V', 'old_label': '192.ow1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.QB', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761375
    {'ambient': '3072.bgb', 'aut_centralizer_order': 256, 'aut_label': '192.QC', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.CN', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.A', '96.NP', '96.PH', '96.QF', '96.QZ', '96.SJ', '96.TA', '96.UR', '96.UU', '96.VA', '96.VI', '96.VJ', '96.VK', '96.VL'], 'contains': ['384.GF', '384.GG'], 'core': '768.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [79804308122845802507662, 25903229681844523013167, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.192.QC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '192.ox1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.QC', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761376
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.BU', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.F'], 'contains': ['48.EN', '48.ER', '48.ES', '48.FU', '48.FV', '48.HE', '48.HF'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 296092500497899884979223, 25903229681844523013167, 122002101738321960, 1313941673647, 134021272934136496216343, 216237613975676641157062], 'label': '3072.bgb.24.BU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.F', 'old_label': '24.bu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BU', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761377
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.QD', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '192.PY', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LS', '96.NN', '96.OX', '96.PI', '96.RA', '96.TH', '96.TN', '96.UF', '96.UO', '96.UV', '96.VG', '96.VI', '96.VM', '96.VN'], 'contains': ['384.FJ', '384.GG', '384.GH'], 'core': '768.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [53952291033879672806278, 79855398717732338388456, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.192.QD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '192.oy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.QD', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184761378
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.QE', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '192.PY', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LL', '96.MQ', '96.PJ', '96.RG', '96.SG', '96.SK', '96.UJ', '96.UP', '96.UY', '96.VB', '96.VI', '96.VO', '96.VP'], 'contains': ['384.FK', '384.GG', '384.GI'], 'core': '768.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [187922594664024732247801, 25903229681844523013167, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.192.QE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '192.oz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.QE', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184761379
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.QF', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '192.QC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KQ', '96.NI', '96.NK', '96.PA', '96.PD', '96.PI', '96.PJ', '96.PL', '96.RZ', '96.SC', '96.SY', '96.TI', '96.UA', '96.UG', '96.VJ'], 'contains': ['384.GG', '384.GJ', '384.GK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 1313941673647, 79804429421968711780537], 'label': '3072.bgb.192.QF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.pa1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.QF', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761380
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.QG', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.PH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.MB', '96.NL', '96.NN', '96.PB', '96.PE', '96.PH', '96.PL', '96.RB', '96.SA', '96.SG', '96.SY', '96.UA', '96.UW'], 'contains': ['384.GG', '384.GK'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 1313941673647, 133970303635757521608262], 'label': '3072.bgb.192.QG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '192.pb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.QG', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761381
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.QH', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.BT', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.MD', '96.NO', '96.PK', '96.QS', '96.QZ', '96.RA', '96.RD', '96.SD', '96.TL', '96.UL', '96.UQ', '96.UW', '96.VC', '96.VO', '96.VQ'], 'contains': ['384.FN', '384.GG'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 404211043484134973872583, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.192.QH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '192.pc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.QH', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761382
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.QI', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.VK', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.ME', '96.QX', '96.RC', '96.TD', '96.UB', '96.UO', '96.UP', '96.VC', '96.VK', '96.VQ', '96.VR'], 'contains': ['384.FO', '384.GG'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108169512287410083283217, 25903229681844523013167, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.192.QI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '192.pd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.QI', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184761383
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.QJ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.V', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.MG', '96.NO', '96.PK', '96.QK', '96.RB', '96.TM', '96.UC', '96.UU', '96.UV', '96.UX', '96.VP'], 'contains': ['384.FP', '384.GG'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 53952412691500576681559, 25903107685154153232142, 1313941673647], 'label': '3072.bgb.192.QJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '192.pe1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.QJ', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761384
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.QK', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.DO', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.MH', '96.QV', '96.RC', '96.TF', '96.UI', '96.UQ', '96.VA', '96.VB', '96.VD', '96.VM', '96.VQ'], 'contains': ['384.FQ', '384.GG'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.192.QK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '192.pf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.QK', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761385
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.QL', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.QL', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LK', '96.MX', '96.OP', '96.OQ', '96.RW', '96.SK', '96.SU', '96.TZ', '96.UF', '96.VE'], 'contains': ['384.GH', '384.GI'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [133970182339249961095537, 79855398717732338388456, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.192.QL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '192.pg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.QL', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184761386
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.QM', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '192.PW', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KP', '96.NT', '96.NW', '96.OP', '96.OR', '96.PA', '96.PF', '96.PI', '96.RM', '96.RQ', '96.RU', '96.RV', '96.SY', '96.TV', '96.VH'], 'contains': ['384.GH', '384.GJ', '384.GK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855398717732338388456, 25903229681844523013167, 1313941673647, 187922594658424724202816], 'label': '3072.bgb.192.QM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.ph1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.QM', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761387
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.BV', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.A', '12.X', '12.Y'], 'contains': ['48.EF', '48.EH', '48.EI', '48.EJ', '48.EM', '48.EQ', '48.FT', '48.FW', '48.GS', '48.KR', '48.KS', '48.KV', '48.KW', '48.LC', '48.LD', '48.LF', '48.NE', '48.NF', '48.NK'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229691554491852799, 1313941673647, 122002101738321960, 25903229681844523013167, 187922473375925652905521, 133970303627361494479417, 108118165248982343710201], 'label': '3072.bgb.24.BV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.bv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BV', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 184761388
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.QN', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '192.NJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LO', '96.NX', '96.NY', '96.OG', '96.OM', '96.PB', '96.PC', '96.PG', '96.PI', '96.RM', '96.RR', '96.RT', '96.RW', '96.SY', '96.VH'], 'contains': ['384.GH', '384.GK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855398717732338388456, 25903229681844523013167, 1313941673647, 134021394929311911342598], 'label': '3072.bgb.192.QN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.pi1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.QN', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761389
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '192.QO', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.EB', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LR', '96.TG', '96.TY', '96.UD', '96.VE', '96.VF', '96.VN'], 'contains': ['384.FU', '384.GH'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 242140721662339602266753, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.192.QO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.EH', 'old_label': '192.pj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.QO', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184761390
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.QP', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.195', 'aut_weyl_index': 64, 'centralizer': '192.QP', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.L', '96.LT', '96.NY', '96.OR', '96.TH', '96.TZ', '96.VF'], 'contains': ['384.GH'], 'core': '768.A', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.192.QP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.C', 'old_label': '192.pk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.QP', 'subgroup_fusion': None, 'weyl_group': '96.195'}
  • id: 184761391
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.QQ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '192.PW', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.KO', '96.MX', '96.NR', '96.OQ', '96.PD', '96.PF', '96.PJ', '96.RH', '96.RN', '96.RO', '96.RT', '96.RU', '96.SV', '96.UA', '96.VH'], 'contains': ['384.GI', '384.GJ', '384.GK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [187922594664024732247801, 25903229681844523013167, 1313941673647, 134021272925740469097576], 'label': '3072.bgb.192.QQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.pl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.QQ', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761392
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '192.QR', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '192.NJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.LH', '96.MW', '96.NW', '96.OH', '96.OZ', '96.PE', '96.PG', '96.PJ', '96.RI', '96.RJ', '96.RN', '96.RW', '96.UA', '96.VH'], 'contains': ['384.GI', '384.GK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [187922594664024732247801, 25903229681844523013167, 1313941673647, 134021394929311911342598], 'label': '3072.bgb.192.QR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '192.pm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.QR', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184761393
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.QS', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '384.E', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.M', '96.L'], 'contains': ['384.GL', '384.GM', '384.GO', '384.GQ', '384.GS', '384.GY', '384.HA'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [378358770650295628183080, 25852272837936812846761, 122002101738321960, 378307680062503632549246], 'label': '3072.bgb.192.QS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.L', 'old_label': '192.pn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.QS', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761394
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.QT', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '384.E', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.L'], 'contains': ['384.GL', '384.GN', '384.GO', '384.GQ', '384.GT', '384.GY', '384.HB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [378358770650295628183080, 51469040697520739881, 122002101738321960, 378307680062503632549246], 'label': '3072.bgb.192.QT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.L', 'old_label': '192.po1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.QT', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761395
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.QU', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '384.E', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.BZ'], 'contains': ['384.GP', '384.GR', '384.GS', '384.GU', '384.GX', '384.GZ', '384.HA'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [378358770650295628183080, 51469040697520739881, 25903107681056726364840, 324406870525295326154166], 'label': '3072.bgb.192.QU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.BZ', 'old_label': '192.pp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.QU', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761396
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.QV', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '384.E', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.BZ'], 'contains': ['384.GP', '384.GR', '384.GT', '384.GV', '384.GX', '384.GZ', '384.HB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [378358770650295628183080, 25903107681056726364840, 25852272837936812846761, 324406870525295326154166], 'label': '3072.bgb.192.QV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.BZ', 'old_label': '192.pq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.QV', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761397
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.QW', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '384.X', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['64.N', '96.HB'], 'contains': ['384.HC', '384.HD', '384.HE', '384.HI', '384.HK', '384.HR', '384.HT'], 'core': '3072.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [187922473021741077083393, 187973685953494069345919, 162121668868625366436606, 162070456280045573438767], 'label': '3072.bgb.192.QW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.HB', 'old_label': '192.pr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.QW', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761398
    {'ambient': '3072.bgb', 'aut_centralizer_order': 1, 'aut_label': '4.I', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1536.408640541', 'aut_weyl_index': 4, 'centralizer': '3072.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.A'], 'contains': ['8.B', '8.L', '8.N', '12.CF', '16.P', '16.Q', '16.R'], 'core': '8.B', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 486427128433516595381056, 187922473375925652905521, 404159831259638948150382, 133970303627361494479417, 108118165248982343710201, 162070456272950954131199, 53952412691500576681559], 'label': '3072.bgb.4.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '4.i1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.I', 'subgroup_fusion': None, 'weyl_group': '1536.408640541'}
  • id: 184761399
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.BW', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.I', '12.T', '12.U'], 'contains': ['48.BN', '48.BO', '48.EO', '48.EU', '48.EW', '48.FX', '48.GB', '48.GV', '48.GY'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 79855520714221614566521, 79855398717732338388456, 25903229681844523013167, 256460345499052777, 122002101738321960, 1313941673647], 'label': '3072.bgb.24.BW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.bw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BW', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184761400
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.QX', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '384.X', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.HB'], 'contains': ['384.HC', '384.HD', '384.HF', '384.HJ', '384.HL', '384.HR', '384.HT'], 'core': '3072.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [187922473375925652905521, 162121669227129588479873, 187973685961890096441600, 162070456272950954131199], 'label': '3072.bgb.192.QX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.HB', 'old_label': '192.pr2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.QX', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761401
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '192.QY', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '384.BM', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.IR'], 'contains': ['384.HG', '384.HH', '384.HI', '384.HL', '384.HO', '384.HQ', '384.HS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [187922473021741077083393, 25852017104276106643073, 187973685956277635081017, 162070456280045573438767], 'label': '3072.bgb.192.QY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.IR', 'old_label': '192.ps1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.QY', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761403
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '256.A', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.GM', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.J', '64.K', '64.L', '128.A', '128.B', '128.C', '128.D', '128.E', '128.F'], 'contains': ['768.A', '1024.a1'], 'core': '768.A', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [25903229681844523013167, 404159831259638948150382, 1313941673647], 'label': '3072.bgb.256.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.C', 'old_label': '256.a1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.A', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 184761404
    {'ambient': '3072.bgb', 'aut_centralizer_order': 24, 'aut_label': '256.B', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '256.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.A', '128.G', '128.H', '128.I'], 'contains': ['512.A', '512.B', '768.Z'], 'core': '3072.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [512279023525993448904377, 216288570482003057040143, 486427128433516595381056], 'label': '3072.bgb.256.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.M', 'old_label': '256.b1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.B', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761405
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '256.C', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '12.4', 'aut_weyl_index': 512, 'centralizer': '384.GM', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.B', '128.G', '128.J', '128.K'], 'contains': ['512.A', '512.C', '768.BA'], 'core': '3072.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [378359026752338661681217, 540644093954862016504456, 378307935804560365900801], 'label': '3072.bgb.256.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.M', 'old_label': '256.c1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.C', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 184761406
    {'ambient': '3072.bgb', 'aut_centralizer_order': 24, 'aut_label': '256.D', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '256.D', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.C', '128.H', '128.J', '128.L'], 'contains': ['512.A', '512.D', '768.BC'], 'core': '3072.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [566495989041738862713598, 53952035293116243360136, 270240861515876502434616], 'label': '3072.bgb.256.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.M', 'old_label': '256.d1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.D', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761407
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '256.E', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '12.4', 'aut_weyl_index': 512, 'centralizer': '768.Z', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.D', '128.G', '128.L', '128.M'], 'contains': ['512.A', '512.E', '768.BE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [566495989041738862713598, 270240861515876502434616, 51212962568394582352], 'label': '3072.bgb.256.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.M', 'old_label': '256.e1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.E', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 184761408
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '256.F', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '12.4', 'aut_weyl_index': 512, 'centralizer': '768.BC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.E', '128.I', '128.J', '128.M'], 'contains': ['512.A', '512.F', '768.BF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [378359026752338661681217, 378358770650295628183080, 540644093954862016504456], 'label': '3072.bgb.256.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.M', 'old_label': '256.f1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.F', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 184761409
    {'ambient': '3072.bgb', 'aut_centralizer_order': 24, 'aut_label': '256.G', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '256.G', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.F', '128.H', '128.K', '128.M'], 'contains': ['512.A', '768.BG'], 'core': '3072.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [486426872699855848892862, 324406614437468765763120, 432525806706613058231617], 'label': '3072.bgb.256.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.M', 'old_label': '256.g1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.G', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761410
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.BX', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.J', '12.T', '12.BA'], 'contains': ['48.BQ', '48.BR', '48.EO', '48.EV', '48.FZ', '48.GX', '48.HB', '48.LG', '48.NL'], 'core': '384.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [242089752358354392177983, 25903229681844523013167, 122002101738321960, 324406991811924875755576, 1313941673647, 134021272934136496216343, 187922594661241166512703], 'label': '3072.bgb.24.BX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BX', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184761411
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '256.H', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '12.4', 'aut_weyl_index': 512, 'centralizer': '768.BG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.G', '128.I', '128.K', '128.L'], 'contains': ['512.A', '768.BI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [25852394494243815333247, 216288570480689195210176, 486478219730068018627222], 'label': '3072.bgb.256.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.M', 'old_label': '256.h1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.H', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 184761412
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '256.I', 'aut_quo_index': None, 'aut_stab_index': 256, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '768.Z', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['64.H', '64.N', '128.G'], 'contains': ['512.B', '512.C', '512.E', '768.BK'], 'core': '3072.a1', 'coset_action_label': None, 'count': 256, 'diagramx': None, 'generators': [25903108050746727640336, 216288570482003057040143, 486427128433516595381056], 'label': '3072.bgb.256.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '128.G', 'old_label': '256.i1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.I', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 184761413
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '256.J', 'aut_quo_index': None, 'aut_stab_index': 256, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '768.BC', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['64.I', '128.J'], 'contains': ['512.C', '512.D', '512.F', '768.BT'], 'core': '3072.a1', 'coset_action_label': None, 'count': 256, 'diagramx': None, 'generators': [378358770650295628183080, 51469040697520739881, 378359026753640149313262], 'label': '3072.bgb.256.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '128.J', 'old_label': '256.j1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.J', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 184761414
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '256.K', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '1536.C', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['64.J', '128.N', '128.O', '128.P'], 'contains': ['768.BZ', '1024.a1'], 'core': '3072.a1', 'coset_action_label': None, 'count': 128, 'diagramx': None, 'generators': [187973685954795477134032, 404159831259638948150382, 162121668868625366436606], 'label': '3072.bgb.256.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.N', 'old_label': '256.k1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.K', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 184761415
    {'ambient': '3072.bgb', 'aut_centralizer_order': 256, 'aut_label': '384.A', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '24.A', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['128.A', '192.A', '192.MH', '192.MI', '192.MJ', '192.MK', '192.ML', '192.MM', '192.MN', '192.MO', '192.MP', '192.MQ', '192.MR', '192.MS'], 'contains': ['768.A', '768.B'], 'core': '384.A', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [25903229681844523013167, 122002101738321960, 1313941673647], 'label': '3072.bgb.384.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '384.A', 'normal_contained_in': ['96.A', '192.A'], 'normal_contains': ['768.A'], 'normalizer': '1.a1', 'old_label': '384.a1', 'projective_image': '3072.bgb', 'quotient_action_image': '24.12', 'quotient_action_kernel': '16.14', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '384.A', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 184761416
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.B', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.KG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.A', '192.C', '192.D', '192.E', '192.F', '192.G', '192.H', '192.I', '192.J', '192.K', '192.L', '192.M', '192.N'], 'contains': ['768.B', '768.C', '768.Z'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 51212588579793007921, 122002101738321960], 'label': '3072.bgb.384.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '384.b1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.B', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761417
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.C', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.JZ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.C', '192.O', '192.P', '192.Q', '192.R', '192.S', '192.T', '192.U', '192.V', '192.MH'], 'contains': ['768.B', '768.D', '768.V'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187973685961890096441600, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.384.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '384.c1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.C', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761418
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.D', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.M', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.D', '192.O', '192.P', '192.W', '192.X', '192.Y', '192.BD', '192.BF', '192.BI', '192.MI'], 'contains': ['768.B', '768.F', '768.S'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 25903229683158464676480, 404210922196204071249966], 'label': '3072.bgb.384.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '384.d1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.D', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761419
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.E', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.O', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.E', '192.F', '192.Q', '192.Z', '192.BA', '192.BB', '192.BC', '192.BE', '192.BG', '192.BH', '192.BI', '192.BJ', '192.MI'], 'contains': ['768.B', '768.F', '768.BA'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [404210922197505558871681, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.384.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '384.e1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.E', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761420
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.F', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.KU', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.G', '192.H', '192.R', '192.W', '192.Z', '192.BA', '192.BK', '192.BM', '192.BO', '192.BP', '192.BQ', '192.BR', '192.MJ'], 'contains': ['768.B', '768.G', '768.BB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855520714221614566521, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.384.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '384.f1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.F', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761421
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.BY', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.J', '12.U', '12.BB'], 'contains': ['48.EO', '48.EX', '48.GA', '48.GZ', '48.HC'], 'core': '384.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229681844523013167, 122002101738321960, 1313941673647, 134021272934136496216343, 378358649363678452761737, 296041409911409376977422, 187922594661241166512703], 'label': '3072.bgb.24.BY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.by1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BY', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184761422
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.G', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '192.MJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.S', '192.BL', '192.BN', '192.BS', '192.BT', '192.MJ'], 'contains': ['768.B', '768.H', '768.BB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79855520714221614566521, 25903229681844523013167, 122002101738321960], 'label': '3072.bgb.384.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BW', 'old_label': '384.f2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.G', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761423
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.H', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.NC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.C', '192.R', '192.X', '192.BI', '192.BU', '192.BV', '192.BW', '192.BX', '192.MK'], 'contains': ['768.B', '768.I', '768.U'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922473375925652905521, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.384.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.g1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.H', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761424
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.I', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.SE', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.S', '192.BY', '192.BZ', '192.CA', '192.CB', '192.ML'], 'contains': ['768.B', '768.K', '768.T'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79855398717732338388456, 122002101738321960, 1313941673647], 'label': '3072.bgb.384.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BX', 'old_label': '384.h1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.I', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761425
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.J', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.KV', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.I', '192.J', '192.BB', '192.BC', '192.BK', '192.BM', '192.CC', '192.CD', '192.CE', '192.CF', '192.CG', '192.CH', '192.CI', '192.CK', '192.MM'], 'contains': ['768.B', '768.M', '768.BC', '768.BD'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 122002101738321960, 53952035291802302422343], 'label': '3072.bgb.384.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '384.i1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.J', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761426
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.K', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '192.MM', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.Y', '192.BL', '192.BN', '192.CJ', '192.CL', '192.MM'], 'contains': ['768.B', '768.M', '768.BD'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [122000787877207687, 25903229681844523013167, 53952035291802302422343], 'label': '3072.bgb.384.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CS', 'old_label': '384.i2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.K', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761427
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.L', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.I', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.D', '192.Q', '192.T', '192.W', '192.BU', '192.BV', '192.CN', '192.CO', '192.MN'], 'contains': ['768.B', '768.N', '768.X'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [122002101738321960, 1313941673647, 51212962568394582352], 'label': '3072.bgb.384.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.j1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.L', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761428
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.M', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.E', '192.K', '192.O', '192.Z', '192.BO', '192.BV', '192.CC', '192.CD', '192.CM', '192.CP', '192.CQ', '192.CR', '192.MN'], 'contains': ['768.B', '768.N', '768.BE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 1313941673647, 51212962568394582352], 'label': '3072.bgb.384.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '384.k1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.M', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761429
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.N', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.EW', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.Y', '192.BY', '192.BZ', '192.CS', '192.CU', '192.MO'], 'contains': ['768.B', '768.O', '768.W'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 378358770650295628183080, 25903229683158464676480], 'label': '3072.bgb.384.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '384.l1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.N', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761430
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.O', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.CZ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.L', '192.BB', '192.BP', '192.BZ', '192.CE', '192.CM', '192.CT', '192.CV', '192.CW', '192.MO'], 'contains': ['768.B', '768.O', '768.BF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770650295628183080, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.384.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.P', 'old_label': '384.m1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.O', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761431
    {'ambient': '3072.bgb', 'aut_centralizer_order': 256, 'aut_label': '384.P', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.DG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.G', '192.U', '192.BD', '192.BE', '192.BS', '192.BW', '192.CA', '192.CI', '192.CJ', '192.CN', '192.CR', '192.CS', '192.CW', '192.CX', '192.CY', '192.CZ', '192.DA', '192.DB', '192.DC', '192.DD', '192.DE', '192.DF', '192.DG', '192.DH', '192.DI', '192.DJ', '192.MP'], 'contains': ['768.B', '768.P', '768.R'], 'core': '3072.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79804308125641822294440, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.384.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '384.n1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.P', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761432
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.BZ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.6536092', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.L', '12.BA', '12.BB'], 'contains': ['48.EO', '48.HA', '48.HD', '48.LH', '48.NM'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 122002101738321960, 1313941673647, 134021272934136496216343, 216237613982764859689536, 187922594661241166512703, 324355901222623977942343], 'label': '3072.bgb.24.BZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.bz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BZ', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 184761433
    {'ambient': '3072.bgb', 'aut_centralizer_order': 256, 'aut_label': '384.Q', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.FC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.H', '192.V', '192.BF', '192.BJ', '192.BT', '192.BX', '192.CB', '192.CK', '192.CL', '192.CO', '192.CP', '192.CT', '192.CU', '192.DK', '192.DL', '192.DM', '192.DN', '192.DO', '192.DP', '192.DQ', '192.MP'], 'contains': ['768.B', '768.Q', '768.R'], 'core': '3072.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903107682370587468807, 79804308125641822294440, 25903229683158464676480], 'label': '3072.bgb.384.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '384.o1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.Q', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761434
    {'ambient': '3072.bgb', 'aut_centralizer_order': 256, 'aut_label': '384.R', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.DG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.I', '192.BG', '192.BK', '192.BL', '192.CM', '192.CX', '192.DK', '192.DR', '192.DS', '192.MQ'], 'contains': ['768.B', '768.BG', '768.BH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903364134488315926527, 25903229681844523013167, 122002101738321960], 'label': '3072.bgb.384.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.R', 'old_label': '384.p1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.R', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761435
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '384.S', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.C', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.J', '192.BH', '192.BM', '192.BN', '192.CQ', '192.CV', '192.CY', '192.DK', '192.DT', '192.MQ'], 'contains': ['768.B', '768.BH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 122002101738321960, 25903364135789722998960], 'label': '3072.bgb.384.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.R', 'old_label': '384.q1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.S', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761436
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.T', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.K', '192.M', '192.T', '192.X', '192.BE', '192.BO', '192.BQ', '192.CE', '192.CF', '192.DL', '192.DR', '192.DT', '192.MI'], 'contains': ['768.B', '768.S'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [122002101738321960, 25903229683158464676480, 404210922196204071249966], 'label': '3072.bgb.384.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '384.r1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.T', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761437
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.U', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.EV', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.N', '192.BC', '192.BR', '192.BY', '192.CF', '192.CQ', '192.CT', '192.CZ', '192.DS', '192.MO'], 'contains': ['768.B', '768.W'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770648994141276807, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.384.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.P', 'old_label': '384.s1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.U', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761438
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.V', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.T', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.F', '192.M', '192.P', '192.BA', '192.BQ', '192.BU', '192.CG', '192.CH', '192.CP', '192.CV', '192.DA', '192.DS', '192.MN'], 'contains': ['768.B', '768.X'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 1313941673647, 25852016759807766522832], 'label': '3072.bgb.384.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '384.t1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.V', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761439
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.W', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.CM', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.L', '192.N', '192.BG', '192.BH', '192.BP', '192.BR', '192.CC', '192.CD', '192.CG', '192.CH', '192.DB', '192.DM', '192.DR', '192.DT', '192.MS'], 'contains': ['768.B', '768.BI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [51347406816160329727, 122002101738321960, 1313941673647], 'label': '3072.bgb.384.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '384.u1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.W', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761603
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '384.GO', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '384.E', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.I', '192.L', '192.QS', '192.QT'], 'contains': ['768.Z', '768.BF', '768.BI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [378358770650295628183080, 122002101738321960, 378307680062503632549246], 'label': '3072.bgb.384.GO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.L', 'old_label': '384.gd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.GO', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761440
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.X', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.JS', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.C', '192.DU', '192.DV', '192.DY', '192.DZ', '192.ED', '192.EF', '192.EG', '192.EH', '192.EI', '192.EJ', '192.EL', '192.EM', '192.EO', '192.MT'], 'contains': ['768.C', '768.D', '768.I', '768.BJ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922473375925652905521, 187973685961890096441600, 25903229683158464676480], 'label': '3072.bgb.384.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '384.v1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.X', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761441
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.Y', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.NB', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.EB', '192.EC', '192.EN', '192.EO', '192.MT'], 'contains': ['768.C', '768.E', '768.J', '768.BJ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 187973685961890096441600], 'label': '3072.bgb.384.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.JW', 'old_label': '384.v2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.Y', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761442
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.Z', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.JI', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.C', '192.DW', '192.DX', '192.EA', '192.EE', '192.EK', '192.EL', '192.EM', '192.EN', '192.MU'], 'contains': ['768.C', '768.D', '768.U'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922594664024732247801, 187973685961890096441600, 25903229683158464676480], 'label': '3072.bgb.384.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '384.w1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.Z', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761443
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.CA', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.53387', 'aut_weyl_index': 24, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.N', '12.Y', '12.BD'], 'contains': ['48.EP', '48.EQ', '48.GD', '48.GJ', '48.GN', '48.LL', '48.LM', '48.NP', '48.OH'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25852138757799544092222, 25903229681844523013167, 187973685961890096441600, 25852138389591620222016, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.24.CA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ca1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CA', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761444
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.BA', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.E', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.D', '192.E', '192.DU', '192.DW', '192.DY', '192.EA', '192.EP', '192.EQ', '192.ET', '192.EV', '192.EX', '192.EY', '192.EZ', '192.FA', '192.MV'], 'contains': ['768.C', '768.F', '768.N', '768.BK'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [51212588579793007921, 1313941673647, 51212962568394582352], 'label': '3072.bgb.384.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.x1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.BA', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761445
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.BB', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.C', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.D', '192.F', '192.DV', '192.DX', '192.DZ', '192.EA', '192.ER', '192.ES', '192.EU', '192.EW', '192.EX', '192.EY', '192.EZ', '192.FB', '192.MV'], 'contains': ['768.C', '768.F', '768.X'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25852017095880079467006, 1313941673647, 25852016759807766522832], 'label': '3072.bgb.384.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.y1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.BB', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761446
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '384.BC', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.EK', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.G', '192.EB', '192.EL', '192.EP', '192.ER', '192.FC', '192.MW'], 'contains': ['768.C', '768.G', '768.P'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804429416356250372480, 51212588579793007921, 25903229683158464676480], 'label': '3072.bgb.384.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '384.z1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.BC', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761447
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '384.BD', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.EP', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.H', '192.EC', '192.EM', '192.EX', '192.FD', '192.FE', '192.MW'], 'contains': ['768.C', '768.G', '768.Q'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [54003382330230002441647, 51212588579793007921, 25903229683158464676480], 'label': '3072.bgb.384.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '384.ba1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.BD', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761448
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.BE', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.KL', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.G', '192.H', '192.ED', '192.EE', '192.EQ', '192.ES', '192.EY', '192.FF', '192.MX'], 'contains': ['768.C', '768.G', '768.R'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [51212588579793007921, 79804308125641822294440, 25903229683158464676480], 'label': '3072.bgb.384.BE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.bb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.BE', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761449
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.BF', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.MK', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.C', '192.ED', '192.ET', '192.EU', '192.EZ', '192.FC', '192.FD', '192.FG', '192.MY'], 'contains': ['768.C', '768.I', '768.V'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [108118165248982343710201, 51212588579793007921, 25903229683158464676480], 'label': '3072.bgb.384.BF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.bc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.BF', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761450
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.BG', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.NQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.EB', '192.EC', '192.EF', '192.EN', '192.MZ'], 'contains': ['768.C', '768.L', '768.Y'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79855520719821622658496, 25903229681844523013167, 51212588579793007921], 'label': '3072.bgb.384.BG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.JW', 'old_label': '384.bd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.BG', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761451
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.BH', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.D', '192.K', '192.DV', '192.DW', '192.EG', '192.EK', '192.EP', '192.EQ', '192.ET', '192.EW', '192.FE', '192.FF', '192.FG', '192.FH', '192.MV'], 'contains': ['768.C', '768.N', '768.S'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25852017095880079467006, 1313941673647, 51212962568394582352], 'label': '3072.bgb.384.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.be1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.BH', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761452
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.BI', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.D', '192.M', '192.DU', '192.DX', '192.EH', '192.EK', '192.ER', '192.ES', '192.EU', '192.EV', '192.FE', '192.FF', '192.FG', '192.FI', '192.MV'], 'contains': ['768.C', '768.S', '768.X'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [51212588579793007921, 1313941673647, 25852016759807766522832], 'label': '3072.bgb.384.BI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.bf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.BI', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761453
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.BJ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.NF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.C', '192.EE', '192.EV', '192.EW', '192.FA', '192.FB', '192.FC', '192.FD', '192.FH', '192.FI', '192.NB'], 'contains': ['768.C', '768.U', '768.V'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922594664024732247801, 51212588579793007921, 25903229683158464676480], 'label': '3072.bgb.384.BJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.bg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.BJ', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761454
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.CB', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.53387', 'aut_weyl_index': 24, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.O', '12.X', '12.BD'], 'contains': ['48.EQ', '48.GN', '48.GQ', '48.LN', '48.OM'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 53952412691500576681559, 187973685961890096441600, 25852138389591620222016, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.24.CB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.cb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CB', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761455
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.BK', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.GO', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.O', '192.Q', '192.DV', '192.DW', '192.DY', '192.EA', '192.FK', '192.FL', '192.FN', '192.FP', '192.FR', '192.FS', '192.GJ', '192.GM', '192.NC'], 'contains': ['768.D', '768.F', '768.N', '768.BL'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229691554491852799, 1313941673647, 51212962568394582352], 'label': '3072.bgb.384.BK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.bh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.BK', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761456
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.BL', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.GI', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.P', '192.Q', '192.DU', '192.DX', '192.DZ', '192.EA', '192.FJ', '192.FM', '192.FO', '192.FQ', '192.FR', '192.FT', '192.GK', '192.GM', '192.NC'], 'contains': ['768.D', '768.F', '768.X'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [9709968839632, 1313941673647, 25852016759807766522832], 'label': '3072.bgb.384.BL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.bi1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.BL', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761604
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '384.GP', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.Z', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.Z', '192.QU', '192.QV'], 'contains': ['768.BA', '768.BB', '768.BE', '768.BS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [25903107682370587468807, 51091300648929957136, 51212962568394582352], 'label': '3072.bgb.384.GP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.BZ', 'old_label': '384.ge1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.GP', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761457
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.BM', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.LY', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.R', '192.ED', '192.EL', '192.EM', '192.FJ', '192.FK', '192.FP', '192.FQ', '192.FV', '192.FW', '192.FX', '192.FY', '192.FZ', '192.HF', '192.ND'], 'contains': ['768.D', '768.G', '768.I', '768.BM'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [108118165248982343710201, 187973685961890096441600, 25903229683158464676480], 'label': '3072.bgb.384.BM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '384.bj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.BM', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761458
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.BN', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.QG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.GB', '192.GC', '192.GO', '192.HG', '192.ND'], 'contains': ['768.E', '768.H', '768.J', '768.BM'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187973685961890096441600], 'label': '3072.bgb.384.BN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.MC', 'old_label': '384.bj2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.BN', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761459
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.BO', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.QG', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.S', '192.FU', '192.GD', '192.GQ', '192.GR', '192.HG', '192.NE'], 'contains': ['768.D', '768.H', '768.K', '768.BN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79855520714221614566521, 79855520719821622658496, 1313941673647], 'label': '3072.bgb.384.BO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CQ', 'old_label': '384.bk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.BO', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761460
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.BP', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.QG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.EB', '192.EC', '192.GN', '192.HF', '192.NE'], 'contains': ['768.E', '768.G', '768.L', '768.BN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79855520714221614566521, 79855520719821622658496, 25903229683158464676480], 'label': '3072.bgb.384.BP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.JW', 'old_label': '384.bk2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.BP', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761461
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.BQ', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.QG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.GB', '192.GC', '192.GP', '192.HG', '192.NE'], 'contains': ['768.E', '768.H', '768.L', '768.BN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79855520714221614566521, 79855520719821622658496, 25903229681844523013167], 'label': '3072.bgb.384.BQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.MC', 'old_label': '384.bk3', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.BQ', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761462
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.BR', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.PR', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.S', '192.GE', '192.GO', '192.GP', '192.GQ', '192.GR', '192.NF'], 'contains': ['768.D', '768.H', '768.T'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229691554491852799, 79855398717732338388456, 1313941673647], 'label': '3072.bgb.384.BR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CQ', 'old_label': '384.bl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.BR', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761463
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.BS', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.KY', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.R', '192.EE', '192.EL', '192.EM', '192.FL', '192.FM', '192.FR', '192.GA', '192.GN', '192.NG'], 'contains': ['768.D', '768.G', '768.U'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922594664024732247801, 79855520714221614566521, 25903229683158464676480], 'label': '3072.bgb.384.BS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '384.bm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.BS', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761464
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.BT', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.QH', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.EN', '192.FU', '192.FZ', '192.GO', '192.HH', '192.HI', '192.NH'], 'contains': ['768.D', '768.J', '768.Y'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229691554491852799, 108118165248982343710201, 1313941673647], 'label': '3072.bgb.384.BT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GB', 'old_label': '384.bn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.BT', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761465
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.CC', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.53387', 'aut_weyl_index': 24, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.O', '12.Y', '12.Z'], 'contains': ['48.EQ', '48.GO', '48.GP', '48.LO', '48.ON'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [162070577934876685646657, 25903229681844523013167, 133970182343548561347240, 25852138389591620222016, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.24.CC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.cc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CC', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761466
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.BU', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.QH', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.EF', '192.FU', '192.GN', '192.GP', '192.HH', '192.HI', '192.NI'], 'contains': ['768.D', '768.L', '768.Y'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79855520719821622658496, 25903229683158464676480, 187922594658424724202816], 'label': '3072.bgb.384.BU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GB', 'old_label': '384.bo1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.BU', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761467
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.BV', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.GN', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.O', '192.T', '192.DU', '192.DW', '192.EG', '192.EK', '192.FJ', '192.FL', '192.FO', '192.FV', '192.GA', '192.GF', '192.GJ', '192.HC', '192.NC'], 'contains': ['768.D', '768.N', '768.S'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [9709968839632, 1313941673647, 51212962568394582352], 'label': '3072.bgb.384.BV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.bp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.BV', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761468
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.BW', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.MB', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.EB', '192.GB', '192.GT', '192.GY', '192.HH', '192.NJ'], 'contains': ['768.E', '768.P', '768.Y'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804429416356250372480, 25903229683158464676480, 79804429421968711780537], 'label': '3072.bgb.384.BW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GB', 'old_label': '384.bq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.BW', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761469
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.BX', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.MB', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.EC', '192.GC', '192.GU', '192.GZ', '192.HI', '192.NJ'], 'contains': ['768.E', '768.Q', '768.Y'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [54003382330230002441647, 25903229683158464676480, 79804429421968711780537], 'label': '3072.bgb.384.BX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GB', 'old_label': '384.br1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.BX', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761470
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.BY', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.KP', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.U', '192.V', '192.ED', '192.EE', '192.FN', '192.FO', '192.FS', '192.FT', '192.GD', '192.GE', '192.GF', '192.GG', '192.GH', '192.GI', '192.NK'], 'contains': ['768.D', '768.R', '768.V'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187973685961890096441600, 79804308125641822294440, 25903229683158464676480], 'label': '3072.bgb.384.BY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '384.bs1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.BY', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761471
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.BZ', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.GH', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.P', '192.T', '192.DV', '192.DX', '192.EH', '192.EK', '192.FK', '192.FM', '192.FN', '192.FW', '192.GA', '192.GG', '192.GK', '192.HC', '192.NC'], 'contains': ['768.D', '768.S', '768.X'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229691554491852799, 1313941673647, 25852016759807766522832], 'label': '3072.bgb.384.BZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.bt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.BZ', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761472
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.CA', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.PZ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.GO', '192.GP', '192.GY', '192.GZ', '192.NN'], 'contains': ['768.E', '768.T', '768.Y'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79855398717732338388456, 1313941673647, 133970303635757521608262], 'label': '3072.bgb.384.CA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.MC', 'old_label': '384.bu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.CA', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761473
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.CB', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.PV', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.EN', '192.GN', '192.GT', '192.GU', '192.NP'], 'contains': ['768.E', '768.U', '768.Y'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922594664024732247801, 25903229683158464676480, 79804429421968711780537], 'label': '3072.bgb.384.CB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.JW', 'old_label': '384.bv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.CB', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761474
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.CC', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.JW', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.EO', '192.GL', '192.GS', '192.GT', '192.GU', '192.GV', '192.GW', '192.HF', '192.NQ'], 'contains': ['768.E', '768.I', '768.BO', '768.BP'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229691554491852799, 187922473375925652905521, 25903229683158464676480], 'label': '3072.bgb.384.CC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '384.bw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.CC', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761475
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.CD', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '48.JW', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.EO', '192.GN', '192.GO', '192.HG', '192.HH', '192.HI', '192.NQ'], 'contains': ['768.D', '768.E', '768.J', '768.BO', '768.BP'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229691554491852799, 25903229681844523013167, 187922473375925652905521], 'label': '3072.bgb.384.CD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GB', 'old_label': '384.bw2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.CD', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761476
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.CD', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.53387', 'aut_weyl_index': 24, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.F', '12.BA', '12.BE'], 'contains': ['48.ER', '48.ET', '48.GT', '48.GX', '48.HA', '48.LQ', '48.LS', '48.OX', '48.PE'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [242089752358354392177983, 25903229681844523013167, 122002101738321960, 1313941673647, 134021272934136496216343, 187922594661241166512703, 324355901222623977942343], 'label': '3072.bgb.24.CD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.cd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CD', 'subgroup_fusion': None, 'weyl_group': '128.1758'}
  • id: 184761477
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.CE', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '48.MC', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.EN', '192.GP', '192.HF', '192.HG', '192.HH', '192.HI', '192.NR'], 'contains': ['768.D', '768.E', '768.L', '768.BQ', '768.BR'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79855520719821622658496, 25903229681844523013167, 187973685961890096441600], 'label': '3072.bgb.384.CE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GB', 'old_label': '384.bx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.CE', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761478
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.CF', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.MC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.GX', '192.GY', '192.GZ', '192.HA', '192.HG', '192.NR'], 'contains': ['768.E', '768.K', '768.BQ', '768.BR'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79855520719821622658496, 187973685961890096441600, 1313941673647], 'label': '3072.bgb.384.CF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GO', 'old_label': '384.bx2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.CF', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761479
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '384.CG', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.GN', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.U', '192.EL', '192.GJ', '192.GK', '192.GQ', '192.HB', '192.HD', '192.HE', '192.HH', '192.NS'], 'contains': ['768.D', '768.P'], 'core': '3072.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79804429416356250372480, 187973685961890096441600, 25903229683158464676480], 'label': '3072.bgb.384.CG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '384.by1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.CG', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761480
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '384.CH', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.GQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.V', '192.EM', '192.GM', '192.GR', '192.HC', '192.HI', '192.NS'], 'contains': ['768.D', '768.Q'], 'core': '3072.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [54003382330230002441647, 187973685961890096441600, 25903229683158464676480], 'label': '3072.bgb.384.CH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '384.bz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.CH', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761481
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.CI', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.BG', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.W', '192.Z', '192.EP', '192.EQ', '192.EX', '192.EY', '192.FJ', '192.FL', '192.FP', '192.FR', '192.HJ', '192.HL', '192.HZ', '192.IA', '192.NT'], 'contains': ['768.F', '768.G', '768.N', '768.BS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [51091300648929957136, 1313941673647, 51212962568394582352], 'label': '3072.bgb.384.CI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.ca1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.CI', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761482
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.CJ', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.BE', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.W', '192.BA', '192.ER', '192.ES', '192.EX', '192.EY', '192.FK', '192.FM', '192.FQ', '192.FR', '192.HK', '192.HM', '192.HZ', '192.IB', '192.NT'], 'contains': ['768.F', '768.G', '768.X'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25852138386775177898303, 1313941673647, 25852016759807766522832], 'label': '3072.bgb.384.CJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.cb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.CJ', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761483
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.CK', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.GT', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.X', '192.BI', '192.DU', '192.DV', '192.ET', '192.EU', '192.FJ', '192.FK', '192.HJ', '192.HK', '192.HN', '192.IE', '192.IG', '192.IR', '192.NW'], 'contains': ['768.F', '768.I', '768.S'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229683158464676480, 404210922196204071249966, 162121668868625366436606], 'label': '3072.bgb.384.CK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.cc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.CK', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761484
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '384.CL', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.BB', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.Y', '192.BB', '192.HO', '192.HP', '192.IK', '192.IL', '192.NU'], 'contains': ['768.F', '768.M', '768.O', '768.BT'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [378358770650295628183080, 25852272837936812846761, 25903229683158464676480], 'label': '3072.bgb.384.CL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.FI', 'old_label': '384.cd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.CL', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761485
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '384.CM', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.CE', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.Y', '192.BC', '192.HQ', '192.HR', '192.IK', '192.IL', '192.NU'], 'contains': ['768.F', '768.M', '768.W'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [51469042011382569606, 378358770648994141276807, 25903229683158464676480], 'label': '3072.bgb.384.CM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.FI', 'old_label': '384.ce1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.CM', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761486
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.CN', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.GQ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.O', '192.Q', '192.ET', '192.EW', '192.EZ', '192.FA', '192.FO', '192.FS', '192.HJ', '192.HM', '192.HS', '192.HZ', '192.IA', '192.IN', '192.NV'], 'contains': ['768.F', '768.N', '768.V'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [122007701746409022, 1313941673647, 51212962568394582352], 'label': '3072.bgb.384.CN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.cf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.CN', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761487
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.CE', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.53387', 'aut_weyl_index': 24, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.F', '12.BB', '12.BG'], 'contains': ['48.ES', '48.ET', '48.GU', '48.GZ', '48.HD'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 122002101738321960, 1313941673647, 134021272934136496216343, 296041409911409376977422, 216237613982764859689536, 187922594661241166512703], 'label': '3072.bgb.24.CE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.ce1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CE', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761488
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.CO', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.CI', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.BD', '192.BE', '192.EP', '192.ER', '192.GJ', '192.GK', '192.HO', '192.HQ', '192.HS', '192.HT', '192.HU', '192.HV', '192.IE', '192.IF', '192.NX'], 'contains': ['768.F', '768.P', '768.S'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804429416356250372480, 25903229683158464676480, 404210922196204071249966], 'label': '3072.bgb.384.CO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '384.cg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.CO', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761489
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.CP', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.BG', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.BE', '192.BF', '192.EQ', '192.ES', '192.FN', '192.FO', '192.HN', '192.HP', '192.HR', '192.HW', '192.HX', '192.HY', '192.IR', '192.IS', '192.NY'], 'contains': ['768.F', '768.R', '768.S'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804308125641822294440, 25903229683158464676480, 404210922196204071249966], 'label': '3072.bgb.384.CP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '384.ch1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.CP', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761490
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.CQ', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.HH', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.X', '192.BI', '192.DW', '192.DX', '192.EV', '192.EW', '192.FL', '192.FM', '192.HL', '192.HM', '192.HY', '192.IF', '192.IG', '192.IS', '192.NZ'], 'contains': ['768.F', '768.S', '768.U'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922594664024732247801, 25903229683158464676480, 404210922196204071249966], 'label': '3072.bgb.384.CQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.ci1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.CQ', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761491
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.CR', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.GK', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.P', '192.Q', '192.EU', '192.EV', '192.EZ', '192.FB', '192.FN', '192.FT', '192.HK', '192.HL', '192.HT', '192.HZ', '192.IB', '192.IN', '192.NV'], 'contains': ['768.F', '768.V', '768.X'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903107687970595565937, 1313941673647, 25852016759807766522832], 'label': '3072.bgb.384.CR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.cj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.CR', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761492
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.CS', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.GV', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.BI', '192.DY', '192.DZ', '192.EZ', '192.FP', '192.FQ', '192.GL', '192.HZ', '192.ID', '192.IF', '192.IH', '192.II', '192.IR', '192.IT', '192.NW'], 'contains': ['768.F', '768.I', '768.BU'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922473375925652905521, 404210922197505558871681, 25903229683158464676480], 'label': '3072.bgb.384.CS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '384.ck1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.CS', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761493
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.CT', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.CX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.BF', '192.BJ', '192.EX', '192.GM', '192.IG', '192.IK', '192.IN', '192.IT', '192.NX'], 'contains': ['768.F', '768.Q'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [54003382330230002441647, 404210922197505558871681, 25903229683158464676480], 'label': '3072.bgb.384.CT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '384.cl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.CT', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761494
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.CU', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.BI', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.BD', '192.BJ', '192.EY', '192.FS', '192.FT', '192.IC', '192.IJ', '192.IL', '192.IM', '192.IO', '192.IP', '192.IQ', '192.IR', '192.IS', '192.NY'], 'contains': ['768.F', '768.R'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [54003503618341535825287, 404210922197505558871681, 25903229683158464676480], 'label': '3072.bgb.384.CU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '384.cm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.CU', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761495
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.CV', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.HJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.BI', '192.EA', '192.FA', '192.FB', '192.FR', '192.IA', '192.IB', '192.IE', '192.IS', '192.IT', '192.NZ'], 'contains': ['768.F', '768.U'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [162121547577898484316726, 404210922197505558871681, 25903229683158464676480], 'label': '3072.bgb.384.CV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.cn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.CV', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761496
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.CW', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.OA', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.R', '192.ED', '192.FC', '192.FD', '192.HJ', '192.HK', '192.HZ', '192.IU', '192.OA'], 'contains': ['768.G', '768.I', '768.V'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79855520714221614566521, 187922473375925652905521, 25903229683158464676480], 'label': '3072.bgb.384.CW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.co1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.CW', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761497
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.CX', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.NQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.EB', '192.EC', '192.FZ', '192.GN', '192.OB'], 'contains': ['768.G', '768.J', '768.Y'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [108118165248982343710201, 1313941673647, 133970303635757521608262], 'label': '3072.bgb.384.CX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.JW', 'old_label': '384.cp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.CX', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761498
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.CF', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.53387', 'aut_weyl_index': 24, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.G', '12.BB', '12.BE'], 'contains': ['48.ET', '48.HA', '48.HC', '48.LT', '48.PH'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 122002101738321960, 1313941673647, 134021272934136496216343, 378358649363678452761737, 187922594661241166512703, 324355901222623977942343], 'label': '3072.bgb.24.CF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.cf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CF', 'subgroup_fusion': None, 'weyl_group': '128.1758'}
  • id: 184761499
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.CY', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.NR', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.FU', '192.GB', '192.GC', '192.GO', '192.OC'], 'contains': ['768.H', '768.J', '768.Y'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922473375925652905521, 1313941673647, 133970303635757521608262], 'label': '3072.bgb.384.CY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.MC', 'old_label': '384.cp2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.CY', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761500
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.CZ', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.NF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.S', '192.GD', '192.IX', '192.IY', '192.OD'], 'contains': ['768.H', '768.K', '768.V'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903107687970595565937, 79855520719821622658496, 1313941673647], 'label': '3072.bgb.384.CZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.EO', 'old_label': '384.cq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.CZ', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761501
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.DA', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.NR', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.FU', '192.GB', '192.GC', '192.GP', '192.OE'], 'contains': ['768.H', '768.L', '768.Y'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [54003503622459465078359, 79855520719821622658496, 25903229681844523013167], 'label': '3072.bgb.384.DA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.MC', 'old_label': '384.cr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.DA', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761502
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.DB', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.BF', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.W', '192.BO', '192.EP', '192.EQ', '192.FE', '192.FF', '192.FK', '192.FL', '192.FV', '192.GA', '192.HJ', '192.HM', '192.IU', '192.IV', '192.NT'], 'contains': ['768.G', '768.N', '768.S'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25852138386775177898303, 1313941673647, 51212962568394582352], 'label': '3072.bgb.384.DB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.cs1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.DB', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761503
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.DC', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.BD', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.W', '192.BQ', '192.ER', '192.ES', '192.FE', '192.FF', '192.FJ', '192.FM', '192.FW', '192.GA', '192.HK', '192.HL', '192.IU', '192.IW', '192.NT'], 'contains': ['768.G', '768.S', '768.X'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [51091300648929957136, 1313941673647, 25852016759807766522832], 'label': '3072.bgb.384.DC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.ct1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.DC', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761504
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.DD', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.OF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.S', '192.GE', '192.IX', '192.IY', '192.OF'], 'contains': ['768.H', '768.T', '768.V'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79855520714221614566521, 79855398717732338388456, 1313941673647], 'label': '3072.bgb.384.DD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.EO', 'old_label': '384.cu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.DD', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761505
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.DE', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.QJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.R', '192.EE', '192.FC', '192.FD', '192.HL', '192.HM', '192.IA', '192.IB', '192.IV', '192.IW', '192.OH'], 'contains': ['768.G', '768.U', '768.V'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922594664024732247801, 108169377837562135992360, 25903229683158464676480], 'label': '3072.bgb.384.DE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.cv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.DE', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761506
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.DF', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.KS', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.BS', '192.GB', '192.GQ', '192.IX', '192.JA', '192.JB', '192.OK'], 'contains': ['768.H', '768.P'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804429416356250372480, 79855398709336311235223, 25903229683158464676480], 'label': '3072.bgb.384.DF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BA', 'old_label': '384.cw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.DF', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761507
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.DG', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.KS', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.BT', '192.GC', '192.GR', '192.IY', '192.OK'], 'contains': ['768.H', '768.Q'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [54003382330230002441647, 79855398709336311235223, 25903229683158464676480], 'label': '3072.bgb.384.DG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BB', 'old_label': '384.cx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.DG', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761508
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.DH', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '192.MH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.BS', '192.BT', '192.GD', '192.GE', '192.IC', '192.IZ', '192.JC', '192.JD', '192.OL'], 'contains': ['768.H', '768.R'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79855398709336311235223, 79804308125641822294440, 25903229683158464676480], 'label': '3072.bgb.384.DH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BN', 'old_label': '384.cy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.DH', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761509
    {'ambient': '3072.bgb', 'aut_centralizer_order': 1, 'aut_label': '4.J', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1536.408550734', 'aut_weyl_index': 4, 'centralizer': '3072.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.D'], 'contains': ['8.B', '8.M', '8.O', '12.CK', '16.S'], 'core': '8.B', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [108118421696801471190456, 25903229681844523013167, 108118165248982343710201, 187922473375925652905521, 133970303627361494479417, 404159831259638948150382, 1313941673647, 378358649363678452761737, 162070456272950954131199], 'label': '3072.bgb.4.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.D', 'old_label': '4.j1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.J', 'subgroup_fusion': None, 'weyl_group': '1536.408550734'}
  • id: 184761510
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.CG', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.53387', 'aut_weyl_index': 24, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.G', '12.BA', '12.BG'], 'contains': ['48.ET', '48.HB', '48.HD', '48.LR', '48.OZ'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 122002101738321960, 324406991811924875755576, 1313941673647, 134021272934136496216343, 216237613982764859689536, 187922594661241166512703], 'label': '3072.bgb.24.CG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.cg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CG', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761511
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.DI', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.QH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.EB', '192.GB', '192.HH', '192.JU', '192.KD', '192.OM'], 'contains': ['768.J', '768.L', '768.P'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804308122845802507662, 25903229681844523013167, 187922473375925652905521], 'label': '3072.bgb.384.DI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GB', 'old_label': '384.cz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.DI', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761512
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.DJ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.QH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.EC', '192.GC', '192.HI', '192.JV', '192.KE', '192.OM'], 'contains': ['768.J', '768.L', '768.Q'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 79804308124159744181057], 'label': '3072.bgb.384.DJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GB', 'old_label': '384.da1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.DJ', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761513
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.DK', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.NQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.EN', '192.GN', '192.KD', '192.KE', '192.ON'], 'contains': ['768.J', '768.L', '768.U'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [133970182339249961095537, 25903229681844523013167, 187922473375925652905521], 'label': '3072.bgb.384.DK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.JW', 'old_label': '384.db1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.DK', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761514
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.DL', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.QG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.EF', '192.HF', '192.ID', '192.JE', '192.JF', '192.JG', '192.KD', '192.KE', '192.OO'], 'contains': ['768.I', '768.L', '768.BV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [53952413035981411118158, 187922473375925652905521, 25903229683158464676480], 'label': '3072.bgb.384.DL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '384.dc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.DL', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761515
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.DM', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.QG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.FU', '192.HG', '192.JU', '192.JV', '192.OO'], 'contains': ['768.J', '768.K', '768.L', '768.BV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [53952413035981411118158, 25903229681844523013167, 187922473375925652905521], 'label': '3072.bgb.384.DM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.MC', 'old_label': '384.dc2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.DM', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761516
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.DN', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.GU', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.BU', '192.BV', '192.DU', '192.DV', '192.EZ', '192.FG', '192.FJ', '192.FK', '192.HZ', '192.IU', '192.JH', '192.JI', '192.JX', '192.JY', '192.OP'], 'contains': ['768.I', '768.N', '768.X'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229337376182892926, 1313941673647, 51212595674412385793], 'label': '3072.bgb.384.DN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.dd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.DN', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761517
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.DO', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.GX', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.BV', '192.DY', '192.EG', '192.ET', '192.FP', '192.FV', '192.GS', '192.HJ', '192.JE', '192.JJ', '192.JK', '192.JL', '192.JY', '192.KF', '192.OP'], 'contains': ['768.I', '768.N', '768.BW'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229337376182892926, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.384.DO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '384.de1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.DO', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761518
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '384.DP', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.LA', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.BW', '192.EL', '192.FC', '192.GT', '192.IE', '192.IF', '192.JH', '192.JL', '192.JM', '192.JN', '192.JO', '192.KD', '192.OQ'], 'contains': ['768.I', '768.P', '768.U'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [187922473375925652905521, 25903229683158464676480, 108118287251071627990321], 'label': '3072.bgb.384.DP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '384.df1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.DP', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761519
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '384.DQ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.LL', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.BX', '192.EM', '192.FD', '192.GU', '192.IG', '192.IT', '192.JI', '192.JJ', '192.JP', '192.JQ', '192.JR', '192.KE', '192.OQ'], 'contains': ['768.I', '768.Q', '768.U'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [187922473375925652905521, 134021272931340477137406, 25903229683158464676480], 'label': '3072.bgb.384.DQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '384.dg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.DQ', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761520
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.DR', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.GW', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.X', '192.EG', '192.EH', '192.FG', '192.FV', '192.FW', '192.GV', '192.HN', '192.IF', '192.IU', '192.JF', '192.JP', '192.JS', '192.KG', '192.NW'], 'contains': ['768.I', '768.S'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922473375925652905521, 25903229683158464676480, 404210922196204071249966], 'label': '3072.bgb.384.DR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '384.dh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.DR', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761521
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.CH', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.H', '12.T', '12.V'], 'contains': ['48.BS', '48.BT', '48.EU', '48.EV', '48.EY', '48.HI', '48.HM', '48.HY', '48.II'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [378358770650295628183080, 270240484111912758504367, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.24.CH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ch1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CH', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184761522
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.DS', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.GY', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.BU', '192.DZ', '192.EH', '192.EU', '192.FQ', '192.FW', '192.GW', '192.HK', '192.JG', '192.JJ', '192.JM', '192.JT', '192.JX', '192.KH', '192.OP'], 'contains': ['768.I', '768.X'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [368207923870206, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.384.DS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '384.di1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.DS', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761523
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.DT', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.PV', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.EF', '192.FZ', '192.GT', '192.GU', '192.IH', '192.JK', '192.JS', '192.JT', '192.OW'], 'contains': ['768.I', '768.Y'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [108118165248982343710201, 25903229683158464676480, 79804429421968711780537], 'label': '3072.bgb.384.DT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '384.dj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.DT', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761524
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.DU', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.HA', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.EI', '192.EJ', '192.FX', '192.FY', '192.GS', '192.GW', '192.ID', '192.II', '192.JF', '192.JK', '192.JN', '192.JQ', '192.JT', '192.KG', '192.OY'], 'contains': ['768.I', '768.BX'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922473375925652905521, 25903229683158464676480, 378358905093235639407953], 'label': '3072.bgb.384.DU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '384.dk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.DU', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761525
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.DV', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.GZ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.EI', '192.EJ', '192.FX', '192.FY', '192.GL', '192.GV', '192.IH', '192.JE', '192.JG', '192.JO', '192.JR', '192.JS', '192.KF', '192.KH', '192.OZ'], 'contains': ['768.I', '768.BY'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [162121669227129588479873, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.384.DV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '384.dl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.DV', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761526
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.DW', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.PN', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.BW', '192.BX', '192.ED', '192.HN', '192.IR', '192.JW', '192.JX', '192.JY', '192.JZ', '192.KB', '192.PA'], 'contains': ['768.I', '768.R'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 187922473375925652905521, 25903229683158464676480], 'label': '3072.bgb.384.DW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '384.dm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.DW', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761527
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.DX', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '192.NR', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.GO', '192.JU', '192.JV', '192.KA', '192.KC', '192.PB'], 'contains': ['768.J', '768.T'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 25852017102974698844878], 'label': '3072.bgb.384.DX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GO', 'old_label': '384.dn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.DX', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761528
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.DY', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.NB', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.EO', '192.FZ', '192.II', '192.KD', '192.KE', '192.KF', '192.KG', '192.KH', '192.PC'], 'contains': ['768.I', '768.J', '768.BZ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 162070456272950954131199], 'label': '3072.bgb.384.DY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '384.do1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.DY', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761529
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.DZ', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.KK', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.BY', '192.BZ', '192.KI', '192.KK', '192.KX', '192.KZ', '192.PD'], 'contains': ['768.K', '768.O', '768.W'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [378358770650295628183080, 108118165251765908747536, 25903229683158464676480], 'label': '3072.bgb.384.DZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.GX', 'old_label': '384.dp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.DZ', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761530
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.EA', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '192.KJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.BZ', '192.GX', '192.KJ', '192.KL', '192.KM', '192.KZ', '192.PD'], 'contains': ['768.K', '768.O', '768.CA'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 134021394933610431760703, 25903229683158464676480], 'label': '3072.bgb.384.EA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CD', 'old_label': '384.dq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.EA', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761531
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '384.EB', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.LR', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.CA', '192.GQ', '192.GY', '192.IX', '192.JU', '192.KI', '192.KM', '192.KN', '192.KO', '192.KP', '192.KQ', '192.KR', '192.PE'], 'contains': ['768.K', '768.P', '768.T'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855398716250260275073, 79855398717732338388456, 1313941673647], 'label': '3072.bgb.384.EB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BA', 'old_label': '384.dr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.EB', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761532
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.CI', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.H', '12.U', '12.V'], 'contains': ['48.EU', '48.EX', '48.EY', '48.HK', '48.HL', '48.IF', '48.IK'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 122002101738321960, 79804308125641822294440, 296041409911409376977422, 378358649363678452761737, 25852272837936812846761], 'label': '3072.bgb.24.CI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ci1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CI', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184761533
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '384.EC', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.LQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.CB', '192.GR', '192.GZ', '192.IY', '192.JV', '192.KJ', '192.KK', '192.KS', '192.KT', '192.PE'], 'contains': ['768.K', '768.Q', '768.T'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952413035981411118158, 79855398717732338388456, 1313941673647], 'label': '3072.bgb.384.EC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BA', 'old_label': '384.ds1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.EC', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761534
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.ED', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '192.KJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.BY', '192.HA', '192.KJ', '192.KN', '192.KU', '192.KX', '192.PD'], 'contains': ['768.K', '768.W'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770648994141276807, 134021394933610431760703, 25903229683158464676480], 'label': '3072.bgb.384.ED', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CD', 'old_label': '384.dt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.ED', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761535
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.EE', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.PZ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.FU', '192.GY', '192.GZ', '192.KL', '192.KU', '192.PJ'], 'contains': ['768.K', '768.Y'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79855520719821622658496, 1313941673647, 134021394929311911342598], 'label': '3072.bgb.384.EE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GO', 'old_label': '384.du1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.EE', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761536
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.EF', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.KS', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.GX', '192.HA', '192.KL', '192.KO', '192.KS', '192.KU', '192.PL'], 'contains': ['768.K', '768.CB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79855520719821622658496, 1313941673647, 134021529040297499210286], 'label': '3072.bgb.384.EF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.LQ', 'old_label': '384.dv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.EF', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761537
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.EG', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.QD', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.CA', '192.CB', '192.GD', '192.IJ', '192.KV', '192.KW', '192.KX', '192.KZ', '192.LA', '192.LB', '192.PM'], 'contains': ['768.K', '768.R'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804308125641822294440, 134021394933610431760703, 25903229683158464676480], 'label': '3072.bgb.384.EG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '384.dw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.EG', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761538
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.EH', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '192.NR', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.GP', '192.JU', '192.JV', '192.KY', '192.LC', '192.PN'], 'contains': ['768.L', '768.T'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922473373129633118743, 79855398717732338388456, 1313941673647], 'label': '3072.bgb.384.EH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GO', 'old_label': '384.dx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.EH', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761539
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '384.EI', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.BC', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.Y', '192.CE', '192.HO', '192.HP', '192.LE', '192.LF', '192.NU'], 'contains': ['768.M', '768.O', '768.S'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [51469042011382569606, 378358770650295628183080, 25903229683158464676480], 'label': '3072.bgb.384.EI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.FI', 'old_label': '384.dy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.EI', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761540
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '384.EJ', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.CF', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.Y', '192.CF', '192.HQ', '192.HR', '192.LE', '192.LF', '192.NU'], 'contains': ['768.M', '768.S', '768.W'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [378358770648994141276807, 25852272837936812846761, 25903229683158464676480], 'label': '3072.bgb.384.EJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.FI', 'old_label': '384.dz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.EJ', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761541
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.EK', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '192.MI', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.CI', '192.CJ', '192.HB', '192.HO', '192.HQ', '192.LD', '192.LH', '192.LI', '192.PO'], 'contains': ['768.M', '768.P'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804429416356250372480, 25903229683158464676480, 53952035291802302422343], 'label': '3072.bgb.384.EK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BO', 'old_label': '384.ea1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.EK', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761542
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.EL', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '192.MO', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.CK', '192.CL', '192.IK', '192.LE', '192.PO'], 'contains': ['768.M', '768.Q'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [54003382330230002441647, 25903229683158464676480, 53952035291802302422343], 'label': '3072.bgb.384.EL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.DA', 'old_label': '384.eb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.EL', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761543
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.CJ', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.6407063', 'aut_weyl_index': 12, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.I', '12.V', '12.BC'], 'contains': ['48.B', '48.EU', '48.EZ', '48.HJ', '48.IN', '48.LV', '48.PM'], 'core': '48.B', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229691554491852799, 1313941673647, 122002101738321960, 25903229681844523013167, 79804429413572684637382, 53952035291802302422343, 79804308125641822294440], 'label': '3072.bgb.24.CJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CJ', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 184761544
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.EM', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '192.MI', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.CI', '192.CL', '192.HP', '192.HR', '192.IM', '192.JW', '192.LJ', '192.LL', '192.PP'], 'contains': ['768.M', '768.R'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [54003503618341535825287, 25903229683158464676480, 53952035291802302422343], 'label': '3072.bgb.384.EM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.DK', 'old_label': '384.ec1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.EM', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761545
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.EN', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '192.MO', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.CJ', '192.CK', '192.IL', '192.KV', '192.LF', '192.LG', '192.LK', '192.LM', '192.PP'], 'contains': ['768.M', '768.R'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804308125641822294440, 25903229683158464676480, 53952035291802302422343], 'label': '3072.bgb.384.EN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '384.ec2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.EN', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761546
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.EO', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.DX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.CO', '192.CP', '192.EX', '192.FE', '192.GM', '192.HC', '192.IN', '192.JI', '192.JJ', '192.LN', '192.PQ'], 'contains': ['768.N', '768.Q', '768.X'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229684640542817862, 1313941673647, 51212962568394582352], 'label': '3072.bgb.384.EO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.ed1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.EO', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761547
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.EP', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.BI', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.CN', '192.CP', '192.EY', '192.FF', '192.FN', '192.FO', '192.JX', '192.JY', '192.LO', '192.LS', '192.PR'], 'contains': ['768.N', '768.R', '768.X'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [122004885304085057, 1313941673647, 51090958997032170942], 'label': '3072.bgb.384.EP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.ee1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.EP', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761548
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.EQ', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.GP', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.O', '192.T', '192.ET', '192.EV', '192.FG', '192.FH', '192.FN', '192.GF', '192.HJ', '192.HL', '192.HS', '192.IU', '192.IV', '192.LN', '192.NV'], 'contains': ['768.N', '768.S', '768.V'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903107687970595565937, 1313941673647, 51212962568394582352], 'label': '3072.bgb.384.EQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.ef1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.EQ', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761549
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.ER', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.HI', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.BU', '192.BV', '192.EA', '192.EK', '192.EV', '192.EW', '192.FR', '192.GA', '192.HL', '192.HM', '192.JH', '192.JJ', '192.LO', '192.LS', '192.PS'], 'contains': ['768.N', '768.U', '768.X'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [1313941673647, 51091307562878992073, 51212962568394582352], 'label': '3072.bgb.384.ER', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.eg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.ER', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761550
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.ES', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.DD', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.CN', '192.CR', '192.EP', '192.GJ', '192.HS', '192.JH', '192.JL', '192.LD', '192.LP', '192.LQ', '192.PQ'], 'contains': ['768.N', '768.P'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [2796019804937, 1313941673647, 51212962568394582352], 'label': '3072.bgb.384.ES', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '384.eh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.ES', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761551
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.ET', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.BL', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.CO', '192.CR', '192.EQ', '192.FS', '192.GF', '192.IZ', '192.JY', '192.KW', '192.LR', '192.LS', '192.PR'], 'contains': ['768.N', '768.R'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25852138757799544092222, 25903107685154153232142, 1313941673647], 'label': '3072.bgb.384.ET', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '384.ei1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.ET', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761552
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.EU', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.HL', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.BV', '192.DW', '192.FA', '192.FH', '192.FL', '192.IA', '192.IV', '192.JI', '192.JL', '192.LS', '192.PS'], 'contains': ['768.N', '768.U'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25852138393689126932998, 1313941673647, 51212962568394582352], 'label': '3072.bgb.384.EU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.ej1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.EU', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761553
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.EV', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.EK', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.CT', '192.CU', '192.IK', '192.KJ', '192.KK', '192.LE', '192.PT'], 'contains': ['768.O', '768.Q', '768.W'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 54003382330230002441647, 25903229683158464676480], 'label': '3072.bgb.384.EV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '384.ek1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.EV', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761554
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.CK', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.H', '12.T', '12.W'], 'contains': ['48.BU', '48.BV', '48.EV', '48.EW', '48.EY', '48.HV', '48.HX', '48.IC', '48.IJ'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [378358770650295628183080, 270240484111912758504367, 108169512287410083283217, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647], 'label': '3072.bgb.24.CK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ck1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CK', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761555
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.EW', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.FU', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.CS', '192.CT', '192.IL', '192.KX', '192.KZ', '192.LF', '192.LT', '192.LU', '192.LV', '192.MA', '192.PU'], 'contains': ['768.O', '768.R', '768.W'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 54003503618341535825287, 25903229683158464676480], 'label': '3072.bgb.384.EW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '384.el1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.EW', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761556
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.EX', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.KJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.BY', '192.BZ', '192.KI', '192.KJ', '192.LT', '192.MA', '192.PV'], 'contains': ['768.O', '768.T', '768.W'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229683158464676480, 134021272934136496216343, 216288705272228144236816], 'label': '3072.bgb.384.EX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.GX', 'old_label': '384.em1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.EX', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761557
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.EY', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.CY', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.CS', '192.CW', '192.HD', '192.HO', '192.JA', '192.KI', '192.KM', '192.LP', '192.LW', '192.LX', '192.PT'], 'contains': ['768.O', '768.P'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804429416356250372480, 378358770650295628183080, 25903229683158464676480], 'label': '3072.bgb.384.EY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '384.en1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.EY', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761558
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.EZ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.DB', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.CU', '192.CW', '192.HP', '192.IO', '192.JZ', '192.KZ', '192.LG', '192.LY', '192.LZ', '192.MA', '192.PU'], 'contains': ['768.O', '768.R'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770650295628183080, 79804308125641822294440, 25903229683158464676480], 'label': '3072.bgb.384.EZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '384.eo1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.EZ', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761559
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.FA', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '192.KK', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.BZ', '192.KA', '192.KK', '192.KM', '192.KY', '192.MA', '192.PV'], 'contains': ['768.O', '768.T'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [108118287253867647069496, 25903229683158464676480, 216288705272228144236816], 'label': '3072.bgb.384.FA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.EH', 'old_label': '384.ep1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.FA', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761560
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '384.FB', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.ND', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.U', '192.FC', '192.HS', '192.HT', '192.IX', '192.LH', '192.LW', '192.MB', '192.PY'], 'contains': ['768.P', '768.V'], 'core': '3072.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79804429416356250372480, 108169377837562135992360, 25903229683158464676480], 'label': '3072.bgb.384.FB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '384.eq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.FB', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761561
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.FC', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.EQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.CS', '192.CZ', '192.HE', '192.HQ', '192.JB', '192.KI', '192.KN', '192.LQ', '192.MB', '192.MC', '192.PT'], 'contains': ['768.P', '768.W'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804429416356250372480, 378358770648994141276807, 25903229683158464676480], 'label': '3072.bgb.384.FC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '384.er1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.FC', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761562
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.FD', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.CE', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.CN', '192.DA', '192.ER', '192.GK', '192.HT', '192.JH', '192.JM', '192.LI', '192.LX', '192.MC', '192.PQ'], 'contains': ['768.P', '768.X'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [2796019804937, 1313941673647, 25852016759807766522832], 'label': '3072.bgb.384.FD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '384.es1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.FD', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761563
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.FE', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.CD', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.DE', '192.DF', '192.HD', '192.HE', '192.HU', '192.HV', '192.JA', '192.JB', '192.KP', '192.KQ', '192.LD', '192.LI', '192.LW', '192.MB', '192.QA'], 'contains': ['768.P'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79855142625594763233847, 2796019804937, 1313941673647], 'label': '3072.bgb.384.FE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '384.et1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.FE', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761564
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.FF', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.QY', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.DI', '192.DJ', '192.HB', '192.HU', '192.HV', '192.LH', '192.LP', '192.LQ', '192.LX', '192.MC', '192.QB'], 'contains': ['768.P'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804429416356250372480, 25903229683158464676480, 134021529384772106263086], 'label': '3072.bgb.384.FF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BO', 'old_label': '384.eu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.FF', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761565
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.CL', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.J', '12.V', '12.W'], 'contains': ['48.EV', '48.EX', '48.EZ', '48.HW', '48.HZ', '48.IE', '48.IL'], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 79804429413572684637382, 378358649363678452761737, 296041409911409376977422], 'label': '3072.bgb.24.CL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.cl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CL', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761566
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.FG', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.CW', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.BF', '192.DL', '192.FE', '192.HC', '192.IG', '192.JP', '192.LE', '192.LN', '192.NX'], 'contains': ['768.Q', '768.S'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [54003382330230002441647, 25903229683158464676480, 404210922196204071249966], 'label': '3072.bgb.384.FG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '384.ev1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.FG', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761568
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.FI', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.BL', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.BD', '192.DL', '192.FF', '192.GF', '192.GG', '192.HN', '192.HY', '192.JC', '192.LA', '192.LF', '192.LJ', '192.LY', '192.MD', '192.ME', '192.NY'], 'contains': ['768.R', '768.S'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [54003503618341535825287, 25903229683158464676480, 404210922196204071249966], 'label': '3072.bgb.384.FI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '384.ex1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.FI', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761569
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.FJ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.UZ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.CA', '192.CB', '192.GE', '192.IP', '192.LK', '192.LR', '192.LT', '192.MA', '192.MD', '192.MF', '192.QD'], 'contains': ['768.R', '768.T'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 79855398717732338388456, 1313941673647], 'label': '3072.bgb.384.FJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '384.ey1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.FJ', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761570
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.FK', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.QW', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.BW', '192.BX', '192.EE', '192.HY', '192.IS', '192.LL', '192.LO', '192.LS', '192.LZ', '192.MG', '192.QE'], 'contains': ['768.R', '768.U'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [187922594664024732247801, 79804308125641822294440, 25903229683158464676480], 'label': '3072.bgb.384.FK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '384.ez1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.FK', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761571
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.FL', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.FT', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.CU', '192.CZ', '192.HR', '192.IQ', '192.KB', '192.KX', '192.LM', '192.LT', '192.ME', '192.MG', '192.PU'], 'contains': ['768.R', '768.W'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770648994141276807, 79804308125641822294440, 25903229683158464676480], 'label': '3072.bgb.384.FL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '384.fa1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.FL', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761572
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.FM', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.BQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.CO', '192.DA', '192.ES', '192.FT', '192.GG', '192.JD', '192.JX', '192.LB', '192.LO', '192.MF', '192.PR'], 'contains': ['768.R', '768.X'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107685154153232142, 1313941673647, 51090958997032170942], 'label': '3072.bgb.384.FM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '384.fb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.FM', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761573
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.FN', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.BU', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.DC', '192.DN', '192.GH', '192.GI', '192.IJ', '192.IP', '192.IZ', '192.JD', '192.LA', '192.LG', '192.LM', '192.LU', '192.LV', '192.MD', '192.QH'], 'contains': ['768.R'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [404211043484134973872583, 79804308125641822294440, 25903229683158464676480], 'label': '3072.bgb.384.FN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '384.fc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.FN', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761574
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.FO', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.MO', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.DD', '192.DO', '192.HW', '192.HX', '192.IO', '192.IQ', '192.JW', '192.KV', '192.LK', '192.LL', '192.LU', '192.LV', '192.LY', '192.ME', '192.QI'], 'contains': ['768.R'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [108169512287410083283217, 54003503618341535825287, 25903229683158464676480], 'label': '3072.bgb.384.FO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '384.fd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.FO', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761575
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.FP', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.BY', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.DG', '192.DP', '192.GH', '192.GI', '192.IC', '192.JC', '192.KW', '192.LB', '192.LR', '192.MF', '192.QJ'], 'contains': ['768.R'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [53952412691500576681559, 122004885304085057, 1313941673647], 'label': '3072.bgb.384.FP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BN', 'old_label': '384.fe1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.FP', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761576
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.CM', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.H', '12.U', '12.W'], 'contains': ['48.EW', '48.EX', '48.EY', '48.IB', '48.ID', '48.IG', '48.IH'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 122002101738321960, 162070321828715682652927, 79804308125641822294440, 296041409911409376977422, 378358649363678452761737], 'label': '3072.bgb.24.CM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.cm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CM', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761577
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.FQ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.CV', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.DH', '192.DQ', '192.HW', '192.HX', '192.IM', '192.JZ', '192.KB', '192.LJ', '192.LZ', '192.MG', '192.QK'], 'contains': ['768.R'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [54003503618341535825287, 25903229683158464676480, 378358649363678452761737], 'label': '3072.bgb.384.FQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.DK', 'old_label': '384.ff1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.FQ', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761578
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.FR', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.GJ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.P', '192.T', '192.EU', '192.EW', '192.FG', '192.FI', '192.FO', '192.GG', '192.HK', '192.HM', '192.HT', '192.IU', '192.IW', '192.LN', '192.NV'], 'contains': ['768.S', '768.V', '768.X'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [122007701746409022, 1313941673647, 25852016759807766522832], 'label': '3072.bgb.384.FR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.fg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.FR', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761579
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.FS', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.HK', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.X', '192.EK', '192.FH', '192.FI', '192.GA', '192.HY', '192.IE', '192.IV', '192.IW', '192.JP', '192.NZ'], 'contains': ['768.S', '768.U'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [162121547577898484316726, 25903229683158464676480, 404210922196204071249966], 'label': '3072.bgb.384.FS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.fh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.FS', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761580
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.FT', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '192.KK', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.BY', '192.KC', '192.KK', '192.KN', '192.LC', '192.LT', '192.PV'], 'contains': ['768.T', '768.W'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [108118287253867647069496, 216288705273529552035263, 25903229683158464676480], 'label': '3072.bgb.384.FT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.EH', 'old_label': '384.fi1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.FT', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761581
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.FU', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.KR', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.KA', '192.KC', '192.KR', '192.KT', '192.KY', '192.LC', '192.QO'], 'contains': ['768.T'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [108118287253867647069496, 242140721662339602266753, 25903229683158464676480], 'label': '3072.bgb.384.FU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.OC', 'old_label': '384.fj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.FU', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761582
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.FV', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.HM', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.BU', '192.DX', '192.FB', '192.FI', '192.FM', '192.IB', '192.IW', '192.JI', '192.JM', '192.LO', '192.PS'], 'contains': ['768.U', '768.X'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25852138393689126932998, 1313941673647, 25852016759807766522832], 'label': '3072.bgb.384.FV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.fk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.FV', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761583
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '384.FW', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '48.DS', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.B', '192.A', '192.MT', '192.MU', '192.MV', '192.MW', '192.MX', '192.MY', '192.MZ', '192.NA', '192.NB'], 'contains': ['768.A', '768.C'], 'core': '768.A', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [25903229681844523013167, 51212588579793007921, 1313941673647], 'label': '3072.bgb.384.FW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '384.fl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.FW', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 184761584
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '384.FX', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.GB', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.MH', '192.MT', '192.MU', '192.NC', '192.ND', '192.NE', '192.NF', '192.NG', '192.NH', '192.NI', '192.NJ', '192.NK', '192.NL', '192.NM', '192.NN', '192.NO', '192.NP', '192.NQ', '192.NR', '192.NS'], 'contains': ['768.A', '768.D', '768.E'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 187973685961890096441600, 1313941673647], 'label': '3072.bgb.384.FX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '384.fm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.FX', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761585
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.FY', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.I', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['128.C', '192.MI', '192.MV', '192.NC', '192.NT', '192.NU', '192.NV', '192.NW', '192.NX', '192.NY', '192.NZ'], 'contains': ['768.A', '768.F', '768.S'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 404210922196204071249966], 'label': '3072.bgb.384.FY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '384.fn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.FY', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761586
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '384.FZ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.FA', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.MJ', '192.MW', '192.MX', '192.ND', '192.NE', '192.NF', '192.NG', '192.NT', '192.OA', '192.OB', '192.OC', '192.OD', '192.OE', '192.OF', '192.OG', '192.OH', '192.OI', '192.OJ', '192.OK', '192.OL'], 'contains': ['768.A', '768.G', '768.H'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79855520714221614566521, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.384.FZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '384.fo1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.FZ', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761587
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '24.CN', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '192.QC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.I', '12.W', '12.BF'], 'contains': ['48.C', '48.EW', '48.EZ', '48.IA', '48.IM'], 'core': '48.C', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118421696801471190456, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 79804429413572684637382, 134021394929311911342598], 'label': '3072.bgb.24.CN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CN', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184761588
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '384.GA', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.JW', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.MK', '192.MT', '192.MY', '192.ND', '192.NH', '192.NQ', '192.NW', '192.OA', '192.OB', '192.OC', '192.OM', '192.ON', '192.OO', '192.OP', '192.OQ', '192.OR', '192.OS', '192.OT', '192.OU', '192.OV', '192.OW', '192.OX', '192.OY', '192.OZ', '192.PA', '192.PB', '192.PC'], 'contains': ['768.A', '768.I', '768.J'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 1313941673647], 'label': '3072.bgb.384.GA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '384.fp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.GA', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761589
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '384.GB', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.MC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.ML', '192.MZ', '192.NE', '192.NI', '192.NR', '192.OD', '192.OE', '192.OM', '192.ON', '192.OO', '192.PD', '192.PE', '192.PF', '192.PG', '192.PH', '192.PI', '192.PJ', '192.PK', '192.PL', '192.PM', '192.PN'], 'contains': ['768.A', '768.K', '768.L'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79855520719821622658496, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.384.GB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '384.fq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.GB', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761590
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.GC', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '192.MM', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.D', '192.MM', '192.NU', '192.PO', '192.PP'], 'contains': ['768.A', '768.M'], 'core': '768.A', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.384.GC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.H', 'old_label': '384.fr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.GC', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 184761591
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.GD', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.G', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.E', '192.MN', '192.MV', '192.NC', '192.NT', '192.NV', '192.OP', '192.PQ', '192.PR', '192.PS'], 'contains': ['768.A', '768.N', '768.X'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 51212962568394582352], 'label': '3072.bgb.384.GD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '384.fs1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.GD', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761592
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '384.GE', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.EG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.F', '192.MO', '192.NU', '192.PD', '192.PT', '192.PU', '192.PV'], 'contains': ['768.A', '768.O', '768.W'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.384.GE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '384.ft1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.GE', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761593
    {'ambient': '3072.bgb', 'aut_centralizer_order': 512, 'aut_label': '384.GF', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.BF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.MP', '192.MW', '192.NJ', '192.NS', '192.NX', '192.OK', '192.OM', '192.OQ', '192.PE', '192.PO', '192.PQ', '192.PT', '192.PW', '192.PX', '192.PY', '192.PZ', '192.QA', '192.QB', '192.QC'], 'contains': ['768.A', '768.P', '768.Q'], 'core': '768.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [79804429416356250372480, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.384.GF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '384.fu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.GF', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761594
    {'ambient': '3072.bgb', 'aut_centralizer_order': 256, 'aut_label': '384.GG', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.CN', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.B', '192.MP', '192.MX', '192.NK', '192.NL', '192.NY', '192.OL', '192.OR', '192.PA', '192.PF', '192.PM', '192.PP', '192.PR', '192.PU', '192.QC', '192.QD', '192.QE', '192.QF', '192.QG', '192.QH', '192.QI', '192.QJ', '192.QK'], 'contains': ['768.A', '768.R'], 'core': '768.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.384.GG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '384.fv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.GG', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761595
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '384.GH', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.LI', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.ML', '192.NA', '192.NF', '192.NM', '192.NN', '192.OF', '192.OG', '192.OR', '192.OS', '192.PB', '192.PE', '192.PG', '192.PN', '192.PV', '192.PW', '192.QD', '192.QL', '192.QM', '192.QN', '192.QO', '192.QP'], 'contains': ['768.A', '768.T'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79855398717732338388456, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.384.GH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '384.fw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.GH', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761596
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '384.GI', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.JP', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.MK', '192.MU', '192.NB', '192.NG', '192.NO', '192.NP', '192.NZ', '192.OH', '192.OI', '192.OJ', '192.ON', '192.OQ', '192.OT', '192.PF', '192.PG', '192.PS', '192.PW', '192.QE', '192.QL', '192.QQ', '192.QR'], 'contains': ['768.A', '768.U'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [187922594664024732247801, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.384.GI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '384.fx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.GI', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761597
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '384.GJ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.JH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.MH', '192.MY', '192.NB', '192.NK', '192.NM', '192.NO', '192.NV', '192.OA', '192.OD', '192.OF', '192.OH', '192.OU', '192.OV', '192.PH', '192.PI', '192.PX', '192.PY', '192.QF', '192.QM', '192.QQ'], 'contains': ['768.A', '768.V'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 108169377837562135992360, 1313941673647], 'label': '3072.bgb.384.GJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '384.fy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.GJ', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 184761598
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '24.CO', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 48, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.M', '12.BC', '12.BF'], 'contains': ['48.EZ', '48.IM', '48.IN', '48.LX', '48.PR'], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118421696801471190456, 25903229681844523013167, 187973685961890096441600, 79804308125641822294440, 122002101738321960, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.24.CO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '24.co1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CO', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184761599
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '384.GK', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.MB', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.MR', '192.MZ', '192.NA', '192.NH', '192.NI', '192.NJ', '192.NL', '192.NN', '192.NP', '192.OB', '192.OC', '192.OE', '192.OG', '192.OI', '192.OJ', '192.OU', '192.OW', '192.OX', '192.PH', '192.PJ', '192.PK', '192.PX', '192.PZ', '192.QF', '192.QG', '192.QM', '192.QN', '192.QQ', '192.QR'], 'contains': ['768.A', '768.Y'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 79804429421968711780537], 'label': '3072.bgb.384.GK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '384.fz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.GK', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761600
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '384.GL', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.E', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.G', '192.E', '192.QS', '192.QT'], 'contains': ['768.Z', '768.BA', '768.BE', '768.BK'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [25903107682370587468807, 51212588579793007921, 51212962568394582352], 'label': '3072.bgb.384.GL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.L', 'old_label': '384.ga1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.GL', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761601
    {'ambient': '3072.bgb', 'aut_centralizer_order': 96, 'aut_label': '384.GM', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '64.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.H', '192.I', '192.QS'], 'contains': ['768.Z', '768.BC', '768.BG'], 'core': '3072.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [25903107682370587468807, 51212587278385209726, 53952035291802302422343], 'label': '3072.bgb.384.GM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.C', 'old_label': '384.gb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.GM', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761606
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '384.GR', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.BB', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.BB', '192.QU', '192.QV'], 'contains': ['768.BA', '768.BD', '768.BF', '768.BT'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [378358770650295628183080, 51469040697520739881, 25903107681056726364840], 'label': '3072.bgb.384.GR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.BZ', 'old_label': '384.gf2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.GR', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761607
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.GS', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.CM', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.K', '192.BG', '192.QS', '192.QU'], 'contains': ['768.BA', '768.BG', '768.BI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [122002101738321960, 404210665744086423369726, 378307935804560365900801], 'label': '3072.bgb.384.GS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.O', 'old_label': '384.gg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.GS', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761608
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.GT', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.CM', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.BG', '192.QT', '192.QV'], 'contains': ['768.BA', '768.BH', '768.BI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [122002101738321960, 378307935804560365900801, 378307680062503632549246], 'label': '3072.bgb.384.GT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.O', 'old_label': '384.gh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.GT', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761609
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.CP', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.G', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.N'], 'contains': ['48.EE', '48.EG', '48.EK', '48.EP', '48.FA', '48.FE', '48.GC', '48.KK', '48.KY', '48.LY', '48.ME'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 25852138389591620222016, 108169377837562135992360, 122002101738321960, 1313941673647, 134021272934136496216343, 51090960298439969137], 'label': '3072.bgb.24.CP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '24.cp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CP', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184761610
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.GU', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.MI', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.BK', '192.BL', '192.QU'], 'contains': ['768.BB', '768.BD', '768.BG'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [122000787877207687, 79855520714221614566521, 53952035291802302422343], 'label': '3072.bgb.384.GU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.FC', 'old_label': '384.gi1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.GU', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761611
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.GV', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.MI', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.BK', '192.BN', '192.QV'], 'contains': ['768.BB', '768.BD', '768.BH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [53952291031063230449401, 122000787877207687, 53952035291802302422343], 'label': '3072.bgb.384.GV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.FC', 'old_label': '384.gj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.GV', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761612
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '384.GW', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.BL', '192.BM', '192.BN'], 'contains': ['768.BB', '768.BD', '768.BH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [122000787877207687, 53952291032377091563446, 53952035291802302422343], 'label': '3072.bgb.384.GW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.LB', 'old_label': '384.gj2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.GW', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761613
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '384.GX', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '384.E', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.BP', '192.QU', '192.QV'], 'contains': ['768.BB', '768.BF', '768.BI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [378358770650295628183080, 122002101738321960, 324406870523993839248121], 'label': '3072.bgb.384.GX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.BZ', 'old_label': '384.gk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.GX', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761614
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '384.GY', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '384.E', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.L', '192.CC', '192.QS', '192.QT'], 'contains': ['768.BC', '768.BE', '768.BI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [25903107682370587468807, 79804173335443638313656, 53952035291802302422343], 'label': '3072.bgb.384.GY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.L', 'old_label': '384.gl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.GY', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761615
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '384.GZ', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '384.E', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.CD', '192.QU', '192.QV'], 'contains': ['768.BD', '768.BE', '768.BI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [54003126248003449434936, 25903107681056726364840, 79855264262271969233416], 'label': '3072.bgb.384.GZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.BZ', 'old_label': '384.gl2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.GZ', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761616
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.HA', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.BJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.M', '192.CM', '192.QS', '192.QU'], 'contains': ['768.BE', '768.BF', '768.BG'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [378358770650295628183080, 324355523484084195000247, 25903107681056726364840], 'label': '3072.bgb.384.HA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.W', 'old_label': '384.gm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.HA', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761617
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.HB', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.BJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.CM', '192.QT', '192.QV'], 'contains': ['768.BE', '768.BF', '768.BH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [378358770650295628183080, 350258752455855349443127, 25903107681056726364840], 'label': '3072.bgb.384.HB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.W', 'old_label': '384.gn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.HB', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761618
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '384.HC', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '192.DY', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.DY', '192.QW', '192.QX'], 'contains': ['768.BJ', '768.BK', '768.BL', '768.BU', '768.BW'], 'core': '3072.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [25903229337376182892926, 51212588579793007921, 25852017102974698844878], 'label': '3072.bgb.384.HC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.HB', 'old_label': '384.go1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.HC', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761619
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '384.HD', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '192.EJ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.EJ', '192.QW', '192.QX'], 'contains': ['768.BJ', '768.BX', '768.BY'], 'core': '3072.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [162121669227129588479873, 51212588579793007921, 25852017102974698844878], 'label': '3072.bgb.384.HD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.HB', 'old_label': '384.gp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.HD', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761620
    {'ambient': '3072.bgb', 'aut_centralizer_order': 1, 'aut_label': '2.A', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '3072.a1', 'complements': ['1536.I', '1536.K'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.A', '4.B', '4.D', '4.I', '6.F', '8.C', '8.D'], 'core': '2.A', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 486427128433516595381056, 187922473375925652905521, 404159831259638948150382, 133970303627361494479417, 566444897749485959875336, 108118165248982343710201, 162070456272950954131199, 53952412691500576681559], 'label': '3072.bgb.2.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.A', '4.B', '4.D'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '3072.bgb', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.A', 'subgroup_fusion': None, 'weyl_group': '3072.bgb'}
  • id: 184761621
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '6.A', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1536.408610986', 'aut_weyl_index': 4, 'centralizer': '768.A', 'complements': ['512.C', '512.E', '512.F'], 'conjugacy_class_count': 1, 'contained_in': ['2.B', '3.a1'], 'contains': ['12.A', '12.B', '12.C', '12.I', '12.M', '12.BC', '12.BF'], 'core': '6.A', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [108118421696801471190456, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 133970303627361494479417, 122002101738321960, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.6.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': ['2.B'], 'normal_contains': ['12.A', '12.B', '12.C', '24.A'], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': '3072.bgb', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.A', 'subgroup_fusion': None, 'weyl_group': '768.1087581'}
  • id: 184761622
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.CQ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.A', '12.BA', '12.BB'], 'contains': ['48.EF', '48.EI', '48.EM', '48.EN', '48.EO', '48.ET', '48.FA', '48.FB', '48.GH', '48.KT', '48.KU', '48.LE', '48.LI', '48.LJ', '48.LK', '48.LZ', '48.MA', '48.MC', '48.NG'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 25903229691554491852799, 25903229681844523013167, 187922473375925652905521, 133970303627361494479417, 122002101738321960, 1313941673647], 'label': '3072.bgb.24.CQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.cq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CQ', 'subgroup_fusion': None, 'weyl_group': '128.1578'}
  • id: 184761623
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.HE', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '96.NB', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['128.N', '192.EO', '192.QW'], 'contains': ['768.BJ', '768.BO', '768.BZ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [187922473375925652905521, 187973685963191504240047, 162070456272950954131199], 'label': '3072.bgb.384.HE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.P', 'old_label': '384.gq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.HE', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 184761624
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.HF', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '96.NB', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.EO', '192.QX'], 'contains': ['768.BJ', '768.BO', '768.BP', '768.BZ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [187922473375925652905521, 187973685961890096441600, 162070456272950954131199], 'label': '3072.bgb.384.HF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.JS', 'old_label': '384.gq2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.HF', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761625
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '384.HG', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '192.FP', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.FP', '192.QY', '192.QZ'], 'contains': ['768.BL', '768.BM', '768.BS', '768.BU', '768.BW'], 'core': '3072.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [25903229691554491852799, 25852138389591620222016, 51212962568394582352], 'label': '3072.bgb.384.HG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.IR', 'old_label': '384.gr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.HG', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761630
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '384.HL', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '192.EM', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.GS', '192.QX', '192.QY'], 'contains': ['768.BO', '768.BW', '768.BX'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [25903229337376182892926, 187973685961890096441600, 25852017102974698844878], 'label': '3072.bgb.384.HL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.DI', 'old_label': '384.gu2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.HL', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761631
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '384.HM', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '384.EC', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.GX'], 'contains': ['768.BQ', '768.CA', '768.CB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [378358770650295628183080, 187922473371828146222776, 404159575153471583875073], 'label': '3072.bgb.384.HM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.IN', 'old_label': '384.gv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.HM', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761632
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.HN', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '96.QG', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.HF', '192.HG'], 'contains': ['768.BM', '768.BN', '768.BP', '768.BQ', '768.BR', '768.BV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [53952413035981411118158, 25903229691554491852799, 187922473375925652905521], 'label': '3072.bgb.384.HN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.QG', 'old_label': '384.gw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.HN', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 184761633
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '24.CR', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.A', '12.Z', '12.BC', '12.BD', '12.BE', '12.BF', '12.BG'], 'contains': ['48.EJ', '48.EQ', '48.ET', '48.EZ', '48.FB', '48.GG', '48.KX', '48.LP', '48.LU', '48.LW', '48.MB', '48.MD', '48.NV'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229691554491852799, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.24.CR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CR', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761634
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.HO', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '96.QG', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.HF', '192.HG', '192.QY'], 'contains': ['768.BM', '768.BN', '768.BO', '768.BQ', '768.BV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [53952413035981411118158, 187922473375925652905521, 25903229690240550179152], 'label': '3072.bgb.384.HO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.LY', 'old_label': '384.gw2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.HO', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761635
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '384.HP', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '96.QG', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.HF', '192.HG', '192.QZ'], 'contains': ['768.BM', '768.BN', '768.BO', '768.BR', '768.BV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [53952413035981411118158, 9709968839632, 187922473375925652905521], 'label': '3072.bgb.384.HP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.LY', 'old_label': '384.gw3', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.HP', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761636
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '384.HQ', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '384.BM', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.ID', '192.QY', '192.QZ'], 'contains': ['768.BU', '768.BV', '768.BX'], 'core': '3072.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [79855398716250260275073, 404159952890736743541118, 187922473375925652905521], 'label': '3072.bgb.384.HQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.IR', 'old_label': '384.gx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.HQ', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761637
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '384.HR', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '384.X', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['128.O', '192.II', '192.QW', '192.QX'], 'contains': ['768.BU', '768.BX', '768.BZ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [404159952890736743541118, 187922473375925652905521, 162070456272950954131199], 'label': '3072.bgb.384.HR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.HB', 'old_label': '384.gy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.HR', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761638
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '384.HS', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '384.BM', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.JE', '192.QY', '192.QZ'], 'contains': ['768.BV', '768.BW', '768.BY'], 'core': '3072.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [162121669227129588479873, 162070456274433112077942, 25852017102974698844878], 'label': '3072.bgb.384.HS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.IR', 'old_label': '384.gz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.HS', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761639
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '384.HT', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '384.X', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['128.P', '192.KF', '192.QW', '192.QX'], 'contains': ['768.BW', '768.BY', '768.BZ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [187922473375925652905521, 162121669227129588479873, 162070456272950954131199], 'label': '3072.bgb.384.HT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.HB', 'old_label': '384.ha1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.HT', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 184761640
    {'ambient': '3072.bgb', 'aut_centralizer_order': 48, 'aut_label': '512.A', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '128.H', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.A', '256.B', '256.C', '256.D', '256.E', '256.F', '256.G', '256.H'], 'contains': ['1024.a1', '1536.B'], 'core': '3072.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [566444897749485959875336, 404159831259638948150382], 'label': '3072.bgb.512.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.M', 'old_label': '512.a1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '512.A', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761641
    {'ambient': '3072.bgb', 'aut_centralizer_order': 24, 'aut_label': '512.B', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '256.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.B', '128.N', '256.B', '256.I'], 'contains': ['1024.a1', '1536.C'], 'core': '3072.a1', 'coset_action_label': None, 'count': 128, 'diagramx': None, 'generators': [216288570482003057040143, 486427128433516595381056], 'label': '3072.bgb.512.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '128.G', 'old_label': '512.b1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '512.B', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761642
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '512.C', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '384.GM', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['128.C', '128.O', '256.C', '256.I', '256.J'], 'contains': ['1024.a1', '1536.E'], 'core': '3072.a1', 'coset_action_label': None, 'count': 128, 'diagramx': None, 'generators': [378359026753640149313262, 378307935804560365900801], 'label': '3072.bgb.512.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.M', 'old_label': '512.c1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '512.C', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 184761643
    {'ambient': '3072.bgb', 'aut_centralizer_order': 24, 'aut_label': '512.D', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '256.D', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.D', '256.D', '256.J'], 'contains': ['1024.a1', '1536.I'], 'core': '3072.a1', 'coset_action_label': None, 'count': 128, 'diagramx': None, 'generators': [270240740222366015020798, 79855264262271969233416], 'label': '3072.bgb.512.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '128.J', 'old_label': '512.d1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '512.D', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761644
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.CS', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.R', '12.T', '12.BH'], 'contains': ['48.BW', '48.BX', '48.FD', '48.FI', '48.FM', '48.FX', '48.FZ', '48.HM', '48.HV'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 122002101738321960, 324406991811924875755576, 79804308125641822294440, 378358770650295628183080, 25852272837936812846761], 'label': '3072.bgb.24.CS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.cs1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CS', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184761645
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '512.E', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '768.Z', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.E', '128.P', '256.E', '256.I'], 'contains': ['1024.a1', '1536.J'], 'core': '3072.a1', 'coset_action_label': None, 'count': 128, 'diagramx': None, 'generators': [378307936172768329324920, 51212962568394582352], 'label': '3072.bgb.512.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '128.G', 'old_label': '512.e1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '512.E', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 184761646
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '512.F', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '768.BC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.F', '256.F', '256.J'], 'contains': ['1024.a1', '1536.K'], 'core': '3072.a1', 'coset_action_label': None, 'count': 128, 'diagramx': None, 'generators': [378358770650295628183080, 378359026753640149313262], 'label': '3072.bgb.512.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '128.J', 'old_label': '512.f1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '512.F', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 184761647
    {'ambient': '3072.bgb', 'aut_centralizer_order': 1024, 'aut_label': '768.A', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '6.A', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['256.A', '384.A', '384.FW', '384.FX', '384.FY', '384.FZ', '384.GA', '384.GB', '384.GC', '384.GD', '384.GE', '384.GF', '384.GG', '384.GH', '384.GI', '384.GJ', '384.GK'], 'contains': ['1536.A'], 'core': '768.A', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647], 'label': '3072.bgb.768.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '768.A', 'normal_contained_in': ['192.B', '384.A'], 'normal_contains': ['3072.a1'], 'normalizer': '1.a1', 'old_label': '768.a1', 'projective_image': '3072.bgb', 'quotient_action_image': '6.1', 'quotient_action_kernel': '128.1578', 'quotient_action_kernel_order': 128, 'quotient_fusion': None, 'short_label': '768.A', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 184761648
    {'ambient': '3072.bgb', 'aut_centralizer_order': 512, 'aut_label': '768.B', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.A', '384.B', '384.C', '384.D', '384.E', '384.F', '384.G', '384.H', '384.I', '384.J', '384.K', '384.L', '384.M', '384.N', '384.O', '384.P', '384.Q', '384.R', '384.S', '384.T', '384.U', '384.V', '384.W'], 'contains': ['1536.A', '1536.B'], 'core': '3072.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 122002101738321960], 'label': '3072.bgb.768.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '384.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '768.b1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.B', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761649
    {'ambient': '3072.bgb', 'aut_centralizer_order': 256, 'aut_label': '768.C', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.T', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.B', '384.X', '384.Y', '384.Z', '384.BA', '384.BB', '384.BC', '384.BD', '384.BE', '384.BF', '384.BG', '384.BH', '384.BI', '384.BJ', '384.FW'], 'contains': ['1536.A', '1536.C'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 51212588579793007921], 'label': '3072.bgb.768.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '768.c1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.C', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761650
    {'ambient': '3072.bgb', 'aut_centralizer_order': 256, 'aut_label': '768.D', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.CG', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.C', '384.X', '384.Z', '384.BK', '384.BL', '384.BM', '384.BO', '384.BR', '384.BS', '384.BT', '384.BU', '384.BV', '384.BY', '384.BZ', '384.CD', '384.CE', '384.CG', '384.CH', '384.FX'], 'contains': ['1536.A', '1536.D'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [187973685961890096441600, 25903229683158464676480], 'label': '3072.bgb.768.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '768.d1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.D', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761651
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '768.E', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.GB', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.Y', '384.BN', '384.BP', '384.BQ', '384.BW', '384.BX', '384.CA', '384.CB', '384.CC', '384.CD', '384.CE', '384.CF', '384.FX'], 'contains': ['1536.A', '1536.D'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 187973685961890096441600], 'label': '3072.bgb.768.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GB', 'old_label': '768.d2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.E', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 184761652
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '768.F', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.E', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.D', '384.E', '384.BA', '384.BB', '384.BK', '384.BL', '384.CI', '384.CJ', '384.CK', '384.CL', '384.CM', '384.CN', '384.CO', '384.CP', '384.CQ', '384.CR', '384.CS', '384.CT', '384.CU', '384.CV', '384.FY'], 'contains': ['1536.A', '1536.E'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [404210922197505558871681, 25903229683158464676480], 'label': '3072.bgb.768.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '768.e1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.F', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761653
    {'ambient': '3072.bgb', 'aut_centralizer_order': 256, 'aut_label': '768.G', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.CP', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.F', '384.BC', '384.BD', '384.BE', '384.BM', '384.BP', '384.BS', '384.CI', '384.CJ', '384.CW', '384.CX', '384.DB', '384.DC', '384.DE', '384.FZ'], 'contains': ['1536.A', '1536.F'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855520714221614566521, 25903229683158464676480], 'label': '3072.bgb.768.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '768.f1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.G', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761654
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '768.H', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '48.FA', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.G', '384.BN', '384.BO', '384.BQ', '384.BR', '384.CY', '384.CZ', '384.DA', '384.DD', '384.DF', '384.DG', '384.DH', '384.FZ'], 'contains': ['1536.A', '1536.F'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79855520714221614566521, 25903229681844523013167], 'label': '3072.bgb.768.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CQ', 'old_label': '768.f2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.H', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761655
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.CT', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.R', '12.U', '12.BH'], 'contains': ['48.CF', '48.CQ', '48.FD', '48.FJ', '48.FL', '48.FX', '48.GA', '48.HK', '48.ID'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 324406870523993839248121, 53952035291802302422343, 378358649363678452761737], 'label': '3072.bgb.24.CT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ct1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CT', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184761656
    {'ambient': '3072.bgb', 'aut_centralizer_order': 256, 'aut_label': '768.I', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.GA', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.H', '384.X', '384.BF', '384.BM', '384.CC', '384.CK', '384.CS', '384.CW', '384.DL', '384.DN', '384.DO', '384.DP', '384.DQ', '384.DR', '384.DS', '384.DT', '384.DU', '384.DV', '384.DW', '384.DY', '384.GA'], 'contains': ['1536.A', '1536.G'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [187922473375925652905521, 25903229683158464676480], 'label': '3072.bgb.768.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '768.g1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.I', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761657
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '768.J', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '48.JW', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.Y', '384.BN', '384.BT', '384.CD', '384.CX', '384.CY', '384.DI', '384.DJ', '384.DK', '384.DM', '384.DX', '384.DY', '384.GA'], 'contains': ['1536.A', '1536.G'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521], 'label': '3072.bgb.768.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GB', 'old_label': '768.g2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.J', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761658
    {'ambient': '3072.bgb', 'aut_centralizer_order': 256, 'aut_label': '768.K', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.GO', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.I', '384.BO', '384.CF', '384.CZ', '384.DM', '384.DZ', '384.EA', '384.EB', '384.EC', '384.ED', '384.EE', '384.EF', '384.EG', '384.GB'], 'contains': ['1536.A', '1536.H'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855520719821622658496, 1313941673647], 'label': '3072.bgb.768.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BA', 'old_label': '768.h1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.K', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761659
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '768.L', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '48.MC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.BG', '384.BP', '384.BQ', '384.BU', '384.CE', '384.DA', '384.DI', '384.DJ', '384.DK', '384.DL', '384.DM', '384.EH', '384.GB'], 'contains': ['1536.A', '1536.H'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79855520719821622658496, 25903229681844523013167], 'label': '3072.bgb.768.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GB', 'old_label': '768.h2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.L', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761660
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '768.M', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '96.KV', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.J', '384.K', '384.CL', '384.CM', '384.EI', '384.EJ', '384.EK', '384.EL', '384.EM', '384.EN', '384.GC'], 'contains': ['1536.A', '1536.I'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229681844523013167, 53952035291802302422343], 'label': '3072.bgb.768.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.FI', 'old_label': '768.i1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.M', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761661
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '768.N', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '48.H', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.L', '384.M', '384.BA', '384.BH', '384.BK', '384.BV', '384.CI', '384.CN', '384.DB', '384.DN', '384.DO', '384.EO', '384.EP', '384.EQ', '384.ER', '384.ES', '384.ET', '384.EU', '384.GD'], 'contains': ['1536.A', '1536.J'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [1313941673647, 51212962568394582352], 'label': '3072.bgb.768.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '768.j1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.N', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761662
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '768.O', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '48.CK', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.N', '384.O', '384.CL', '384.DZ', '384.EA', '384.EI', '384.EV', '384.EW', '384.EX', '384.EY', '384.EZ', '384.FA', '384.GE'], 'contains': ['1536.A', '1536.K'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 25903229683158464676480], 'label': '3072.bgb.768.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '768.k1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.O', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761663
    {'ambient': '3072.bgb', 'aut_centralizer_order': 1024, 'aut_label': '768.P', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '6.I', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.P', '384.BC', '384.BW', '384.CG', '384.CO', '384.DF', '384.DI', '384.DP', '384.EB', '384.EK', '384.ES', '384.EY', '384.FB', '384.FC', '384.FD', '384.FE', '384.FF', '384.GF'], 'contains': ['1536.A'], 'core': '3072.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [79804429416356250372480, 25903229683158464676480], 'label': '3072.bgb.768.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '768.l1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.P', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761664
    {'ambient': '3072.bgb', 'aut_centralizer_order': 1024, 'aut_label': '768.Q', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '6.K', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.Q', '384.BD', '384.BX', '384.CH', '384.CT', '384.DG', '384.DJ', '384.DQ', '384.EC', '384.EL', '384.EO', '384.EV', '384.FG', '384.FH', '384.GF'], 'contains': ['1536.A'], 'core': '3072.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [54003382330230002441647, 25903229683158464676480], 'label': '3072.bgb.768.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '768.m1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.Q', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761665
    {'ambient': '3072.bgb', 'aut_centralizer_order': 512, 'aut_label': '768.R', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.W', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.P', '384.Q', '384.BE', '384.BY', '384.CP', '384.CU', '384.DH', '384.DW', '384.EG', '384.EM', '384.EN', '384.EP', '384.ET', '384.EW', '384.EZ', '384.FI', '384.FJ', '384.FK', '384.FL', '384.FM', '384.FN', '384.FO', '384.FP', '384.FQ', '384.GG'], 'contains': ['1536.A'], 'core': '3072.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79804308125641822294440, 25903229683158464676480], 'label': '3072.bgb.768.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '768.n1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.R', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761685
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '768.BJ', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '48.JS', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.X', '384.Y', '384.HC', '384.HD', '384.HE', '384.HF'], 'contains': ['1536.C', '1536.D', '1536.G'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [187922473375925652905521, 187973685961890096441600], 'label': '3072.bgb.768.BJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.JS', 'old_label': '768.be1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.BJ', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 184761666
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.CU', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.S', '12.T', '12.BH'], 'contains': ['48.BY', '48.BZ', '48.FD', '48.FK', '48.FQ', '48.FZ', '48.GB', '48.HY', '48.IJ'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 122002101738321960, 162070321828715682652927, 324406991811924875755576, 79804308125641822294440, 378358770650295628183080], 'label': '3072.bgb.24.CU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.cu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CU', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184761667
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '768.S', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.D', '384.T', '384.BH', '384.BI', '384.BV', '384.BZ', '384.CK', '384.CO', '384.CP', '384.CQ', '384.DB', '384.DC', '384.DR', '384.EI', '384.EJ', '384.EQ', '384.FG', '384.FI', '384.FR', '384.FS', '384.FY'], 'contains': ['1536.A'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229683158464676480, 404210922196204071249966], 'label': '3072.bgb.768.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '768.o1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.S', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761668
    {'ambient': '3072.bgb', 'aut_centralizer_order': 256, 'aut_label': '768.T', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.GI', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.I', '384.BR', '384.CA', '384.DD', '384.DX', '384.EB', '384.EC', '384.EH', '384.EX', '384.FA', '384.FJ', '384.FT', '384.FU', '384.GH'], 'contains': ['1536.A'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855398717732338388456, 1313941673647], 'label': '3072.bgb.768.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BA', 'old_label': '768.p1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.T', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761669
    {'ambient': '3072.bgb', 'aut_centralizer_order': 256, 'aut_label': '768.U', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.FS', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.H', '384.Z', '384.BJ', '384.BS', '384.CB', '384.CQ', '384.CV', '384.DE', '384.DK', '384.DP', '384.DQ', '384.ER', '384.EU', '384.FK', '384.FS', '384.FV', '384.GI'], 'contains': ['1536.A'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [187922594664024732247801, 25903229683158464676480], 'label': '3072.bgb.768.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '768.q1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.U', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761670
    {'ambient': '3072.bgb', 'aut_centralizer_order': 256, 'aut_label': '768.V', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.FL', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.C', '384.BF', '384.BJ', '384.BY', '384.CN', '384.CR', '384.CW', '384.CZ', '384.DD', '384.DE', '384.EQ', '384.FB', '384.FH', '384.FR', '384.GJ'], 'contains': ['1536.A'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108169377837562135992360, 25903229683158464676480], 'label': '3072.bgb.768.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '768.r1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.V', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761671
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '768.W', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '48.DA', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.N', '384.U', '384.CM', '384.DZ', '384.ED', '384.EJ', '384.EV', '384.EW', '384.EX', '384.FC', '384.FL', '384.FT', '384.GE'], 'contains': ['1536.A'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770648994141276807, 25903229683158464676480], 'label': '3072.bgb.768.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '768.s1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.W', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761672
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '768.X', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '48.E', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.L', '384.V', '384.BB', '384.BI', '384.BL', '384.BZ', '384.CJ', '384.CR', '384.DC', '384.DN', '384.DS', '384.EO', '384.EP', '384.ER', '384.FD', '384.FM', '384.FR', '384.FV', '384.GD'], 'contains': ['1536.A'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [1313941673647, 25852016759807766522832], 'label': '3072.bgb.768.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '768.t1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.X', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761673
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '768.Y', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '48.MB', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.BG', '384.BT', '384.BU', '384.BW', '384.BX', '384.CA', '384.CB', '384.CX', '384.CY', '384.DA', '384.DT', '384.EE', '384.GK'], 'contains': ['1536.A'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229683158464676480, 79804429421968711780537], 'label': '3072.bgb.768.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GB', 'old_label': '768.u1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.Y', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761674
    {'ambient': '3072.bgb', 'aut_centralizer_order': 192, 'aut_label': '768.Z', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '32.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['256.B', '384.B', '384.GL', '384.GM', '384.GN', '384.GO'], 'contains': ['1536.B', '1536.C'], 'core': '3072.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [51212588579793007921, 122002101738321960], 'label': '3072.bgb.768.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.C', 'old_label': '768.v1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.Z', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761675
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '768.BA', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '48.O', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['256.C', '384.E', '384.GL', '384.GP', '384.GQ', '384.GR', '384.GS', '384.GT'], 'contains': ['1536.B', '1536.E'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [122002101738321960, 378307935804560365900801], 'label': '3072.bgb.768.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.O', 'old_label': '768.w1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.BA', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 184761676
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '768.BB', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '96.KU', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.F', '384.G', '384.GP', '384.GU', '384.GV', '384.GW', '384.GX'], 'contains': ['1536.B', '1536.F'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79855520714221614566521, 122002101738321960], 'label': '3072.bgb.768.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.FC', 'old_label': '768.x1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.BB', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761677
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.CV', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.S', '12.U', '12.BH'], 'contains': ['48.FD', '48.FO', '48.FP', '48.GA', '48.GB', '48.IG', '48.IK'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108169512287410083283217, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 324406870523993839248121, 378358649363678452761737], 'label': '3072.bgb.24.CV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.cv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CV', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184761678
    {'ambient': '3072.bgb', 'aut_centralizer_order': 192, 'aut_label': '768.BC', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '32.D', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['256.D', '384.J', '384.GM', '384.GN', '384.GQ', '384.GY'], 'contains': ['1536.B', '1536.I'], 'core': '3072.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [25903107682370587468807, 53952035291802302422343], 'label': '3072.bgb.768.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.C', 'old_label': '768.y1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.BC', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761679
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '768.BD', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '96.KV', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.J', '384.K', '384.GR', '384.GU', '384.GV', '384.GW', '384.GZ'], 'contains': ['1536.B', '1536.I'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [122002101738321960, 53952035291802302422343], 'label': '3072.bgb.768.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.FC', 'old_label': '768.y2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.BD', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761680
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '768.BE', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '96.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['256.E', '384.M', '384.GL', '384.GP', '384.GY', '384.GZ', '384.HA', '384.HB'], 'contains': ['1536.B', '1536.J'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903107682370587468807, 51212962568394582352], 'label': '3072.bgb.768.BE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.W', 'old_label': '768.z1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.BE', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761681
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '768.BF', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '96.CZ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['256.F', '384.O', '384.GO', '384.GQ', '384.GR', '384.GX', '384.HA', '384.HB'], 'contains': ['1536.B', '1536.K'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [378358770650295628183080, 122002101738321960], 'label': '3072.bgb.768.BF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.W', 'old_label': '768.ba1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.BF', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761682
    {'ambient': '3072.bgb', 'aut_centralizer_order': 768, 'aut_label': '768.BG', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '8.I', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['256.G', '384.R', '384.GM', '384.GS', '384.GU', '384.HA'], 'contains': ['1536.B'], 'core': '3072.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [25903364134488315926527, 122002101738321960], 'label': '3072.bgb.768.BG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.H', 'old_label': '768.bb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.BG', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761683
    {'ambient': '3072.bgb', 'aut_centralizer_order': 256, 'aut_label': '768.BH', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.DG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.R', '384.S', '384.GN', '384.GT', '384.GV', '384.GW', '384.HB'], 'contains': ['1536.B'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [122002101738321960, 25903364135789722998960], 'label': '3072.bgb.768.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.R', 'old_label': '768.bc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.BH', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761684
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '768.BI', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '96.CM', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['256.H', '384.W', '384.GO', '384.GS', '384.GT', '384.GX', '384.GY', '384.GZ'], 'contains': ['1536.B'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [51347406816160329727, 122002101738321960], 'label': '3072.bgb.768.BI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.O', 'old_label': '768.bd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.BI', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761686
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '768.BK', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '96.E', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['256.I', '384.BA', '384.GL', '384.HC'], 'contains': ['1536.C', '1536.E', '1536.J'], 'core': '3072.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [51212588579793007921, 51212962568394582352], 'label': '3072.bgb.768.BK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.E', 'old_label': '768.bf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.BK', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 184761687
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '768.BL', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '96.GO', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.BK', '384.HC', '384.HG'], 'contains': ['1536.D', '1536.E', '1536.J'], 'core': '3072.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [25903229691554491852799, 51212962568394582352], 'label': '3072.bgb.768.BL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.GO', 'old_label': '768.bg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.BL', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 184761688
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.CW', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.P', '12.T', '12.BI'], 'contains': ['48.CB', '48.CC', '48.CK', '48.DA', '48.FH', '48.FI', '48.FK', '48.GV', '48.GX', '48.HI', '48.HX', '48.MH', '48.MK'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [242089752358354392177983, 25903229681844523013167, 122002101738321960, 1313941673647, 134021272934136496216343, 53952035291802302422343, 187922594661241166512703], 'label': '3072.bgb.24.CW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.cw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CW', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184761689
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '768.BM', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '48.LY', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.BM', '384.BN', '384.HG', '384.HH', '384.HN', '384.HO', '384.HP'], 'contains': ['1536.D', '1536.F', '1536.G'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [108118165248982343710201, 187973685961890096441600], 'label': '3072.bgb.768.BM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.LY', 'old_label': '768.bh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.BM', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 184761690
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '768.BN', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '96.QG', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.BO', '384.BP', '384.BQ', '384.HN', '384.HO', '384.HP'], 'contains': ['1536.D', '1536.F', '1536.H'], 'core': '3072.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [79855520714221614566521, 79855520719821622658496], 'label': '3072.bgb.768.BN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.QG', 'old_label': '768.bi1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.BN', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 184761691
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '768.BO', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '48.JW', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.CC', '384.CD', '384.HE', '384.HF', '384.HI', '384.HJ', '384.HK', '384.HL', '384.HO', '384.HP'], 'contains': ['1536.D', '1536.G'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [9709968839632, 187922473375925652905521], 'label': '3072.bgb.768.BO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '768.bj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.BO', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761692
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '768.BP', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '48.JW', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.CC', '384.CD', '384.HF', '384.HN'], 'contains': ['1536.D', '1536.G'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229691554491852799, 187922473375925652905521], 'label': '3072.bgb.768.BP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.JW', 'old_label': '768.bj2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.BP', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 184761693
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '768.BQ', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '48.MC', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.CE', '384.CF', '384.HM', '384.HN', '384.HO'], 'contains': ['1536.D', '1536.H'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79855520719821622658496, 162070456280045573438767], 'label': '3072.bgb.768.BQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GO', 'old_label': '768.bk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.BQ', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761694
    {'ambient': '3072.bgb', 'aut_centralizer_order': 64, 'aut_label': '768.BR', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '48.MC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.CE', '384.CF', '384.HN', '384.HP'], 'contains': ['1536.D', '1536.H'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79855520719821622658496, 187973685961890096441600], 'label': '3072.bgb.768.BR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.MC', 'old_label': '768.bk2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.BR', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 184761695
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '768.BS', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '96.BG', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.CI', '384.GP', '384.HG'], 'contains': ['1536.E', '1536.F', '1536.J'], 'core': '3072.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [51091300648929957136, 51212962568394582352], 'label': '3072.bgb.768.BS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.BG', 'old_label': '768.bl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.BS', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 184761696
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '768.BT', 'aut_quo_index': None, 'aut_stab_index': 384, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '192.BB', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['256.J', '384.CL', '384.GQ', '384.GR'], 'contains': ['1536.E', '1536.I', '1536.K'], 'core': '3072.a1', 'coset_action_label': None, 'count': 384, 'diagramx': None, 'generators': [378358770650295628183080, 25852272837936812846761], 'label': '3072.bgb.768.BT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '192.BB', 'old_label': '768.bm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.BT', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 184761697
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '768.BU', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '96.GV', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.CS', '384.HC', '384.HG', '384.HI', '384.HJ', '384.HQ', '384.HR'], 'contains': ['1536.E', '1536.G'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [187922473375925652905521, 378307935804560365900801], 'label': '3072.bgb.768.BU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.DG', 'old_label': '768.bn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.BU', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761698
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '768.BV', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '96.QG', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.DL', '384.DM', '384.HN', '384.HO', '384.HP', '384.HQ', '384.HS'], 'contains': ['1536.G', '1536.H'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [53952413035981411118158, 187922473375925652905521], 'label': '3072.bgb.768.BV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.LY', 'old_label': '768.bo1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.BV', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761699
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.CX', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.Q', '12.U', '12.BI'], 'contains': ['48.FH', '48.FJ', '48.FP', '48.GV', '48.HC', '48.HL', '48.IH', '48.MI', '48.ML'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 122002101738321960, 1313941673647, 134021272934136496216343, 53952035291802302422343, 378358649363678452761737, 187922594661241166512703], 'label': '3072.bgb.24.CX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.cx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CX', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184761700
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '768.BW', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '96.GX', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.DO', '384.HC', '384.HG', '384.HK', '384.HL', '384.HS', '384.HT'], 'contains': ['1536.G', '1536.J'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [25903229337376182892926, 25852017102974698844878], 'label': '3072.bgb.768.BW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.DI', 'old_label': '768.bp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.BW', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761701
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '768.BX', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '96.HA', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.DU', '384.HD', '384.HH', '384.HK', '384.HL', '384.HQ', '384.HR'], 'contains': ['1536.G'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [404159952890736743541118, 187922473375925652905521], 'label': '3072.bgb.768.BX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.DI', 'old_label': '768.bq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.BX', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761702
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '768.BY', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '96.GZ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['384.DV', '384.HD', '384.HH', '384.HI', '384.HJ', '384.HS', '384.HT'], 'contains': ['1536.G'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [162121669227129588479873, 25852017102974698844878], 'label': '3072.bgb.768.BY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.DG', 'old_label': '768.br1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.BY', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761703
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '768.BZ', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '96.NB', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['256.K', '384.DY', '384.HE', '384.HF', '384.HR', '384.HT'], 'contains': ['1536.G'], 'core': '3072.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [187922473375925652905521, 162070456272950954131199], 'label': '3072.bgb.768.BZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.P', 'old_label': '768.bs1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.BZ', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 184761704
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '768.CA', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '192.KJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.EA', '384.HM'], 'contains': ['1536.H', '1536.K'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [378358770650295628183080, 134021394933610431760703], 'label': '3072.bgb.768.CA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.IN', 'old_label': '768.bt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.CA', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761705
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '768.CB', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '192.KS', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.EF', '384.HM'], 'contains': ['1536.H'], 'core': '3072.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [79855520719821622658496, 134021529040297499210286], 'label': '3072.bgb.768.CB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.IN', 'old_label': '768.bu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.CB', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184761706
    {'ambient': '3072.bgb', 'aut_centralizer_order': 48, 'aut_label': '1024.a1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '128.H', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['256.A', '256.K', '512.A', '512.B', '512.C', '512.D', '512.E', '512.F'], 'contains': ['3072.a1'], 'core': '3072.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [404159831259638948150382], 'label': '3072.bgb.1024.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.M', 'old_label': '1024.a1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1024.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 184762348
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '64.I', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '768.BC', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.S', '32.D'], 'contains': ['128.C', '128.D', '128.F', '192.NU', '256.J'], 'core': '768.A', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 25852272837936812846761, 404159831259638948150382, 1313941673647], 'label': '3072.bgb.64.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.D', 'old_label': '64.i1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.I', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 184761707
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2048, 'aut_label': '1536.A', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['768.A', '768.B', '768.C', '768.D', '768.E', '768.F', '768.G', '768.H', '768.I', '768.J', '768.K', '768.L', '768.M', '768.N', '768.O', '768.P', '768.Q', '768.R', '768.S', '768.T', '768.U', '768.V', '768.W', '768.X', '768.Y'], 'contains': ['3072.a1'], 'core': '3072.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229681844523013167], 'label': '3072.bgb.1536.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '768.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '1536.a1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.A', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 184761708
    {'ambient': '3072.bgb', 'aut_centralizer_order': 1536, 'aut_label': '1536.B', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '4.H', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['512.A', '768.B', '768.Z', '768.BA', '768.BB', '768.BC', '768.BD', '768.BE', '768.BF', '768.BG', '768.BH', '768.BI'], 'contains': ['3072.a1'], 'core': '3072.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [122002101738321960], 'label': '3072.bgb.1536.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '384.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.H', 'old_label': '1536.b1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.B', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 184761709
    {'ambient': '3072.bgb', 'aut_centralizer_order': 768, 'aut_label': '1536.C', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '8.C', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['512.B', '768.C', '768.Z', '768.BJ', '768.BK'], 'contains': ['3072.a1'], 'core': '3072.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [51212588579793007921], 'label': '3072.bgb.1536.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.C', 'old_label': '1536.c1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.C', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 184761710
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.CY', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.P', '12.U', '12.BJ'], 'contains': ['48.FH', '48.FL', '48.FO', '48.GY', '48.GZ', '48.IB', '48.IF'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 122002101738321960, 1313941673647, 134021272934136496216343, 296041409911409376977422, 404210922196204071249966, 187922594661241166512703], 'label': '3072.bgb.24.CY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.cy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CY', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761711
    {'ambient': '3072.bgb', 'aut_centralizer_order': 256, 'aut_label': '1536.D', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.CG', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['768.D', '768.E', '768.BJ', '768.BL', '768.BM', '768.BN', '768.BO', '768.BP', '768.BQ', '768.BR'], 'contains': ['3072.a1'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187973685961890096441600], 'label': '3072.bgb.1536.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.CG', 'old_label': '1536.d1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.D', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 184761712
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '1536.E', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '24.E', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['512.C', '768.F', '768.BA', '768.BK', '768.BL', '768.BS', '768.BT', '768.BU'], 'contains': ['3072.a1'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [378307935804560365900801], 'label': '3072.bgb.1536.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.E', 'old_label': '1536.e1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.E', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 184761713
    {'ambient': '3072.bgb', 'aut_centralizer_order': 256, 'aut_label': '1536.F', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '24.CP', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['768.G', '768.H', '768.BB', '768.BM', '768.BN', '768.BS'], 'contains': ['3072.a1'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79855520714221614566521], 'label': '3072.bgb.1536.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CP', 'old_label': '1536.f1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.F', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 184761714
    {'ambient': '3072.bgb', 'aut_centralizer_order': 256, 'aut_label': '1536.G', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '24.GA', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['768.I', '768.J', '768.BJ', '768.BM', '768.BO', '768.BP', '768.BU', '768.BV', '768.BW', '768.BX', '768.BY', '768.BZ'], 'contains': ['3072.a1'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922473375925652905521], 'label': '3072.bgb.1536.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '1536.g1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.G', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 184761715
    {'ambient': '3072.bgb', 'aut_centralizer_order': 256, 'aut_label': '1536.H', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '24.GO', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['768.K', '768.L', '768.BN', '768.BQ', '768.BR', '768.BV', '768.CA', '768.CB'], 'contains': ['3072.a1'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79855520719821622658496], 'label': '3072.bgb.1536.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GO', 'old_label': '1536.h1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.H', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 184761716
    {'ambient': '3072.bgb', 'aut_centralizer_order': 192, 'aut_label': '1536.I', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '32.D', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['512.D', '768.M', '768.BC', '768.BD', '768.BT'], 'contains': ['3072.a1'], 'core': '3072.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [53952035291802302422343], 'label': '3072.bgb.1536.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.D', 'old_label': '1536.i1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.I', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 184761717
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '1536.J', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '48.H', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['512.E', '768.N', '768.BE', '768.BK', '768.BL', '768.BS', '768.BW'], 'contains': ['3072.a1'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [51212962568394582352], 'label': '3072.bgb.1536.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.H', 'old_label': '1536.j1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.J', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 184761718
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '1536.K', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '48.CK', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['512.F', '768.O', '768.BF', '768.BT', '768.CA'], 'contains': ['3072.a1'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [378358770650295628183080], 'label': '3072.bgb.1536.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.CK', 'old_label': '1536.k1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.K', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 184761719
    {'ambient': '3072.bgb', 'aut_centralizer_order': None, 'aut_label': '3072.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1024.a1', '1536.A', '1536.B', '1536.C', '1536.D', '1536.E', '1536.F', '1536.G', '1536.H', '1536.I', '1536.J', '1536.K'], 'contains': [], 'core': '3072.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [], 'label': '3072.bgb.3072.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '3072.a1', 'normal_contained_in': ['768.A'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '3072.a1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3072.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 184761720
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.CZ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.Q', '12.T', '12.BJ'], 'contains': ['48.CD', '48.CE', '48.FH', '48.FM', '48.FQ', '48.GY', '48.HB', '48.IC', '48.II'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 122002101738321960, 324406991811924875755576, 1313941673647, 134021272934136496216343, 404210922196204071249966, 187922594661241166512703], 'label': '3072.bgb.24.CZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.cz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CZ', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761721
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '6.B', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.D', '12.E', '12.H', '12.I', '12.J', '12.P', '12.Q', '12.R', '12.S', '12.T', '12.U', '12.V', '12.W', '12.BH', '12.BI', '12.BJ', '12.BN', '12.BO', '12.BR'], 'core': '24.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 122002101738321960, 79804429413572684637382, 53952035291802302422343, 187922473375925652905521, 296041409911409376977422, 108118165248982343710201, 378358649363678452761737], 'label': '3072.bgb.6.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.b1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.B', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184761722
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.DA', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.P', '12.V', '12.BH'], 'contains': ['48.FI', '48.FN', '48.FO', '48.HJ', '48.HK', '48.HW', '48.HY'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 25852272837936812846761, 79804308125641822294440, 122002101738321960, 1313941673647, 296041409911409376977422], 'label': '3072.bgb.24.DA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.da1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DA', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184761723
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.DB', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.Q', '12.V', '12.BH'], 'contains': ['48.FJ', '48.FN', '48.FQ', '48.HJ', '48.HM', '48.IE', '48.IK'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [270240484111912758504367, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 53952035291802302422343, 378358649363678452761737], 'label': '3072.bgb.24.DB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.db1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DB', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184761724
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.DC', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.H', '12.R', '12.V', '12.BI'], 'contains': ['48.B', '48.FI', '48.FJ', '48.FR', '48.HI', '48.HL', '48.HZ', '48.MM', '48.MN'], 'core': '48.B', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 79804429413572684637382, 53952035291802302422343, 378358649363678452761737], 'label': '3072.bgb.24.DC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.dc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DC', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184761725
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.DD', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.P', '12.W', '12.BH'], 'contains': ['48.FK', '48.FL', '48.FN', '48.HV', '48.HW', '48.IA', '48.IG'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 162070321828715682652927, 79804308125641822294440, 122002101738321960, 1313941673647, 296041409911409376977422], 'label': '3072.bgb.24.DD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.dd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DD', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761726
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.DE', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.S', '12.W', '12.BI'], 'contains': ['48.FK', '48.FP', '48.FR', '48.HX', '48.HZ', '48.IH', '48.IM', '48.MO', '48.MP'], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 79804429413572684637382, 378358649363678452761737, 162070200540784685681302], 'label': '3072.bgb.24.DE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.de1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DE', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761727
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.DF', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.Q', '12.W', '12.BH'], 'contains': ['48.FM', '48.FN', '48.FP', '48.IA', '48.ID', '48.IE', '48.IJ'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [270240484111912758504367, 108169512287410083283217, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.24.DF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.df1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DF', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761728
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '24.DG', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '192.CX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.I', '12.R', '12.W', '12.BJ'], 'contains': ['48.C', '48.FL', '48.FM', '48.FR', '48.IB', '48.IC', '48.IL'], 'core': '48.C', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 378307558065813088567696, 79804308125641822294440, 122002101738321960, 1313941673647, 79804429413572684637382, 404210922196204071249966], 'label': '3072.bgb.24.DG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.dg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DG', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184761729
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.DH', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.S', '12.V', '12.BJ'], 'contains': ['48.FO', '48.FQ', '48.FR', '48.IF', '48.II', '48.IL', '48.IN'], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 79804429413572684637382, 296041409911409376977422, 404210922196204071249966], 'label': '3072.bgb.24.DH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.dh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DH', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761730
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.DI', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.E', '12.X', '12.BH'], 'contains': ['48.FD', '48.FN', '48.FS', '48.FW', '48.GQ', '48.MQ', '48.MR'], 'core': '384.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [79855520714221614566521, 25903229681844523013167, 53952412691500576681559, 25852138389591620222016, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.24.DI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.di1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DI', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184761731
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.DJ', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 12, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.E', '12.Z', '12.BI', '12.BJ', '12.BK', '12.BL', '12.BM'], 'contains': ['48.FH', '48.FR', '48.FS', '48.GG', '48.GP', '48.MU', '48.MY', '48.NB', '48.ND'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 79804429413572684637382, 404210922196204071249966], 'label': '3072.bgb.24.DJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.dj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DJ', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 184761732
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '6.C', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.E', '12.L', '12.M', '12.BK', '12.BL', '12.BS', '12.BT'], 'core': '48.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118421696801471190456, 108118165248982343710201, 25903229681844523013167, 404210787739267985320182, 187922473375925652905521, 296092500500710274860657, 122002101738321960, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.6.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.c1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.C', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184761733
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.DK', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.D', '12.BH', '12.BI'], 'contains': ['48.CA', '48.CG', '48.CH', '48.CL', '48.FI', '48.FJ', '48.FK', '48.FP', '48.FS', '48.GI', '48.GK', '48.MW', '48.NC'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 53952035291802302422343, 378358649363678452761737], 'label': '3072.bgb.24.DK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.dk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DK', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184761734
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.DL', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.D', '12.BH', '12.BJ'], 'contains': ['48.CI', '48.CJ', '48.FL', '48.FM', '48.FO', '48.FQ', '48.FS', '48.GL', '48.GM'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 296041409911409376977422, 404210922196204071249966], 'label': '3072.bgb.24.DL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.dl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DL', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761735
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.DM', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.6536092', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.N', '12.X', '12.BM'], 'contains': ['48.FE', '48.FG', '48.FS', '48.GN', '48.GS', '48.MS', '48.MV', '48.MZ', '48.NA'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 133970303627361494479417, 122002101738321960, 1313941673647, 404210922196204071249966], 'label': '3072.bgb.24.DM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.dm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DM', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 184761736
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.DN', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.F'], 'contains': ['48.FT', '48.FU', '48.FV', '48.GE', '48.GF', '48.GT', '48.GU'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [242089752358354392177983, 25903229681844523013167, 133970303627361494479417, 122002101738321960, 1313941673647, 296041409911409376977422, 25852017102974698844878], 'label': '3072.bgb.24.DN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.F', 'old_label': '24.dn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DN', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761737
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.DO', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.I', '12.BH', '12.BN'], 'contains': ['48.FW', '48.FX', '48.GB', '48.GI', '48.GL', '48.HJ', '48.IA'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 133970303635757521608262, 53952035291802302422343], 'label': '3072.bgb.24.DO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.do1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DO', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184761738
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.DP', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.E', '12.Y', '12.BN'], 'contains': ['48.FW', '48.FY', '48.GJ', '48.GP', '48.HQ', '48.NH', '48.NN'], 'core': '384.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [79855520714221614566521, 25852138757799544092222, 25903229681844523013167, 25852138389591620222016, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.24.DP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.dp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DP', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184761739
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.DQ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.J', '12.BH', '12.BN'], 'contains': ['48.FW', '48.FZ', '48.GA', '48.GK', '48.GM', '48.HW', '48.IE'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [270240484111912758504367, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.24.DQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.dq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DQ', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184761740
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.DR', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.6536092', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.K', '12.X', '12.Y'], 'contains': ['48.FW', '48.GN', '48.GO', '48.NI', '48.NJ'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79855520714221614566521, 162070577934876685646657, 25903229681844523013167, 25852138389591620222016, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.24.DR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.dr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DR', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 184761741
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.DS', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.R', '12.T', '12.BN'], 'contains': ['48.CM', '48.CN', '48.CO', '48.CP', '48.FX', '48.FY', '48.FZ', '48.HH', '48.HI', '48.HN', '48.IC'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 324406991811924875755576, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.24.DS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ds1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DS', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184761742
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.DT', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.R', '12.U', '12.BN'], 'contains': ['48.FX', '48.FY', '48.GA', '48.HG', '48.HL', '48.HP', '48.IB'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 122002101738321960, 324406870523993839248121, 79804308125641822294440, 378358649363678452761737, 25852272837936812846761], 'label': '3072.bgb.24.DT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.dt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DT', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184761743
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '6.D', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.I', '12.K', '12.L', '12.BP', '12.BQ', '12.BW', '12.BX'], 'core': '24.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 122002101738321960, 404210787739267985320182, 79804429413572684637382, 53952035291802302422343, 187922473375925652905521, 296092500500710274860657, 108118165248982343710201], 'label': '3072.bgb.6.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.d1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.D', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184761744
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.DU', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.S', '12.T', '12.BN'], 'contains': ['48.CR', '48.CS', '48.FY', '48.FZ', '48.GB', '48.HO', '48.HS', '48.HX', '48.II'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [378358770650295628183080, 108169512287410083283217, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 324406991811924875755576, 1313941673647], 'label': '3072.bgb.24.DU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.du1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DU', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184761745
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.DV', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.S', '12.U', '12.BN'], 'contains': ['48.FY', '48.GA', '48.GB', '48.HR', '48.HT', '48.IF', '48.IH'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 122002101738321960, 162070321828715682652927, 324406870523993839248121, 79804308125641822294440, 378358649363678452761737], 'label': '3072.bgb.24.DV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.dv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DV', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184761746
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.DW', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.6407063', 'aut_weyl_index': 12, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.B', '12.I', '12.BC', '12.BI', '12.BO', '12.BP', '12.BQ'], 'contains': ['48.B', '48.GG', '48.GI', '48.GV', '48.IM', '48.NQ', '48.OG', '48.PB', '48.PL'], 'core': '48.B', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 79804429413572684637382, 53952035291802302422343], 'label': '3072.bgb.24.DW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.dw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DW', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 184761747
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.DX', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 12, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.E', '12.BD', '12.BO', '12.BR', '12.BS', '12.BT', '12.CA'], 'contains': ['48.GG', '48.GJ', '48.GQ', '48.GW', '48.HU', '48.NR', '48.OI', '48.PC', '48.PN'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 53952412691500576681559, 122002101738321960, 1313941673647, 79804429413572684637382, 25852017102974698844878], 'label': '3072.bgb.24.DX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.dx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DX', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 184761748
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.DY', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 12, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.J', '12.BE', '12.BI', '12.BR', '12.BU', '12.BV', '12.CB'], 'contains': ['48.GG', '48.GK', '48.GX', '48.HC', '48.HZ', '48.NT', '48.OK', '48.PF', '48.PO'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 79804429413572684637382, 378358649363678452761737], 'label': '3072.bgb.24.DY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.dy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DY', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 184761749
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '24.DZ', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.C', '12.I', '12.BF', '12.BJ', '12.BR', '12.BW', '12.BX'], 'contains': ['48.C', '48.GG', '48.GL', '48.GY', '48.IN'], 'core': '48.C', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 79804429413572684637382, 25903364135789722998960], 'label': '3072.bgb.24.DZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.dz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DZ', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761750
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.EA', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 12, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.J', '12.BG', '12.BJ', '12.BO', '12.BY', '12.BZ', '12.CC'], 'contains': ['48.GG', '48.GM', '48.GZ', '48.HB', '48.IL'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 79804052047512561508433, 122002101738321960, 1313941673647, 79804429413572684637382, 25852017102974698844878], 'label': '3072.bgb.24.EA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.ea1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EA', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 184761751
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.EB', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 12, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.K', '12.BD', '12.BM', '12.BP', '12.BU', '12.BW', '12.BY'], 'contains': ['48.GG', '48.GN', '48.NW', '48.OO'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 79804429413572684637382, 378358905093235639407953], 'label': '3072.bgb.24.EB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.eb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EB', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 184761752
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.EC', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 12, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.K', '12.Z', '12.BQ', '12.BV', '12.BX', '12.BZ', '12.CA'], 'contains': ['48.GG', '48.GO', '48.NX', '48.OP'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 122002101738321960, 1313941673647, 79804429413572684637382, 25852017102974698844878, 108169256203674548203560], 'label': '3072.bgb.24.EC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.ec1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EC', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 184761753
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.ED', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 12, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.L', '12.BE', '12.BK', '12.BQ', '12.BS', '12.BW', '12.CC'], 'contains': ['48.GG', '48.HA', '48.NY', '48.PI'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 122002101738321960, 1313941673647, 79804429413572684637382, 134021529040297499210286, 25852017102974698844878], 'label': '3072.bgb.24.ED', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.ed1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ED', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 184761754
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '6.E', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.J', '12.K', '12.M', '12.BU', '12.BV', '12.BY', '12.BZ'], 'core': '48.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118421696801471190456, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 79804429413572684637382, 378358649363678452761737, 296041409911409376977422], 'label': '3072.bgb.6.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.e1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.E', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184761755
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '24.EE', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.B', '12.M', '12.BF', '12.BL', '12.BS', '12.BU', '12.BZ'], 'contains': ['48.GG', '48.IM', '48.OQ', '48.PJ'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118421696801471190456, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.24.EE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.ee1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EE', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761756
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.EF', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.6407063', 'aut_weyl_index': 12, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.C', '12.M', '12.BC', '12.BK', '12.BT', '12.BV', '12.BY'], 'contains': ['48.GG', '48.IN', '48.NZ', '48.PP'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 79804429413572684637382, 187973308217542771509839], 'label': '3072.bgb.24.EF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.ef1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EF', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 184761757
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.EG', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 12, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.L', '12.BG', '12.BL', '12.BP', '12.BT', '12.BX', '12.CB'], 'contains': ['48.GG', '48.HD', '48.OR', '48.PQ'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 404210787739267985320182, 187922473375925652905521, 122002101738321960, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.24.EG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.eg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EG', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 184761758
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.EH', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.6536092', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.F', '12.BA', '12.CB'], 'contains': ['48.GE', '48.GH', '48.GX', '48.HD', '48.HE', '48.OC', '48.OJ', '48.OY', '48.PD'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [242089752358354392177983, 53952291033879672806278, 25903229681844523013167, 133970303627361494479417, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.24.EH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.eh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EH', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 184761759
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.EI', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.6536092', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.F', '12.BB', '12.CC'], 'contains': ['48.GF', '48.GH', '48.GZ', '48.HA', '48.HF'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 187922473375925652905521, 133970303627361494479417, 122002101738321960, 1313941673647, 134021529040297499210286], 'label': '3072.bgb.24.EI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.ei1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EI', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 184761760
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.EJ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.6536092', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.G', '12.BA', '12.CC'], 'contains': ['48.GH', '48.HA', '48.HB', '48.OD', '48.PA'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 79855142625594763233847, 25903229681844523013167, 187922473375925652905521, 133970303627361494479417, 122002101738321960, 1313941673647], 'label': '3072.bgb.24.EJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.ej1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EJ', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 184761761
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.EK', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.6536092', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.G', '12.BB', '12.CB'], 'contains': ['48.GH', '48.HC', '48.HD', '48.OL', '48.PG'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 133970303627361494479417, 122002101738321960, 1313941673647, 378358649363678452761737, 25852017102974698844878], 'label': '3072.bgb.24.EK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.ek1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EK', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 184761762
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.EL', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.D', '12.BN', '12.BO'], 'contains': ['48.CT', '48.CU', '48.GI', '48.GJ', '48.GM', '48.HG', '48.HH', '48.HR', '48.HS'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804052047512561508433, 25852138389591620222016, 122002101738321960, 1313941673647, 54003125882410914585582, 25852017102974698844878], 'label': '3072.bgb.24.EL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.el1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EL', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184761763
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.EM', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.H', '12.BI', '12.BN'], 'contains': ['48.GI', '48.GK', '48.GP', '48.HI', '48.HL', '48.HX', '48.IH', '48.OF', '48.PK'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 25852272837936812846761, 122002101738321960, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.24.EM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.em1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EM', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184761764
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.EN', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.H', '12.BH', '12.BO'], 'contains': ['48.GI', '48.GM', '48.GQ', '48.HK', '48.HM', '48.IG', '48.IJ'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903363795619943623743, 25903229681844523013167, 25852138389591620222016, 122002101738321960, 1313941673647, 25852017102974698844878, 54003125882410914585582], 'label': '3072.bgb.24.EN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.en1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EN', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184761765
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '6.F', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.A', '3.a1'], 'contains': ['12.A', '12.E', '12.K', '12.N', '12.O', '12.X', '12.Y', '12.Z', '12.BD', '12.BM', '12.CA', '12.CD', '12.CE', '12.CF', '12.CG'], 'core': '12.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 122002101738321960, 187922473375925652905521, 133970303627361494479417, 108118165248982343710201, 162070456272950954131199, 187973685961890096441600, 53952412691500576681559], 'label': '3072.bgb.6.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.f1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.F', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184761766
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.EO', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.D', '12.BN', '12.BR'], 'contains': ['48.CV', '48.CW', '48.CX', '48.CY', '48.GJ', '48.GK', '48.GL', '48.HN', '48.HO', '48.HP', '48.HT'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 324355523485385682622200, 378358649363678452761737], 'label': '3072.bgb.24.EO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.eo1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EO', 'subgroup_fusion': None, 'weyl_group': '128.2264'}
  • id: 184761767
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.EP', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.H', '12.BH', '12.BR'], 'contains': ['48.GK', '48.GL', '48.GQ', '48.HV', '48.HY', '48.ID', '48.IK'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [324355644776280741499582, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.24.EP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ep1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EP', 'subgroup_fusion': None, 'weyl_group': '128.2264'}
  • id: 184761768
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.EQ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.H', '12.BJ', '12.BN'], 'contains': ['48.GL', '48.GM', '48.GP', '48.IB', '48.IC', '48.IF', '48.II'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 404211043484134973872583, 187922473375925652905521, 122002101738321960, 1313941673647, 296041409911409376977422], 'label': '3072.bgb.24.EQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.eq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EQ', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761769
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.ER', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.6536092', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.N', '12.Y', '12.CA'], 'contains': ['48.GC', '48.GJ', '48.GO', '48.GR', '48.GS', '48.NO', '48.NS', '48.OS', '48.OU'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 133970303627361494479417, 122002101738321960, 1313941673647, 25852017102974698844878, 108169256203674548203560], 'label': '3072.bgb.24.ER', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.er1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ER', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 184761770
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.ES', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.6536092', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.O', '12.Y', '12.BM'], 'contains': ['48.GN', '48.GP', '48.GS', '48.OA', '48.OV'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 133970303627361494479417, 122002101738321960, 1313941673647, 378358905093235639407953], 'label': '3072.bgb.24.ES', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.es1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ES', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 184761771
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.ET', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.6536092', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.O', '12.X', '12.CA'], 'contains': ['48.GO', '48.GQ', '48.GS', '48.OB', '48.OW'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 53952412691500576681559, 133970303627361494479417, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.24.ET', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.et1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ET', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 184761772
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.EU', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.P', '12.U', '12.BO'], 'contains': ['48.GV', '48.GW', '48.GZ', '48.HG', '48.HK', '48.HR', '48.IG'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 79855398717732338388456, 25903229681844523013167, 256460345499052777, 79804052047512561508433, 122002101738321960, 1313941673647], 'label': '3072.bgb.24.EU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.eu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EU', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184761773
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.EV', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.Q', '12.T', '12.BO'], 'contains': ['48.CZ', '48.DB', '48.GV', '48.GW', '48.HB', '48.HH', '48.HM', '48.HS', '48.IJ'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 25903363795619943623743, 79855398717732338388456, 25903229681844523013167, 256460345499052777, 122002101738321960, 1313941673647], 'label': '3072.bgb.24.EV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ev1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EV', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184761774
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.EW', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.P', '12.T', '12.BR'], 'contains': ['48.DC', '48.DD', '48.DE', '48.DF', '48.GW', '48.GX', '48.GY', '48.HN', '48.HO', '48.HV', '48.HY'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [242089752358354392177983, 324355644776280741499582, 25903229681844523013167, 122002101738321960, 1313941673647, 134021272934136496216343, 187922594661241166512703], 'label': '3072.bgb.24.EW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ew1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EW', 'subgroup_fusion': None, 'weyl_group': '128.2264'}
  • id: 184761775
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.EX', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.Q', '12.U', '12.BR'], 'contains': ['48.GW', '48.GY', '48.HC', '48.HP', '48.HT', '48.ID', '48.IK'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [324355644776280741499582, 25903229681844523013167, 122002101738321960, 1313941673647, 134021272934136496216343, 378358649363678452761737, 187922594661241166512703], 'label': '3072.bgb.24.EX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ex1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EX', 'subgroup_fusion': None, 'weyl_group': '128.2264'}
  • id: 184761776
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '6.G', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.C', '3.a1'], 'contains': ['12.A', '12.F', '12.G', '12.J', '12.L', '12.BA', '12.BB', '12.BE', '12.BG', '12.CB', '12.CC'], 'core': '12.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 122002101738321960, 187922473375925652905521, 133970303627361494479417, 296041409911409376977422, 108118165248982343710201, 162070456272950954131199, 378358649363678452761737], 'label': '3072.bgb.6.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.g1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.G', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184761777
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.EY', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.P', '12.V', '12.BN'], 'contains': ['48.HG', '48.HI', '48.HJ', '48.HO', '48.HQ', '48.HW', '48.IF'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 53952035291802302422343, 296041409911409376977422], 'label': '3072.bgb.24.EY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ey1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EY', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184761778
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.EZ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.Q', '12.V', '12.BN'], 'contains': ['48.HH', '48.HJ', '48.HL', '48.HQ', '48.HT', '48.IE', '48.II'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [270240484111912758504367, 25903229681844523013167, 25852272837936812846761, 79804308125641822294440, 122002101738321960, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.24.EZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ez1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EZ', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184761779
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.FA', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.J', '12.R', '12.V', '12.BO'], 'contains': ['48.B', '48.HG', '48.HH', '48.HK', '48.HM', '48.HU', '48.IL'], 'core': '48.B', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79855142625594763233847, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 79804429413572684637382, 53952035291802302422343], 'label': '3072.bgb.24.FA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.fa1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FA', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184761780
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.FB', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.P', '12.W', '12.BN'], 'contains': ['48.HN', '48.HQ', '48.HR', '48.HW', '48.HX', '48.IA', '48.IB'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [378358770650295628183080, 108169512287410083283217, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 296041409911409376977422], 'label': '3072.bgb.24.FB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.fb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FB', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761781
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '24.FC', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '384.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.K', '12.R', '12.W', '12.BR'], 'contains': ['48.C', '48.HN', '48.HP', '48.HU', '48.HV', '48.HZ', '48.ID'], 'core': '48.C', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [324355644776280741499582, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 79804429413572684637382, 378358649363678452761737], 'label': '3072.bgb.24.FC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.fc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FC', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184761782
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.FD', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.S', '12.V', '12.BR'], 'contains': ['48.HO', '48.HT', '48.HU', '48.HY', '48.HZ', '48.IK', '48.IN'], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 242089374621089192981063, 1313941673647, 79804429413572684637382, 378358649363678452761737], 'label': '3072.bgb.24.FD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.fd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FD', 'subgroup_fusion': None, 'weyl_group': '128.2264'}
  • id: 184761783
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.FE', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.Q', '12.W', '12.BN'], 'contains': ['48.HP', '48.HQ', '48.HS', '48.IA', '48.IC', '48.IE', '48.IH'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [270240484111912758504367, 25903229681844523013167, 162070321828715682652927, 79804308125641822294440, 122002101738321960, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.24.FE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.fe1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FE', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761784
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.FF', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.S', '12.W', '12.BO'], 'contains': ['48.HR', '48.HS', '48.HU', '48.IG', '48.IJ', '48.IL', '48.IM'], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79855142625594763233847, 25903229681844523013167, 256460345499052777, 79804308125641822294440, 122002101738321960, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.24.FF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ff1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FF', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761785
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.FG', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.N', '12.CD', '12.CE'], 'contains': ['48.IO', '48.IQ', '48.IR', '48.IU', '48.IX', '48.ME', '48.MF', '48.MV', '48.MX', '48.NS', '48.OH'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 133970182343548561347240, 25852138389591620222016, 1313941673647, 108118287251071627990321, 25852017102974698844878, 108169256203674548203560], 'label': '3072.bgb.24.FG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.fg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FG', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 184761786
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.FH', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.N', '12.CD', '12.CF'], 'contains': ['48.IR', '48.IY', '48.JA', '48.KC', '48.KD', '48.KK', '48.KM', '48.MX', '48.NA', '48.OH', '48.OU'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 51212588579793007921, 133970303627361494479417, 1313941673647, 25852017102974698844878, 108169256203674548203560], 'label': '3072.bgb.24.FH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.fh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FH', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 184761787
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '6.H', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.Z', '12.BC', '12.BE', '12.BI', '12.BK', '12.BQ', '12.BV', '12.CH', '12.CI'], 'core': '48.B', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229681844523013167, 108118165248982343710201, 187922473375925652905521, 296092500500710274860657, 122002101738321960, 1313941673647, 53952035291802302422343, 79804429413572684637382, 378358649363678452761737], 'label': '3072.bgb.6.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.h1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.H', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184761788
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.FI', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.E', '12.CD', '12.CG'], 'contains': ['48.IR', '48.IZ', '48.JE', '48.JX', '48.JZ', '48.KN', '48.KP', '48.MQ', '48.MU', '48.NH', '48.NR'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855520714221614566521, 25903229681844523013167, 53952412691500576681559, 25852138389591620222016, 54003382328928594643200, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.24.FI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.fi1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FI', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761789
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.FJ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.E', '12.CE', '12.CF'], 'contains': ['48.IR', '48.IZ', '48.JF', '48.JY', '48.KA', '48.KO', '48.KQ', '48.MQ', '48.MY', '48.NH', '48.OI'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 53952412691500576681559, 51212588579793007921, 1313941673647, 79804429413572684637382, 25852017102974698844878], 'label': '3072.bgb.24.FJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.fj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FJ', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 184761790
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.FK', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.E'], 'contains': ['48.IS', '48.JD', '48.JG', '48.JX', '48.KA', '48.KN', '48.KQ', '48.MR', '48.NB', '48.NN', '48.PC'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952413035981411118158, 79855520714221614566521, 25903229681844523013167, 53952412691500576681559, 79804308125641822294440, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.24.FK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '24.fk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FK', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 184761791
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.FL', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.V', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.E'], 'contains': ['48.IS', '48.JD', '48.JH', '48.JY', '48.JZ', '48.KO', '48.KP', '48.MR', '48.ND', '48.NN', '48.PN'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 79804429416356250372480, 79855398717732338388456, 25903229681844523013167, 53952412691500576681559, 51212588579793007921, 1313941673647], 'label': '3072.bgb.24.FL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '24.fl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FL', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184761792
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.FM', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.O', '12.CD', '12.CE'], 'contains': ['48.IU', '48.IY', '48.IZ', '48.OA', '48.OB', '48.OM', '48.ON'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 53952412691500576681559, 133970182343548561347240, 25852138389591620222016, 1313941673647, 108118287251071627990321, 25852017102974698844878], 'label': '3072.bgb.24.FM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.fm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FM', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 184761793
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.FN', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.O', '12.CD', '12.CF'], 'contains': ['48.IX', '48.IZ', '48.JA', '48.OM', '48.ON', '48.OV', '48.OW'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 53952412691500576681559, 51212588579793007921, 133970303627361494479417, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.24.FN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.fn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FN', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 184761794
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.FO', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.K', '12.CD', '12.CG'], 'contains': ['48.IX', '48.IY', '48.JE', '48.NI', '48.NJ', '48.NW', '48.NX'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855520714221614566521, 162070577934876685646657, 25903229681844523013167, 25852138389591620222016, 54003382328928594643200, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.24.FO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.fo1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FO', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761795
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.FP', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.K', '12.CE', '12.CF'], 'contains': ['48.IX', '48.IY', '48.JF', '48.NI', '48.NJ', '48.OO', '48.OP'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 51212588579793007921, 1313941673647, 79804429413572684637382, 25852017102974698844878, 108169256203674548203560], 'label': '3072.bgb.24.FP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.fp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FP', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 184761796
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.FQ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.A', '12.CD'], 'contains': ['48.IT', '48.IU', '48.IV', '48.JA', '48.JE', '48.KF', '48.KG', '48.KI', '48.KJ', '48.KT', '48.KU', '48.KW', '48.KX', '48.NE', '48.NF', '48.NG', '48.NK', '48.NV', '48.OT'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [162070578272437343706839, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 133970303627361494479417, 1313941673647], 'label': '3072.bgb.24.FQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.fq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FQ', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 184761797
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.FR', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.28334', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.N'], 'contains': ['48.IP', '48.IQ', '48.JJ', '48.JO', '48.JQ', '48.KK', '48.KL', '48.MS', '48.MT', '48.NO', '48.NP'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 25852138389591620222016, 108169377837562135992360, 1313941673647, 108118287251071627990321, 134021272934136496216343, 51090960298439969137], 'label': '3072.bgb.24.FR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '24.fr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FR', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 184761798
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '6.I', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 12, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.Z', '12.BF', '12.BG', '12.BJ', '12.BL', '12.BX', '12.BZ'], 'core': '48.C', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118421696801471190456, 108118165248982343710201, 25903229681844523013167, 404210787739267985320182, 187922473375925652905521, 122002101738321960, 1313941673647, 79804429413572684637382, 296041409911409376977422], 'label': '3072.bgb.6.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.i1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.I', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 184761799
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.FS', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.U', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.N'], 'contains': ['48.JI', '48.JP', '48.KC', '48.KE', '48.KH', '48.KY', '48.LA', '48.LL', '48.MF', '48.MS', '48.NO'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25852017094578671678641, 25903229681844523013167, 25852138389591620222016, 1313941673647, 108118287251071627990321, 134021272934136496216343, 51090960298439969137], 'label': '3072.bgb.24.FS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '24.fr2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FS', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184761800
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.FT', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.N', '12.CE', '12.CG'], 'contains': ['48.IR', '48.IY', '48.JI', '48.JU', '48.KB', '48.KL', '48.LB', '48.LM', '48.LY', '48.MV', '48.NS'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 51212588579793007921, 25852138389591620222016, 1313941673647, 108118287251071627990321, 25852017102974698844878, 108169256203674548203560], 'label': '3072.bgb.24.FT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.fs1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FT', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761801
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.FU', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.N', '12.CF', '12.CG'], 'contains': ['48.IP', '48.IR', '48.IX', '48.JS', '48.JV', '48.KY', '48.LB', '48.LM', '48.MG', '48.NA', '48.OU'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 162121669227129588479873, 187973685961890096441600, 25852138389591620222016, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.24.FU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ft1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FU', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761802
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.FV', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.O', '12.CE', '12.CG'], 'contains': ['48.IX', '48.IZ', '48.JU', '48.LN', '48.LO', '48.OA', '48.OB'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 53952412691500576681559, 51212588579793007921, 25852138389591620222016, 1313941673647, 108118287251071627990321, 25852017102974698844878], 'label': '3072.bgb.24.FV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.fu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FV', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761803
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.FW', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.O', '12.CF', '12.CG'], 'contains': ['48.IY', '48.IZ', '48.JV', '48.LN', '48.LO', '48.OV', '48.OW'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 53952412691500576681559, 187973685961890096441600, 25852138389591620222016, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.24.FW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.fv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FW', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761804
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.FX', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.A'], 'contains': ['48.IT', '48.IW', '48.JB', '48.JC', '48.JH', '48.JK', '48.JL', '48.JM', '48.JO', '48.JP', '48.JR', '48.JT', '48.KF', '48.KJ', '48.KR', '48.KS', '48.KT', '48.KV', '48.KX', '48.LC', '48.LE', '48.LI', '48.LJ', '48.LK', '48.LW', '48.LZ', '48.MB', '48.NE', '48.NU'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 162070578272437343706839, 25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 133970303627361494479417, 1313941673647], 'label': '3072.bgb.24.FX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '24.fw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FX', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184761805
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.FY', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.A', '12.CE'], 'contains': ['48.IU', '48.JC', '48.JF', '48.JG', '48.JK', '48.JL', '48.JN', '48.JU', '48.KG', '48.KR', '48.KS', '48.KU', '48.LD', '48.LK', '48.LP', '48.LU', '48.MA', '48.NF', '48.OE'], 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [162070578272437343706839, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.24.FY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.fx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FY', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 184761806
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.FZ', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '768.1090187', 'aut_weyl_index': 8, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.L', '12.A', '12.CF'], 'contains': ['48.D', '48.IW', '48.JA', '48.JF', '48.JV', '48.LE', '48.LF', '48.LP', '48.NK'], 'core': '48.D', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 133970303627361494479417, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.24.FZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '24.fy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FZ', 'subgroup_fusion': None, 'weyl_group': '384.20163'}
  • id: 184761807
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.GA', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.I', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.N'], 'contains': ['48.DG', '48.DH', '48.DI', '48.DJ', '48.IO', '48.JJ', '48.JQ', '48.JS', '48.JW', '48.KM', '48.LA', '48.LL', '48.LY', '48.MZ', '48.OS'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 162121669227129588479873, 187973685961890096441600, 1313941673647, 25852017101492540879976, 162070456272950954131199], 'label': '3072.bgb.24.GA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '24.fz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GA', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 184761808
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '24.GB', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.A', '12.CG'], 'contains': ['48.IV', '48.JE', '48.JM', '48.JN', '48.JR', '48.JT', '48.JU', '48.JV', '48.JW', '48.KW', '48.LC', '48.LD', '48.LF', '48.LZ', '48.MA', '48.MB', '48.MC', '48.MD', '48.OT'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [162070578272437343706839, 25903229691554491852799, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 133970303627361494479417, 1313941673647], 'label': '3072.bgb.24.GB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ga1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GB', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184761809
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '6.J', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.BC', '12.BD', '12.BG', '12.BO', '12.BP', '12.BT', '12.BY'], 'core': '48.B', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 122002101738321960, 404210787739267985320182, 79804429413572684637382, 53952035291802302422343, 187922473375925652905521, 296041409911409376977422, 108118165248982343710201], 'label': '3072.bgb.6.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.j1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.J', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184761810
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.GC', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.28334', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.N'], 'contains': ['48.KB', '48.KD', '48.KE', '48.KH', '48.KI', '48.ME', '48.MG', '48.MT', '48.MZ', '48.NP', '48.OS'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 162121669227129588479873, 187922473375925652905521, 1313941673647, 25852017101492540879976, 187922594658424724202816, 162070456272950954131199], 'label': '3072.bgb.24.GC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '24.gb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GC', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 184761811
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.GD', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.X', '12.CE', '12.CG'], 'contains': ['48.LB', '48.LD', '48.LN', '48.MQ', '48.MV', '48.NI', '48.OB'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 53952412691500576681559, 187973685961890096441600, 25852138389591620222016, 1313941673647, 108118287251071627990321, 25852017102974698844878], 'label': '3072.bgb.24.GD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.gc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GD', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761812
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.GE', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.X', '12.CF', '12.CG'], 'contains': ['48.LB', '48.LF', '48.LN', '48.MQ', '48.NA', '48.NJ', '48.OW'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 53952412691500576681559, 187973685961890096441600, 133970303627361494479417, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.24.GE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.gd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GE', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761813
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.GF', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.Z', '12.CE', '12.CF'], 'contains': ['48.LB', '48.LO', '48.LP', '48.MX', '48.MY', '48.ON', '48.OP'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 187973685961890096441600, 1313941673647, 79804429413572684637382, 25852017102974698844878, 108169256203674548203560], 'label': '3072.bgb.24.GF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ge1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GF', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761814
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.GG', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.Y', '12.CE', '12.CG'], 'contains': ['48.LD', '48.LM', '48.LO', '48.NH', '48.NJ', '48.NS', '48.OA'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 187973685961890096441600, 25852138389591620222016, 1313941673647, 108118287251071627990321, 25852017102974698844878, 108169256203674548203560], 'label': '3072.bgb.24.GG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.gf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GG', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761815
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.GH', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.Y', '12.CF', '12.CG'], 'contains': ['48.LF', '48.LM', '48.LO', '48.NH', '48.NI', '48.OU', '48.OV'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187973685961890096441600, 133970303627361494479417, 1313941673647, 25852017102974698844878, 108169256203674548203560], 'label': '3072.bgb.24.GH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.gg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GH', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761816
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.GI', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.T', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BA'], 'contains': ['48.LI', '48.LQ', '48.LR', '48.NL', '48.NM', '48.OY', '48.PA'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 79804429416356250372480, 296092500497899884979223, 25903229681844523013167, 378307558065813088567696, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.24.GI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BA', 'old_label': '24.gh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GI', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184761817
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.GJ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.28334', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BA'], 'contains': ['48.LG', '48.LH', '48.LJ', '48.OX', '48.OY', '48.OZ', '48.PA'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 79804429416356250372480, 296092500497899884979223, 25903229681844523013167, 324406991811924875755576, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.24.GJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BA', 'old_label': '24.gh2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GJ', 'subgroup_fusion': None, 'weyl_group': '128.1135'}
  • id: 184761818
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.GK', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BD', '12.CE', '12.CF'], 'contains': ['48.LM', '48.LN', '48.LP', '48.OH', '48.OI', '48.OM', '48.OO'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 53952412691500576681559, 187973685961890096441600, 1313941673647, 79804429413572684637382, 25852017102974698844878], 'label': '3072.bgb.24.GK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.gi1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GK', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761819
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.GL', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BE'], 'contains': ['48.LS', '48.LT', '48.LU', '48.PE', '48.PF', '48.PH', '48.PI'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 404159696441402621126383, 1313941673647, 108118287251071627990321, 79804429413572684637382, 378358649363678452761737], 'label': '3072.bgb.24.GL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BE', 'old_label': '24.gj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GL', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184761836
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.GZ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BL', '12.CJ', '12.CK'], 'contains': ['48.MY', '48.OQ', '48.OR'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118421696801471190456, 108118165248982343710201, 25903229681844523013167, 404210787739267985320182, 187922473375925652905521, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.24.GZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '24.gx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GZ', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 184761820
    {'ambient': '3072.bgb', 'aut_centralizer_order': 1, 'aut_label': '2.B', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '3072.a1', 'complements': ['1536.E', '1536.K', '1536.J'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.A', '4.C', '4.F', '6.A', '8.E'], 'core': '2.B', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [108118421696801471190456, 25903229681844523013167, 108118165248982343710201, 187922473375925652905521, 566444897749485959875336, 133970303627361494479417, 404159831259638948150382, 1313941673647, 486427128433516595381056, 162070456272950954131199], 'label': '3072.bgb.2.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.A', '4.C', '4.F', '6.A'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '3072.bgb', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.B', 'subgroup_fusion': None, 'weyl_group': '3072.bgb'}
  • id: 184761821
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '6.K', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 12, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.BD', '12.BE', '12.BF', '12.BR', '12.BS', '12.BU', '12.BW'], 'core': '48.C', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118421696801471190456, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 296092500500710274860657, 122002101738321960, 1313941673647, 79804429413572684637382, 378358649363678452761737], 'label': '3072.bgb.6.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.k1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.K', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 184761822
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.GM', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BC'], 'contains': ['48.LV', '48.LW', '48.LX', '48.PL', '48.PM', '48.PP', '48.PR'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 79804429416356250372480, 79855398717732338388456, 25903229681844523013167, 256460345499052777, 187973685961890096441600, 1313941673647], 'label': '3072.bgb.24.GM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BC', 'old_label': '24.gk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GM', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184761823
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '24.GN', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '384.CG', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.Z', '12.CG', '12.CH'], 'contains': ['48.LB', '48.LO', '48.MD', '48.MU', '48.NX'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [162070577934876685646657, 25903229681844523013167, 187973685961890096441600, 25852138389591620222016, 54003382328928594643200, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.24.GN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.gl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GN', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 184761824
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.GO', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.K', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BA'], 'contains': ['48.DK', '48.DL', '48.LG', '48.LH', '48.LQ', '48.LR', '48.MC', '48.OC', '48.OD'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [242089752358354392177983, 25903229681844523013167, 133970303627361494479417, 378307558065813088567696, 54003382328928594643200, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.24.GO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BA', 'old_label': '24.gm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GO', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184761825
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.GP', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BC', '12.CH'], 'contains': ['48.LV', '48.LX', '48.MD', '48.NQ', '48.NZ'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79804308122845802507662, 25903229691554491852799, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.24.GP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '24.gn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GP', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761826
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '24.GQ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '384.CH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BD', '12.CG'], 'contains': ['48.LM', '48.LN', '48.MD', '48.NR', '48.NW'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 53952412691500576681559, 187973685961890096441600, 25852138389591620222016, 54003382328928594643200, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.24.GQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.go1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GQ', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184761827
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.GR', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BE', '12.CH'], 'contains': ['48.LS', '48.LT', '48.MD', '48.NT', '48.NY'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79804308122845802507662, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 296092500500710274860657, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.24.GR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '24.gp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GR', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 184761828
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.GS', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.X', '12.CD', '12.CE'], 'contains': ['48.MQ', '48.MV', '48.MX', '48.NF', '48.NJ', '48.OB', '48.OM'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855520714221614566521, 25903229681844523013167, 53952412691500576681559, 25852138389591620222016, 1313941673647, 108118287251071627990321, 25852017102974698844878], 'label': '3072.bgb.24.GS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.gq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GS', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 184761829
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.GT', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.X', '12.CD', '12.CF'], 'contains': ['48.MQ', '48.MX', '48.NA', '48.NI', '48.NK', '48.OM', '48.OW'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 53952412691500576681559, 25852138389591620222016, 1313941673647, 79804429421968711780537, 162070456272950954131199], 'label': '3072.bgb.24.GT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.gr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GT', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 184761830
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.GU', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BI', '12.CH', '12.CI'], 'contains': ['48.MH', '48.MI', '48.MM', '48.MO', '48.MU', '48.MW', '48.NQ', '48.NT', '48.OF'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804308122845802507662, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647, 53952035291802302422343, 378358649363678452761737], 'label': '3072.bgb.24.GU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '24.gs1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GU', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 184761831
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.GV', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.Z', '12.CD', '12.CI'], 'contains': ['48.MU', '48.MX', '48.NV', '48.NX', '48.ON'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [162070577934876685646657, 25903229681844523013167, 133970182343548561347240, 25852138389591620222016, 54003382328928594643200, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.24.GV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.gt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GV', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 184761832
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '6.L', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.D', '3.a1'], 'contains': ['12.B', '12.BI', '12.BL', '12.BM', '12.BP', '12.BU', '12.CB', '12.CJ', '12.CK'], 'core': '12.B', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118421696801471190456, 25903229681844523013167, 108118165248982343710201, 187922473375925652905521, 133970303627361494479417, 122002101738321960, 1313941673647, 378358649363678452761737, 162070456272950954131199], 'label': '3072.bgb.6.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.l1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.L', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184761833
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.GW', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BK', '12.CH', '12.CI'], 'contains': ['48.MU', '48.NY', '48.NZ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804308122845802507662, 108118165248982343710201, 25903229681844523013167, 404211043484134973872583, 187922473375925652905521, 296092500500710274860657, 1313941673647], 'label': '3072.bgb.24.GW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '24.gu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GW', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 184761834
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.GX', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.406983', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BM', '12.CE', '12.CJ'], 'contains': ['48.MV', '48.MY', '48.OA', '48.OE', '48.OO'], 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [162070578272437343706839, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647, 79804429413572684637382, 378358905093235639407953], 'label': '3072.bgb.24.GX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.gv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GX', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184761835
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.GY', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BI', '12.CJ', '12.CK'], 'contains': ['48.MK', '48.ML', '48.MN', '48.MP', '48.MW', '48.MY', '48.OF', '48.OG', '48.OK'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647, 79804429413572684637382, 53952035291802302422343, 378358649363678452761737], 'label': '3072.bgb.24.GY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '24.gw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GY', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 184761837
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.HA', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BM', '12.CD', '12.CG'], 'contains': ['48.MU', '48.MV', '48.NA', '48.NW', '48.OA', '48.OT', '48.OV'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [162070578272437343706839, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 133970303627361494479417, 1313941673647, 378358905093235639407953], 'label': '3072.bgb.24.HA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.gy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HA', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761838
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.HB', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.406983', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.B', '12.BM', '12.CF', '12.CK'], 'contains': ['48.D', '48.MY', '48.NA', '48.OO', '48.OV'], 'core': '48.D', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 108118165248982343710201, 187922473375925652905521, 133970303627361494479417, 1313941673647, 378358905093235639407953, 162070456272950954131199], 'label': '3072.bgb.24.HB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.gz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HB', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184761839
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.HC', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BI'], 'contains': ['48.MH', '48.MI', '48.MN', '48.MP', '48.NB', '48.NC', '48.PB', '48.PF', '48.PK'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 1313941673647, 108118287251071627990321, 79804429413572684637382, 378358649363678452761737, 162070200540784685681302], 'label': '3072.bgb.24.HC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '24.ha1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HC', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761840
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.HD', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BI'], 'contains': ['48.MK', '48.ML', '48.MM', '48.MO', '48.NC', '48.ND', '48.PK', '48.PL', '48.PO'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [242089752358354392177983, 187922594664024732247801, 25903229681844523013167, 1313941673647, 134021272934136496216343, 53952035291802302422343, 187922594661241166512703], 'label': '3072.bgb.24.HD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '24.hb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HD', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761841
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.HE', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.Y', '12.CD', '12.CE'], 'contains': ['48.NF', '48.NH', '48.NI', '48.NS', '48.OA', '48.OH', '48.ON'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855520714221614566521, 25903229681844523013167, 25852138389591620222016, 1313941673647, 108118287251071627990321, 25852017102974698844878, 108169256203674548203560], 'label': '3072.bgb.24.HE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.hc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HE', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 184761842
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.HF', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.28334', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BA'], 'contains': ['48.NG', '48.NL', '48.NM', '48.OC', '48.OD', '48.OX', '48.OZ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [242089752358354392177983, 25903229681844523013167, 133970303627361494479417, 54003382328928594643200, 324406991811924875755576, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.24.HF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BA', 'old_label': '24.hd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HF', 'subgroup_fusion': None, 'weyl_group': '128.1135'}
  • id: 184761843
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '6.M', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.E', '3.a1'], 'contains': ['12.C', '12.BJ', '12.BK', '12.BM', '12.BW', '12.BY', '12.CC'], 'core': '12.C', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 122002101738321960, 187922473375925652905521, 133970303627361494479417, 378358905093235639407953, 296041409911409376977422, 108118165248982343710201, 162070456272950954131199], 'label': '3072.bgb.6.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.m1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.M', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184761844
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.HG', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.Y', '12.CD', '12.CF'], 'contains': ['48.NH', '48.NJ', '48.NK', '48.OH', '48.ON', '48.OU', '48.OV'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 162121669227129588479873, 25852138389591620222016, 1313941673647, 79804429421968711780537, 162070456272950954131199], 'label': '3072.bgb.24.HG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.he1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HG', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 184761845
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.HH', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BC', '12.CI'], 'contains': ['48.NQ', '48.NV', '48.NZ', '48.PM', '48.PR'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79804308122845802507662, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647, 53952035291802302422343, 79804429421968711780537], 'label': '3072.bgb.24.HH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '24.hf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HH', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761846
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.HI', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BQ', '12.CH', '12.CI'], 'contains': ['48.NQ', '48.NX', '48.NY'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [162121412784889831356736, 25903229681844523013167, 25852138389591620222016, 54003382328928594643200, 1313941673647, 25852017102974698844878, 54003125882410914585582], 'label': '3072.bgb.24.HI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '24.hg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HI', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 184761847
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.HJ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BD', '12.CD'], 'contains': ['48.NR', '48.NV', '48.NW', '48.OH', '48.OM'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 53952412691500576681559, 133970182343548561347240, 25852138389591620222016, 54003382328928594643200, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.24.HJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.hh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HJ', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761848
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.HK', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.CB'], 'contains': ['48.NU', '48.OJ', '48.OL', '48.PD', '48.PG', '48.PO', '48.PQ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 187922594664024732247801, 25903229681844523013167, 133970303627361494479417, 1313941673647, 378358649363678452761737, 25852017102974698844878], 'label': '3072.bgb.24.HK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.CB', 'old_label': '24.hi1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HK', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761849
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '24.HL', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BE', '12.CI'], 'contains': ['48.NT', '48.NV', '48.NY', '48.PE', '48.PH'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79804308122845802507662, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 270189392822449473928912, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.24.HL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '24.hj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HL', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 184761850
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.HM', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BV', '12.CH', '12.CI'], 'contains': ['48.NT', '48.NX', '48.NZ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804308122845802507662, 324406614064956014978497, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.24.HM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '24.hk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HM', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 184761851
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.HN', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.B', '12.CJ'], 'contains': ['48.OE', '48.OG', '48.OQ', '48.PB', '48.PJ'], 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118421696801471190456, 162070578272437343706839, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.24.HN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '24.hl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HN', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761852
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.HO', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.406983', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.CA', '12.CE'], 'contains': ['48.NS', '48.OB', '48.OE', '48.OI', '48.OP'], 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 187922594664024732247801, 25903229681844523013167, 53952412691500576681559, 1313941673647, 79804429413572684637382, 25852017102974698844878], 'label': '3072.bgb.24.HO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.hm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HO', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 184761853
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.HP', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.406983', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.CB', '12.CJ'], 'contains': ['48.OE', '48.OK', '48.OR', '48.PD', '48.PG'], 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [162070578272437343706839, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647, 79804429413572684637382, 378358649363678452761737], 'label': '3072.bgb.24.HP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '24.hn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HP', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 184761854
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '6.N', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.F', '3.a1'], 'contains': ['12.B', '12.BO', '12.BQ', '12.BS', '12.BZ', '12.CA', '12.CC'], 'core': '12.B', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118421696801471190456, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 133970303627361494479417, 122002101738321960, 1313941673647, 134021529040297499210286, 162070456272950954131199], 'label': '3072.bgb.6.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.n1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.N', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184761855
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.HQ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BP', '12.CJ', '12.CK'], 'contains': ['48.OG', '48.OO', '48.OR'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 404210787739267985320182, 79804429413572684637382, 53952035291802302422343, 187922473375925652905521, 108118165248982343710201], 'label': '3072.bgb.24.HQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '24.ho1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HQ', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 184761856
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.HR', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BU', '12.CJ', '12.CK'], 'contains': ['48.OK', '48.OO', '48.OQ'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118421696801471190456, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647, 79804429413572684637382, 378358649363678452761737], 'label': '3072.bgb.24.HR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '24.hp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HR', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 184761857
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.HS', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.CA', '12.CD', '12.CG'], 'contains': ['48.NR', '48.NS', '48.NX', '48.OB', '48.OT', '48.OU', '48.OW'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [187922594664024732247801, 25903229681844523013167, 108118165248982343710201, 53952412691500576681559, 133970303627361494479417, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.24.HS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.hq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HS', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184761858
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.HT', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '768.1087582', 'aut_weyl_index': 8, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.M', '12.B', '12.CK'], 'contains': ['48.D', '48.OG', '48.OQ'], 'core': '48.D', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [108118421696801471190456, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 133970303627361494479417, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.24.HT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.D', 'old_label': '24.hr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HT', 'subgroup_fusion': None, 'weyl_group': '384.17948'}
  • id: 184761859
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.HU', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.406983', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.N', '12.CA', '12.CF'], 'contains': ['48.D', '48.OI', '48.OP', '48.OU', '48.OW'], 'core': '48.D', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 53952412691500576681559, 133970303627361494479417, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.24.HU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.hs1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HU', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 184761860
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.HV', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.406983', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.O', '12.CB', '12.CK'], 'contains': ['48.D', '48.OJ', '48.OK', '48.OL', '48.OR'], 'core': '48.D', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 108118165248982343710201, 187922473375925652905521, 133970303627361494479417, 1313941673647, 378358649363678452761737, 162070456272950954131199], 'label': '3072.bgb.24.HV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '24.ht1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HV', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 184761861
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '24.HW', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BS'], 'contains': ['48.PC', '48.PI', '48.PJ'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952413035981411118158, 108118421696801471190456, 25903229681844523013167, 79804308125641822294440, 1313941673647, 79804429413572684637382, 134021529040297499210286], 'label': '3072.bgb.24.HW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BS', 'old_label': '24.hu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HW', 'subgroup_fusion': None, 'weyl_group': '64.32'}
  • id: 184761862
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '24.HX', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BT'], 'contains': ['48.PN', '48.PP', '48.PQ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [324355644776280741499582, 187922594664024732247801, 25903229681844523013167, 1313941673647, 134021272934136496216343, 216237613982764859689536, 187922594661241166512703], 'label': '3072.bgb.24.HX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BT', 'old_label': '24.hv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HX', 'subgroup_fusion': None, 'weyl_group': '128.850'}
  • id: 184761863
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '32.A', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '96.226', 'aut_weyl_index': 64, 'centralizer': '768.Z', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.C', '8.D', '16.C'], 'contains': ['64.A', '64.B', '64.D', '64.H', '96.KG', '128.G'], 'core': '192.A', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [121659103022301503, 25903229681844523013167, 216288570480689195210176, 1313941673647, 486427128433516595381056, 486478219730068018627222], 'label': '3072.bgb.32.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.C', 'old_label': '32.a1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.A', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 184761864
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '32.B', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '96.226', 'aut_weyl_index': 64, 'centralizer': '1536.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.E', '16.C'], 'contains': ['64.A', '64.C', '64.F', '96.KJ', '128.H'], 'core': '192.A', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [51347037126292956736, 25903229681844523013167, 216288570480689195210176, 1313941673647, 486427128433516595381056, 486478219730068018627222], 'label': '3072.bgb.32.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.C', 'old_label': '32.b1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.B', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 184761865
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '6.O', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.G', '3.a1'], 'contains': ['12.C', '12.BR', '12.BT', '12.BV', '12.BX', '12.CA', '12.CB'], 'core': '12.C', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 122002101738321960, 187922473375925652905521, 133970303627361494479417, 108118165248982343710201, 162070456272950954131199, 378358649363678452761737, 324406614064956014978497], 'label': '3072.bgb.6.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.o1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.O', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184761866
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '32.C', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '96.226', 'aut_weyl_index': 64, 'centralizer': '1536.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.F', '8.G', '16.C'], 'contains': ['64.A', '64.E', '64.G', '96.KK', '128.I'], 'core': '192.A', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [51347406816160329727, 378358770650295628183080, 404159952546255909825352, 25903229681844523013167, 1313941673647, 594545172394561848633606], 'label': '3072.bgb.32.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.C', 'old_label': '32.c1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.C', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 184761867
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '32.D', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '96.226', 'aut_weyl_index': 64, 'centralizer': '768.BC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.H', '16.C'], 'contains': ['64.B', '64.C', '64.E', '64.I', '96.KV', '128.J'], 'core': '384.A', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 566444897749485959875336, 25852272837936812846761, 404159831259638948150382, 1313941673647], 'label': '3072.bgb.32.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.C', 'old_label': '32.d1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.D', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 184761868
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '32.E', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '96.226', 'aut_weyl_index': 64, 'centralizer': '768.BG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.I', '16.C'], 'contains': ['64.B', '64.F', '64.G', '96.KW', '128.K'], 'core': '384.A', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [51347406816160329727, 404159952546255909825352, 25903229681844523013167, 1313941673647, 404210922196204071249966, 594545172394561848633606], 'label': '3072.bgb.32.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.C', 'old_label': '32.e1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.E', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 184761869
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '32.F', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '384.5678', 'aut_weyl_index': 16, 'centralizer': '1536.C', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.A', '16.B', '16.F', '16.H'], 'contains': ['64.J', '96.LM', '128.A'], 'core': '384.A', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 566444897749485959875336, 404159831259638948150382, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.32.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.C', 'old_label': '32.f1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.F', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 184761870
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '32.G', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '384.5677', 'aut_weyl_index': 16, 'centralizer': '3072.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.A', '16.E', '16.I', '16.J'], 'contains': ['64.L', '96.LT', '128.A'], 'core': '384.A', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 566444897749485959875336, 404159831259638948150382, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.32.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.G', 'old_label': '32.g1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.G', 'subgroup_fusion': None, 'weyl_group': '384.5677'}
  • id: 184761871
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '32.H', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '96.226', 'aut_weyl_index': 64, 'centralizer': '1536.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.J', '16.C'], 'contains': ['64.C', '64.D', '64.G', '96.LU', '128.L'], 'core': '384.A', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [566495989041738862713598, 54003126248003449434936, 25903229681844523013167, 296041666021875301271736, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.32.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.C', 'old_label': '32.h1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.H', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 184761872
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '32.I', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '96.226', 'aut_weyl_index': 64, 'centralizer': '1536.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.K', '16.C'], 'contains': ['64.D', '64.E', '64.F', '96.LW', '128.M'], 'core': '384.A', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [486427128437815115841359, 378358770650295628183080, 25903229681844523013167, 1313941673647, 324406735729665311536697, 51212962568394582352], 'label': '3072.bgb.32.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.C', 'old_label': '32.i1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.I', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 184761873
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '32.J', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '192.956', 'aut_weyl_index': 32, 'centralizer': '768.BG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.A', '16.D', '16.G', '16.K', '16.L', '16.M', '16.N', '16.O'], 'contains': ['64.K', '96.A', '128.A'], 'core': '96.A', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [25903229681844523013167, 566444897749485959875336, 404159831259638948150382, 79804308125641822294440, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.32.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.H', 'old_label': '32.j1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.J', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 184761874
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '32.K', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '384.5678', 'aut_weyl_index': 16, 'centralizer': '1536.C', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.L', '16.B', '16.P'], 'contains': ['64.J', '96.NB', '128.B', '128.N'], 'core': '768.A', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 404159831259638948150382, 1313941673647, 486427128433516595381056, 162070456272950954131199], 'label': '3072.bgb.32.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.C', 'old_label': '32.k1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.K', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 184761875
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '32.L', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '192.956', 'aut_weyl_index': 32, 'centralizer': '1536.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.L', '16.D', '16.Q'], 'contains': ['64.K', '96.NQ', '128.B'], 'core': '192.B', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 1313941673647, 79804429413572684637382, 486427128433516595381056, 270189770923792213003566], 'label': '3072.bgb.32.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.D', 'old_label': '32.l1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.L', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 184761876
    {'ambient': '3072.bgb', 'aut_centralizer_order': 1, 'aut_label': '8.A', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '3072.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.A', '4.B', '4.C', '4.D', '4.E', '4.F', '4.G'], 'contains': ['16.A', '24.B', '32.F', '32.G', '32.J'], 'core': '8.A', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [25903229681844523013167, 108118165248982343710201, 187922473375925652905521, 566444897749485959875336, 133970303627361494479417, 404159831259638948150382, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.8.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': ['4.A', '4.B', '4.C', '4.D', '4.E', '4.F', '4.G'], 'normal_contains': ['16.A', '24.B'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.A', 'subgroup_fusion': None, 'weyl_group': '3072.bgb'}
  • id: 184761877
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '32.M', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '384.5678', 'aut_weyl_index': 16, 'centralizer': '1536.C', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.L', '16.B', '16.R'], 'contains': ['64.J', '96.NV', '128.B'], 'core': '768.A', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 133970303627361494479417, 216288570480689195210176, 1313941673647, 486427128433516595381056], 'label': '3072.bgb.32.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.C', 'old_label': '32.m1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.M', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 184761878
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '32.N', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '192.1008', 'aut_weyl_index': 32, 'centralizer': '3072.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.L', '16.E'], 'contains': ['64.L', '96.NY', '128.B'], 'core': '768.A', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 216288570480689195210176, 1313941673647, 134021272934136496216343, 486427128433516595381056], 'label': '3072.bgb.32.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.E', 'old_label': '32.n1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.N', 'subgroup_fusion': None, 'weyl_group': '192.1008'}
  • id: 184761879
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '32.O', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '192.955', 'aut_weyl_index': 32, 'centralizer': '1536.C', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.B', '16.F', '16.P', '16.R'], 'contains': ['64.J', '96.QR', '128.C', '128.O'], 'core': '768.A', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 404159831259638948150382, 1313941673647, 378358905093235639407953, 162070456272950954131199], 'label': '3072.bgb.32.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.C', 'old_label': '32.o1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.O', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 184761880
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '32.P', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '192.956', 'aut_weyl_index': 32, 'centralizer': '768.BG', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.B', '16.G', '16.Q', '16.S'], 'contains': ['64.K', '96.RD', '128.C'], 'core': '192.B', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [25903229681844523013167, 404159831259638948150382, 79804308125641822294440, 1313941673647, 79804429413572684637382, 404210922196204071249966], 'label': '3072.bgb.32.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.H', 'old_label': '32.p1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.P', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 184761881
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '32.Q', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '192.955', 'aut_weyl_index': 32, 'centralizer': '1536.C', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.N', '16.H', '16.P', '16.R'], 'contains': ['64.J', '96.TP', '128.E', '128.P'], 'core': '768.A', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 378307936172768329324920, 162121669227129588479873, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.32.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.C', 'old_label': '32.q1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.Q', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 184761882
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '32.R', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '192.956', 'aut_weyl_index': 32, 'centralizer': '1536.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.M', '16.K', '16.S'], 'contains': ['64.K', '96.US', '128.D'], 'core': '192.B', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [25903229681844523013167, 404159831259638948150382, 79804308125641822294440, 1313941673647, 79804429413572684637382, 53952035291802302422343], 'label': '3072.bgb.32.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.H', 'old_label': '32.r1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.R', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 184761883
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '32.S', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '192.956', 'aut_weyl_index': 32, 'centralizer': '1536.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.N', '16.L', '16.Q'], 'contains': ['64.K', '96.UX', '128.E'], 'core': '192.B', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [378307814169184473345982, 25903229681844523013167, 53952412691500576681559, 79804308125641822294440, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.32.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.D', 'old_label': '32.s1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.S', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 184761884
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '32.T', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '192.956', 'aut_weyl_index': 32, 'centralizer': '1536.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.O', '16.M', '16.S'], 'contains': ['64.K', '96.VD', '128.F'], 'core': '192.B', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [25903229681844523013167, 404159831259638948150382, 79804308125641822294440, 1313941673647, 79804429413572684637382, 378358649363678452761737], 'label': '3072.bgb.32.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.H', 'old_label': '32.t1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.T', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 184761885
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '32.U', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '192.956', 'aut_weyl_index': 32, 'centralizer': '3072.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.O', '16.I'], 'contains': ['64.L', '96.VF', '128.F'], 'core': '768.A', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [53952291033879672806278, 296092500497899884979223, 25903229681844523013167, 1313941673647, 134021272934136496216343, 270189770923792213003566], 'label': '3072.bgb.32.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.I', 'old_label': '32.u1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.U', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 184761886
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '48.A', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '384.17948', 'aut_weyl_index': 16, 'centralizer': '384.A', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.D', '24.A', '24.R', '24.BA', '24.BJ', '24.BK'], 'contains': ['96.A', '96.KH', '96.LD', '96.NP', '96.NQ'], 'core': '48.A', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [79855520714221614566521, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.48.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': ['12.A', '24.A'], 'normal_contains': ['96.A', '192.A'], 'normalizer': '1.a1', 'old_label': '48.a1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.A', 'subgroup_fusion': None, 'weyl_group': '384.17948'}
  • id: 184761887
    {'ambient': '3072.bgb', 'aut_centralizer_order': 1, 'aut_label': '8.B', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '3072.bgb', 'aut_weyl_index': 2, 'centralizer': '3072.a1', 'complements': ['384.GM', '384.GN', '384.GV', '384.GU', '384.GW', '384.HA', '384.HB', '384.GX', '384.GO', '384.HM', '384.GY', '384.GZ'], 'conjugacy_class_count': 2, 'contained_in': ['4.B', '4.I', '4.J'], 'contains': ['16.A', '24.HB', '32.O', '32.P'], 'core': '8.B', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [25903229681844523013167, 108118165248982343710201, 187922473375925652905521, 133970303627361494479417, 404159831259638948150382, 1313941673647, 378358905093235639407953, 162070456272950954131199], 'label': '3072.bgb.8.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': ['4.B'], 'normal_contains': ['16.A'], 'normalizer': '1.a1', 'old_label': '8.b1', 'projective_image': '3072.bgb', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.B', 'subgroup_fusion': None, 'weyl_group': '3072.bgb'}
  • id: 184761888
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '48.B', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '384.17948', 'aut_weyl_index': 16, 'centralizer': '384.A', 'complements': ['64.N'], 'conjugacy_class_count': 1, 'contained_in': ['16.K', '24.A', '24.CJ', '24.DC', '24.DW', '24.FA'], 'contains': ['96.A', '96.LV', '96.UR', '96.US'], 'core': '48.B', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 79804429413572684637382, 53952035291802302422343], 'label': '3072.bgb.48.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.B', 'normal_contained_in': ['12.B', '24.A'], 'normal_contains': ['96.A'], 'normalizer': '1.a1', 'old_label': '48.b1', 'projective_image': '3072.bgb', 'quotient_action_image': '48.48', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '48.B', 'subgroup_fusion': None, 'weyl_group': '384.17948'}
  • id: 184761905
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.R', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '384.T', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.D', '24.W'], 'contains': ['96.K', '96.O', '96.Q', '96.W', '96.BC', '96.CC', '96.CJ', '96.CM', '96.DH', '96.EZ', '96.FX'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [122002101738321960, 25903229683158464676480, 378358770648994141276807, 324406870523993839248121, 79804308125641822294440, 25852272837936812846761], 'label': '3072.bgb.48.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.r1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.R', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184761889
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '48.C', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '48.C', 'complements': ['64.N'], 'conjugacy_class_count': 1, 'contained_in': ['16.N', '24.A', '24.CN', '24.DG', '24.DZ', '24.FC'], 'contains': ['96.A', '96.MA'], 'core': '48.C', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 79804429413572684637382, 25903364135789722998960], 'label': '3072.bgb.48.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.C', 'normal_contained_in': ['12.C', '24.A'], 'normal_contains': ['96.A'], 'normalizer': '1.a1', 'old_label': '48.c1', 'projective_image': '3072.bgb', 'quotient_action_image': '48.48', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '48.C', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 184761890
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.D', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1536.408610986', 'aut_weyl_index': 4, 'centralizer': '768.A', 'complements': ['64.M'], 'conjugacy_class_count': 1, 'contained_in': ['16.A', '24.B', '24.FZ', '24.HB', '24.HT', '24.HU', '24.HV'], 'contains': ['96.TH', '96.TN', '96.TQ'], 'core': '48.D', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 133970303627361494479417, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.48.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.D', 'normal_contained_in': ['16.A', '24.B'], 'normal_contains': ['192.B'], 'normalizer': '1.a1', 'old_label': '48.d1', 'projective_image': '3072.bgb', 'quotient_action_image': '48.38', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '48.D', 'subgroup_fusion': None, 'weyl_group': '768.1087581'}
  • id: 184761891
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.E', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.X', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.L'], 'contains': ['96.B', '96.C', '96.G', '96.I', '96.T', '96.BD', '96.BE', '96.BI', '96.BQ', '96.CE', '96.DX', '96.GH', '96.GI', '96.GJ', '96.GK', '96.GU', '96.GY', '96.HI', '96.HM'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 25852138757799544092222, 51212588579793007921, 25852138389591620222016, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '48.e1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.E', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184761892
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.F', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.S', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.C', '24.D', '24.L'], 'contains': ['96.B', '96.D', '96.F', '96.H', '96.K', '96.BD', '96.BF', '96.BH', '96.BK', '96.CX', '96.DW', '96.GH', '96.GJ', '96.GN', '96.GP', '96.GT', '96.GW', '96.HH', '96.HK'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25852138757799544092222, 51212588579793007921, 25852138389591620222016, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.f1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.F', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184761893
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.G', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.F', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.E', '24.F', '24.L'], 'contains': ['96.C', '96.E', '96.F', '96.H', '96.J', '96.BE', '96.BG', '96.BH', '96.BJ', '96.CX', '96.DY', '96.GI', '96.GK', '96.GO', '96.GQ', '96.GT', '96.GV', '96.HH', '96.HJ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [51212588579793007921, 25852138389591620222016, 122002101738321960, 1313941673647, 25852017102974698844878, 51090958997032170942], 'label': '3072.bgb.48.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.g1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.G', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184761894
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.H', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.N', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.L'], 'contains': ['96.D', '96.E', '96.G', '96.I', '96.P', '96.BF', '96.BG', '96.BI', '96.BL', '96.DD', '96.DX', '96.GN', '96.GO', '96.GP', '96.GQ', '96.GU', '96.GX', '96.HI', '96.HL'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 25852138757799544092222, 25852017095880079467006, 25852138389591620222016, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '48.h1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.H', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184761895
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.I', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.FY', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.D', '24.E', '24.N'], 'contains': ['96.F', '96.Q', '96.X', '96.BO', '96.BT', '96.DU', '96.EB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 187922473375925652905521, 134021394930826866723126, 25903229683158464676480, 53952035291802302422343, 162070456280045573438767], 'label': '3072.bgb.48.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.i1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.I', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184761896
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.J', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.C', '24.F', '24.N'], 'contains': ['96.F', '96.R', '96.X', '96.BO', '96.BU', '96.DU', '96.EC'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 187922473375925652905521, 134021394930826866723126, 187973685961890096441600, 25903229683158464676480, 53952035291802302422343], 'label': '3072.bgb.48.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.j1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.J', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184761897
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.K', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.F', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.C', '24.E', '24.O'], 'contains': ['96.F', '96.V', '96.Y', '96.BS', '96.BW', '96.EA', '96.EE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 187922473375925652905521, 134021394930826866723126, 25903229683158464676480, 296041409911409376977422, 378358649362364591657542], 'label': '3072.bgb.48.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.k1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.K', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184761898
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '8.C', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '384.5678', 'aut_weyl_index': 16, 'centralizer': '1536.C', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.A'], 'contains': ['16.B', '16.F', '16.H', '16.P', '16.R', '24.T', '32.A'], 'core': '192.A', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [162070577934876685646657, 25903229681844523013167, 187922473375925652905521, 566444897749485959875336, 404159831259638948150382, 1313941673647, 486427128433516595381056, 162070456272950954131199], 'label': '3072.bgb.8.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.C', 'old_label': '8.c1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.C', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 184761899
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.L', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.S', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.D', '24.F', '24.O'], 'contains': ['96.F', '96.W', '96.Y', '96.BV', '96.BW', '96.ED', '96.EE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 187922473375925652905521, 134021394930826866723126, 25903229683158464676480, 378358649363678452761737, 296041409911409376977422], 'label': '3072.bgb.48.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.l1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.L', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184761900
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.M', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.D', '24.E', '24.X'], 'contains': ['96.H', '96.Q', '96.Y', '96.CK', '96.CN', '96.ER', '96.FG'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 54003503618341535825287, 324406991811924875755576, 25903229683158464676480, 53952035291802302422343, 378358649362364591657542], 'label': '3072.bgb.48.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.m1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.M', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184761901
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.N', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.C', '24.F', '24.X'], 'contains': ['96.H', '96.R', '96.Y', '96.CK', '96.CP', '96.ER', '96.FH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 54003503618341535825287, 324406991811924875755576, 25903229683158464676480, 53952035291802302422343, 378358649363678452761737], 'label': '3072.bgb.48.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.n1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.N', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184761902
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.O', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '384.E', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.E', '24.W'], 'contains': ['96.J', '96.L', '96.Q', '96.V', '96.Z', '96.BZ', '96.CI', '96.CM', '96.DE', '96.ET', '96.FL'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [51469042011382569606, 378358770650295628183080, 79804308125641822294440, 122002101738321960, 25903229683158464676480, 324406870523993839248121], 'label': '3072.bgb.48.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.o1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.O', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184761903
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.P', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 48, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.F', '24.W'], 'contains': ['96.J', '96.M', '96.R', '96.W', '96.BA', '96.CA', '96.CJ', '96.CO', '96.DF', '96.ET', '96.FM'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [51469042011382569606, 378358770648994141276807, 79804308125641822294440, 122002101738321960, 25903229683158464676480, 324406870523993839248121], 'label': '3072.bgb.48.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.p1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.P', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 184761904
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.Q', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 48, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.C', '24.W'], 'contains': ['96.K', '96.N', '96.R', '96.V', '96.BB', '96.CB', '96.CI', '96.CO', '96.DG', '96.EZ', '96.FV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [122002101738321960, 25903229683158464676480, 324406870523993839248121, 79804308125641822294440, 378358770650295628183080, 25852272837936812846761], 'label': '3072.bgb.48.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.q1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.Q', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 184761906
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.S', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.F', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.C', '24.E', '24.Y'], 'contains': ['96.H', '96.V', '96.X', '96.CL', '96.CR', '96.FF', '96.FJ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [122002101738321960, 25903229683158464676480, 162070321828715682652927, 324406870523993839248121, 79804308125641822294440, 378358770650295628183080], 'label': '3072.bgb.48.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.s1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.S', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184761907
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.T', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.S', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.D', '24.F', '24.Y'], 'contains': ['96.H', '96.W', '96.X', '96.CQ', '96.CR', '96.FI', '96.FJ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [122002101738321960, 25903229683158464676480, 162070321828715682652927, 378358770648994141276807, 324406870523993839248121, 79804308125641822294440], 'label': '3072.bgb.48.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.t1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.T', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184761908
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.U', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.F', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.E', '24.F', '24.Z'], 'contains': ['96.J', '96.X', '96.Y', '96.CS', '96.CT', '96.FN', '96.FO'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 108169512287410083283217, 54003503618341535825287, 324406991811924875755576, 25903229683158464676480, 378358649363678452761737], 'label': '3072.bgb.48.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.u1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.U', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184761909
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '8.D', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '768.1089093', 'aut_weyl_index': 8, 'centralizer': '1536.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.A', '4.H'], 'contains': ['16.D', '16.G', '16.L', '16.Q', '24.BA', '32.A'], 'core': '48.A', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [121659103022301503, 25903229681844523013167, 79804308125641822294440, 1313941673647, 79804429413572684637382, 486427128433516595381056, 486478219730068018627222, 270189770923792213003566], 'label': '3072.bgb.8.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.H', 'old_label': '8.d1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.D', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 184761910
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.V', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.S', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.C', '24.D', '24.Z'], 'contains': ['96.K', '96.X', '96.Y', '96.CS', '96.CT', '96.GB', '96.GC'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 54003503618341535825287, 324406991811924875755576, 25903229683158464676480, 133970560084911187416382, 378358649362364591657542], 'label': '3072.bgb.48.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.v1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.V', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184761911
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.W', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.W'], 'contains': ['96.L', '96.M', '96.N', '96.O', '96.P', '96.S', '96.U', '96.BZ', '96.CA', '96.CB', '96.CC', '96.CZ', '96.DC', '96.ES', '96.FE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 54003503618341535825287, 25852272837936812846761, 122002101738321960, 324406870525295326154166, 25903229683158464676480], 'label': '3072.bgb.48.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '48.w1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.W', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184761912
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.X', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.W'], 'contains': ['96.S', '96.T', '96.U', '96.Z', '96.BA', '96.BB', '96.BC', '96.DE', '96.DF', '96.DG', '96.DH', '96.ES', '96.EV', '96.FE', '96.GF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770648994141276807, 54003503618341535825287, 25852272837936812846761, 122002101738321960, 324406870525295326154166, 25903229683158464676480], 'label': '3072.bgb.48.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '48.x1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.X', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184761913
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '48.Y', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.G', '24.H', '24.BN'], 'contains': ['96.BJ', '96.BM', '96.BX', '96.CD', '96.CF', '96.DM', '96.EI', '96.HP', '96.HR', '96.HV', '96.HX'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79855520714221614566521, 79855398717732338388456, 53952412691500576681559, 122002101738321960, 1313941673647, 79855520715724195809353], 'label': '3072.bgb.48.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.y1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.Y', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761914
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '48.Z', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.I', '24.J', '24.BN'], 'contains': ['96.BK', '96.BM', '96.BX', '96.CD', '96.CF', '96.DQ', '96.EO', '96.HQ', '96.HS', '96.HW', '96.HY'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [53952291032377091563446, 79855398717732338388456, 79855399081842795124439, 122002101738321960, 1313941673647, 79855520715724195809353], 'label': '3072.bgb.48.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.z1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.Z', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761915
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.BA', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.F', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.C', '24.E', '24.BO'], 'contains': ['96.BH', '96.BO', '96.BS', '96.CI', '96.CT', '96.ER', '96.FF', '96.HZ', '96.IB', '96.IZ', '96.JB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 270240484111912758504367, 25852272837936812846761, 79804308125641822294440, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.48.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.ba1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BA', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184761916
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.BB', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.S', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.D', '24.F', '24.BO'], 'contains': ['96.BH', '96.BO', '96.BV', '96.CJ', '96.CT', '96.ER', '96.FI', '96.IA', '96.IC', '96.JA', '96.JD'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [122002101738321960, 25903229683158464676480, 378358770648994141276807, 270240484111912758504367, 79804308125641822294440, 25852272837936812846761], 'label': '3072.bgb.48.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.bb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BB', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184761917
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '48.BC', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.G', '24.H', '24.BO'], 'contains': ['96.BJ', '96.BP', '96.BR', '96.CG', '96.CU', '96.EU', '96.FK', '96.HZ', '96.IA', '96.IZ', '96.JA'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 378358770650295628183080, 54003503618341535825287, 25852272837936812846761, 25903229683158464676480, 270240484110598816830720], 'label': '3072.bgb.48.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.bc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BC', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761918
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.BD', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.F', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.E', '24.F', '24.BP'], 'contains': ['96.BJ', '96.BO', '96.BW', '96.CK', '96.CR', '96.ET', '96.FO'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 54003503618341535825287, 25903229683158464676480, 53952035291802302422343, 378358649363678452761737, 296041409911409376977422], 'label': '3072.bgb.48.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.bd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BD', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184761919
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '48.BE', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.I', '24.J', '24.BO'], 'contains': ['96.BK', '96.BP', '96.BR', '96.CG', '96.CU', '96.FA', '96.FR', '96.IB', '96.IC', '96.JB', '96.JD'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [51469042011382569606, 25903107682370587468807, 378358770648994141276807, 54003503618341535825287, 25903229683158464676480, 270240484110598816830720], 'label': '3072.bgb.48.BE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.be1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BE', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761920
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '8.E', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '384.17949', 'aut_weyl_index': 16, 'centralizer': '1536.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.B', '4.H'], 'contains': ['16.D', '16.K', '16.N', '24.A', '32.B'], 'core': '24.A', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 1313941673647, 79804429413572684637382, 53952035291802302422343, 486427128433516595381056, 486478219730068018627222, 270189770923792213003566], 'label': '3072.bgb.8.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.H', 'old_label': '8.e1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.E', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 184761921
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.BF', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.S', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.C', '24.D', '24.BP'], 'contains': ['96.BK', '96.BO', '96.BW', '96.CK', '96.CR', '96.EZ', '96.GC'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 54003503618341535825287, 25903229683158464676480, 296041409911409376977422, 378358649362364591657542, 79855264262271969233416], 'label': '3072.bgb.48.BF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.bf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BF', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184761922
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.BG', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.CP', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.D', '24.E', '24.BR'], 'contains': ['96.BH', '96.BT', '96.BW', '96.CM', '96.CS', '96.FG', '96.FJ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 108169512287410083283217, 54003503618341535825287, 25903229683158464676480, 296041409911409376977422, 378358649362364591657542], 'label': '3072.bgb.48.BG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.bg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BG', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184761923
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.BH', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.C', '24.F', '24.BR'], 'contains': ['96.BH', '96.BU', '96.BW', '96.CO', '96.CS', '96.FH', '96.FJ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 108169512287410083283217, 54003503618341535825287, 25903229683158464676480, 378358649363678452761737, 296041409911409376977422], 'label': '3072.bgb.48.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.bh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BH', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 184761924
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.BI', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.CU', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.E', '24.H', '24.BQ'], 'contains': ['96.BJ', '96.BS', '96.BT', '96.CL', '96.CN', '96.FL', '96.FN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770650295628183080, 270240484111912758504367, 187973308220359388001840, 79804308125641822294440, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.48.BI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.bi1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BI', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184761925
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.BJ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.F', '24.G', '24.BQ'], 'contains': ['96.BJ', '96.BU', '96.BV', '96.CP', '96.CQ', '96.FM', '96.FN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770648994141276807, 270240484111912758504367, 187973308220359388001840, 79804308125641822294440, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.48.BJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.bj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BJ', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761926
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.BK', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.C', '24.J', '24.BQ'], 'contains': ['96.BK', '96.BS', '96.BU', '96.CL', '96.CP', '96.FV', '96.GB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770650295628183080, 270240484111912758504367, 162070321828715682652927, 79804308125641822294440, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.48.BK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.bk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BK', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761927
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.BL', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.FI', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.D', '24.I', '24.BQ'], 'contains': ['96.BK', '96.BT', '96.BV', '96.CN', '96.CQ', '96.FX', '96.GB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [122002101738321960, 25903229683158464676480, 162070321828715682652927, 378358770648994141276807, 270240484111912758504367, 79804308125641822294440], 'label': '3072.bgb.48.BL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.bl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BL', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184761928
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '48.BM', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BN'], 'contains': ['96.BL', '96.BN', '96.BY', '96.CW', '96.CY', '96.DL', '96.EH', '96.HP', '96.HQ', '96.HR', '96.HS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 79855520714221614566521, 79855398717732338388456, 79855399081842795124439, 1313941673647, 79855520715724195809353], 'label': '3072.bgb.48.BM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BN', 'old_label': '48.bm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BM', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 184761929
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.BN', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.H', '24.I', '24.BW'], 'contains': ['96.BM', '96.BP', '96.BT', '96.DI', '96.DR', '96.EF', '96.EM'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [53952291032377091563446, 79855398717732338388456, 256460345499052777, 122002101738321960, 1313941673647, 79855520715724195809353], 'label': '3072.bgb.48.BN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.bn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BN', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184761930
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.BO', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.G', '24.J', '24.BW'], 'contains': ['96.BM', '96.BP', '96.BU', '96.DJ', '96.DR', '96.EF', '96.EN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79855520714221614566521, 79855398717732338388456, 256460345499052777, 122002101738321960, 1313941673647, 79855520715724195809353], 'label': '3072.bgb.48.BO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.bo1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BO', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184761931
    {'ambient': '3072.bgb', 'aut_centralizer_order': 1, 'aut_label': '2.C', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '3072.a1', 'complements': ['1536.I', '1536.E', '1536.J'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.A', '4.E', '4.G', '6.G', '8.F', '8.G'], 'core': '2.C', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [25903229681844523013167, 134021529040297499210286, 1313941673647, 187922473375925652905521, 404159831259638948150382, 133970303627361494479417, 566444897749485959875336, 108118165248982343710201, 162070456272950954131199, 378358649363678452761737], 'label': '3072.bgb.2.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.A', '4.E', '4.G'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '3072.bgb', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.C', 'subgroup_fusion': None, 'weyl_group': '3072.bgb'}
  • id: 184761932
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '8.F', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '768.1089093', 'aut_weyl_index': 8, 'centralizer': '1536.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.C', '4.H'], 'contains': ['16.D', '16.M', '16.O', '24.BJ', '32.C'], 'core': '48.A', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [79855142625594763233847, 25903229681844523013167, 566444897749485959875336, 404159831259638948150382, 79804308125641822294440, 1313941673647, 79804429413572684637382, 378358649363678452761737], 'label': '3072.bgb.8.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.H', 'old_label': '8.f1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.F', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 184761933
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '48.BP', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BN'], 'contains': ['96.BN', '96.BQ', '96.BY', '96.DL', '96.DS', '96.EH', '96.EQ', '96.HV', '96.HW', '96.HX', '96.HY'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 53952291032377091563446, 79855398717732338388456, 79855399081842795124439, 1313941673647, 79855520715724195809353], 'label': '3072.bgb.48.BP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BN', 'old_label': '48.bp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BP', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 184761934
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '48.BQ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.G', '24.I', '24.BX'], 'contains': ['96.BM', '96.BR', '96.BV', '96.DN', '96.DP', '96.EJ', '96.EP', '96.IF', '96.IH', '96.JP', '96.JR'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [122002101738321960, 324406991811924875755576, 25903229683158464676480, 134021272934136496216343, 187922594661241166512703, 242089752359655799966096], 'label': '3072.bgb.48.BQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.bq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BQ', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761935
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '48.BR', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.H', '24.J', '24.BX'], 'contains': ['96.BM', '96.BR', '96.BS', '96.DN', '96.DO', '96.EL', '96.EP', '96.IF', '96.IG', '96.JP', '96.JQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [242089752358354392177983, 122002101738321960, 324406991811924875755576, 25903229683158464676480, 134021272934136496216343, 187922594661241166512703], 'label': '3072.bgb.48.BR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.br1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BR', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761936
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '48.BS', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.H', '24.J', '24.CH'], 'contains': ['96.BP', '96.BS', '96.BX', '96.EX', '96.FB', '96.FW', '96.GD'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 270240484111912758504367, 79804308125641822294440, 122002101738321960, 25903229683158464676480, 53952035291802302422343], 'label': '3072.bgb.48.BS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.bs1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BS', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761937
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '48.BT', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.G', '24.I', '24.CH'], 'contains': ['96.BP', '96.BV', '96.BX', '96.EY', '96.FB', '96.GA', '96.GD'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770648994141276807, 270240484111912758504367, 79804308125641822294440, 122002101738321960, 25903229683158464676480, 53952035291802302422343], 'label': '3072.bgb.48.BT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.bt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BT', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761938
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.BU', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.FN', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.H', '24.I', '24.CK'], 'contains': ['96.BR', '96.BT', '96.BX', '96.FP', '96.FS', '96.FY', '96.GE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 378358770648994141276807, 270240484111912758504367, 108169512287410083283217, 54003503618341535825287, 25903229683158464676480], 'label': '3072.bgb.48.BU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.bu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BU', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184761939
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.BV', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.G', '24.J', '24.CK'], 'contains': ['96.BR', '96.BU', '96.BX', '96.FQ', '96.FS', '96.FZ', '96.GE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 378358770650295628183080, 270240484111912758504367, 108169512287410083283217, 54003503618341535825287, 25903229683158464676480], 'label': '3072.bgb.48.BV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.bv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BV', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 184761940
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.BW', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.H', '24.I', '24.CS'], 'contains': ['96.CD', '96.CG', '96.CN', '96.DI', '96.DN', '96.FB', '96.FP'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 378358770650295628183080, 54003503618341535825287, 25852272837936812846761, 324406991811924875755576, 25903229683158464676480], 'label': '3072.bgb.48.BW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.bw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BW', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184761941
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.BX', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.G', '24.J', '24.CS'], 'contains': ['96.CD', '96.CG', '96.CP', '96.DJ', '96.DN', '96.FB', '96.FQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 378358770648994141276807, 54003503618341535825287, 25852272837936812846761, 324406991811924875755576, 25903229683158464676480], 'label': '3072.bgb.48.BX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.bx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BX', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184761942
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '48.BY', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.H', '24.J', '24.CU'], 'contains': ['96.CD', '96.CL', '96.CU', '96.DO', '96.DR', '96.FW', '96.GE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [122002101738321960, 25903229683158464676480, 162070321828715682652927, 324406991811924875755576, 79804308125641822294440, 378358770650295628183080], 'label': '3072.bgb.48.BY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.by1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BY', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761943
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '8.G', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '384.5677', 'aut_weyl_index': 16, 'centralizer': '3072.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.C'], 'contains': ['16.E', '16.I', '16.J', '24.BL', '32.C'], 'core': '192.A', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [53952291033879672806278, 296092500497899884979223, 187922217292190117815823, 25903229681844523013167, 1313941673647, 566445019748791678392366, 134021272934136496216343, 270189770923792213003566], 'label': '3072.bgb.8.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.G', 'old_label': '8.g1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.G', 'subgroup_fusion': None, 'weyl_group': '384.5677'}
  • id: 184761944
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '48.BZ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.G', '24.I', '24.CU'], 'contains': ['96.CD', '96.CQ', '96.CU', '96.DP', '96.DR', '96.GA', '96.GE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [122002101738321960, 25903229683158464676480, 162070321828715682652927, 378358770648994141276807, 324406991811924875755576, 79804308125641822294440], 'label': '3072.bgb.48.BZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.bz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BZ', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761945
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '48.CA', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.DK'], 'contains': ['96.CE', '96.CH', '96.CV', '96.DV', '96.DZ', '96.FC', '96.FT', '96.IX', '96.IY', '96.JC', '96.JE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922473375925652905521, 134021394930826866723126, 122002101738321960, 25903229683158464676480, 53952035291802302422343, 378358649363678452761737], 'label': '3072.bgb.48.CA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.DK', 'old_label': '48.ca1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CA', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 184761946
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '48.CB', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.G', '24.I', '24.CW'], 'contains': ['96.CF', '96.CG', '96.CQ', '96.EF', '96.EJ', '96.EY', '96.FS', '96.JG', '96.JI', '96.KB', '96.KD'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [122002101738321960, 25903229683158464676480, 134021272934136496216343, 53952035291802302422343, 187922594661241166512703, 242089752359655799966096], 'label': '3072.bgb.48.CB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.cb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CB', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761947
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '48.CC', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.H', '24.J', '24.CW'], 'contains': ['96.CF', '96.CG', '96.CL', '96.EF', '96.EL', '96.EX', '96.FS', '96.JH', '96.JJ', '96.KC', '96.KE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [242089752358354392177983, 122002101738321960, 25903229683158464676480, 134021272934136496216343, 53952035291802302422343, 187922594661241166512703], 'label': '3072.bgb.48.CC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.cc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CC', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761948
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.CD', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.FE', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.H', '24.I', '24.CZ'], 'contains': ['96.CF', '96.CN', '96.CU', '96.EM', '96.EP', '96.FY', '96.GD'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 404210922197505558871681, 162121547575114918571536, 324406991811924875755576, 25903229683158464676480, 134021272934136496216343], 'label': '3072.bgb.48.CD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.cd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CD', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184761949
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.CE', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.G', '24.J', '24.CZ'], 'contains': ['96.CF', '96.CP', '96.CU', '96.EN', '96.EP', '96.FZ', '96.GD'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 162121547575114918571536, 324406991811924875755576, 25903229683158464676480, 134021272934136496216343, 404210922196204071249966], 'label': '3072.bgb.48.CE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.ce1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CE', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 184761950
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.CF', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CT'], 'contains': ['96.CW', '96.DA', '96.DC', '96.DK', '96.DT', '96.FD', '96.GG'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [54003503618341535825287, 122002101738321960, 25903229683158464676480, 324406870523993839248121, 53952035291802302422343, 378358649362364591657542], 'label': '3072.bgb.48.CF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CT', 'old_label': '48.cf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CF', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184761951
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.CG', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.F', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.C', '24.E', '24.DK'], 'contains': ['96.CI', '96.CK', '96.CL', '96.CS', '96.CX', '96.DU', '96.EA', '96.IX', '96.JC', '96.JK', '96.JM'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 187922473375925652905521, 134021394930826866723126, 25903229683158464676480, 378358649362364591657542, 79855264262271969233416], 'label': '3072.bgb.48.CG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.cg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CG', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184761952
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.CH', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.S', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.D', '24.F', '24.DK'], 'contains': ['96.CJ', '96.CK', '96.CQ', '96.CS', '96.CX', '96.DU', '96.ED', '96.IY', '96.JE', '96.JL', '96.JN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 187922473375925652905521, 134021394930826866723126, 25903229683158464676480, 378358649363678452761737, 79855264262271969233416], 'label': '3072.bgb.48.CH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.ch1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CH', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184761953
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.CI', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.CO', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.D', '24.E', '24.DL'], 'contains': ['96.CM', '96.CN', '96.CR', '96.CT', '96.CX', '96.EB', '96.EE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 187922473375925652905521, 134021394930826866723126, 404210922197505558871681, 25903229683158464676480, 296041409911409376977422], 'label': '3072.bgb.48.CI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.ci1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CI', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184761954
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '8.H', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '768.1089093', 'aut_weyl_index': 8, 'centralizer': '1536.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.D', '4.H'], 'contains': ['16.G', '16.K', '16.M', '16.S', '24.DC', '32.D'], 'core': '48.B', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [25903229681844523013167, 566444897749485959875336, 404159831259638948150382, 79804308125641822294440, 1313941673647, 79804429413572684637382, 53952035291802302422343, 378358649363678452761737], 'label': '3072.bgb.8.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.H', 'old_label': '8.h1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.H', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 184761955
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.CJ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.C', '24.F', '24.DL'], 'contains': ['96.CO', '96.CP', '96.CR', '96.CT', '96.CX', '96.EC', '96.EE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 187922473375925652905521, 134021394930826866723126, 25903229683158464676480, 296041409911409376977422, 404210922196204071249966], 'label': '3072.bgb.48.CJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.cj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CJ', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 184761956
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.CK', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.O', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CW'], 'contains': ['96.CY', '96.CZ', '96.DB', '96.EG', '96.EK', '96.EW', '96.FU', '96.JG', '96.JH', '96.JI', '96.JJ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 25903229683158464676480, 134021272934136496216343, 187922594661241166512703, 242089752359655799966096, 79855264262271969233416], 'label': '3072.bgb.48.CK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '48.ck1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CK', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184761957
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '48.CL', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.DK'], 'contains': ['96.CH', '96.CV', '96.DA', '96.DB', '96.DD', '96.DV', '96.DZ', '96.JK', '96.JL', '96.JM', '96.JN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922473375925652905521, 134021394930826866723126, 122002101738321960, 25903229683158464676480, 53952035291802302422343, 378358649362364591657542], 'label': '3072.bgb.48.CL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.DK', 'old_label': '48.cl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CL', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 184761958
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.CM', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.H', '24.DS'], 'contains': ['96.DI', '96.DM', '96.DO', '96.EU', '96.EX', '96.FL', '96.FY'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770650295628183080, 79804308125641822294440, 122002101738321960, 324406991811924875755576, 25903229683158464676480, 53952035291802302422343], 'label': '3072.bgb.48.CM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.cm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CM', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184761959
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.CN', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.G', '24.DS'], 'contains': ['96.DJ', '96.DM', '96.DP', '96.EU', '96.EY', '96.FM', '96.FZ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770648994141276807, 79804308125641822294440, 122002101738321960, 324406991811924875755576, 25903229683158464676480, 53952035291802302422343], 'label': '3072.bgb.48.CN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.cn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CN', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184761960
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.CO', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.J', '24.DS'], 'contains': ['96.DJ', '96.DO', '96.DQ', '96.EX', '96.FA', '96.FV', '96.FZ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770650295628183080, 79804308125641822294440, 122002101738321960, 324406991811924875755576, 25903229683158464676480, 79855264262271969233416], 'label': '3072.bgb.48.CO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.co1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CO', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184761961
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.CP', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.I', '24.DS'], 'contains': ['96.DI', '96.DP', '96.DQ', '96.EY', '96.FA', '96.FX', '96.FY'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770648994141276807, 79804308125641822294440, 122002101738321960, 324406991811924875755576, 25903229683158464676480, 79855264262271969233416], 'label': '3072.bgb.48.CP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.cp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CP', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184761962
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.CQ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CT'], 'contains': ['96.DK', '96.DS', '96.DT', '96.FC', '96.FD', '96.GF', '96.GG'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [54003503618341535825287, 122002101738321960, 25903229683158464676480, 324406870523993839248121, 53952035291802302422343, 378358649363678452761737], 'label': '3072.bgb.48.CQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CT', 'old_label': '48.cq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CQ', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184761963
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '48.CR', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.G', '24.H', '24.DU'], 'contains': ['96.DM', '96.DN', '96.DR', '96.FK', '96.FN', '96.FS', '96.GD'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 378358770650295628183080, 108169512287410083283217, 54003503618341535825287, 324406991811924875755576, 25903229683158464676480], 'label': '3072.bgb.48.CR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.cr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CR', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761964
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '48.CS', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.I', '24.J', '24.DU'], 'contains': ['96.DN', '96.DQ', '96.DR', '96.FR', '96.FS', '96.GB', '96.GD'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 378358770648994141276807, 54003503618341535825287, 324406991811924875755576, 25903229683158464676480, 133970560084911187416382], 'label': '3072.bgb.48.CS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.cs1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CS', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761965
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '8.I', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '384.17949', 'aut_weyl_index': 16, 'centralizer': '768.BG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.E', '4.H'], 'contains': ['16.G', '16.N', '16.O', '24.DG', '32.E'], 'core': '48.C', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [79855142625594763233847, 25903229681844523013167, 566444897749485959875336, 404159831259638948150382, 79804308125641822294440, 1313941673647, 79804429413572684637382, 404210922196204071249966], 'label': '3072.bgb.8.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.H', 'old_label': '8.i1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.I', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 184761966
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.CT', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.S', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.C', '24.D', '24.EL'], 'contains': ['96.DU', '96.DW', '96.EE', '96.ER', '96.EZ', '96.FJ', '96.GB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 79804052047512561508433, 1313941673647, 25852017102974698844878, 51091303465372291183, 54003125882410914585582], 'label': '3072.bgb.48.CT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.ct1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CT', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184761967
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.CU', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.F', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.E', '24.F', '24.EL'], 'contains': ['96.DU', '96.DY', '96.EE', '96.ER', '96.ET', '96.FJ', '96.FN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 79804052047512561508433, 1313941673647, 51091303465372291183, 25852017102974698844878, 79804173679912018708417], 'label': '3072.bgb.48.CU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.cu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CU', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184761968
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.CV', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.C', '24.EO'], 'contains': ['96.DW', '96.EA', '96.EC', '96.FF', '96.FH', '96.FV', '96.GC'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 324355523484084195000247, 187922473375925652905521, 134021394930826866723126, 25903229683158464676480, 378358649362364591657542], 'label': '3072.bgb.48.CV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.cv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CV', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184761969
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.CW', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.FG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.D', '24.EO'], 'contains': ['96.DW', '96.EB', '96.ED', '96.FG', '96.FI', '96.FX', '96.GC'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 324355523484084195000247, 187922473375925652905521, 134021394930826866723126, 25903229683158464676480, 378358649363678452761737], 'label': '3072.bgb.48.CW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.cw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CW', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184761970
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.CX', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.CT', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.E', '24.EO'], 'contains': ['96.DY', '96.EA', '96.EB', '96.FF', '96.FG', '96.FL', '96.FO'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 187922473375925652905521, 134021394930826866723126, 25903229683158464676480, 324355523485385682622200, 378358649362364591657542], 'label': '3072.bgb.48.CX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.cx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CX', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184761971
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.CY', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.F', '24.EO'], 'contains': ['96.DY', '96.EC', '96.ED', '96.FH', '96.FI', '96.FM', '96.FO'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 187922473375925652905521, 134021394930826866723126, 25903229683158464676480, 324355523485385682622200, 378358649363678452761737], 'label': '3072.bgb.48.CY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '48.cy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CY', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184761972
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '48.CZ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.G', '24.H', '24.EV'], 'contains': ['96.EF', '96.EI', '96.EP', '96.EU', '96.FB', '96.FN', '96.GE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903363795619943623743, 79855398717732338388456, 256460345499052777, 122002101738321960, 1313941673647, 79855520715724195809353], 'label': '3072.bgb.48.CZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.cz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CZ', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761973
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.DA', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.W', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CW'], 'contains': ['96.EG', '96.EK', '96.EQ', '96.EV', '96.EW', '96.FT', '96.FU', '96.KB', '96.KC', '96.KD', '96.KE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 242089752358354392177983, 25903229683158464676480, 134021272934136496216343, 187922594661241166512703, 79855264262271969233416], 'label': '3072.bgb.48.DA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '48.da1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DA', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184761974
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '48.DB', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.I', '24.J', '24.EV'], 'contains': ['96.EF', '96.EO', '96.EP', '96.FA', '96.FB', '96.GB', '96.GE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903363795619943623743, 79855398717732338388456, 122002101738321960, 25903485430815165863622, 1313941673647, 79855520715724195809353], 'label': '3072.bgb.48.DB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.db1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DB', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184761975
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.DC', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.G', '24.EW'], 'contains': ['96.EI', '96.EJ', '96.EN', '96.FK', '96.FM', '96.FQ', '96.GA'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 242089752358354392177983, 324355644776280741499582, 162121547575114918571536, 25903229683158464676480, 134021272934136496216343], 'label': '3072.bgb.48.DC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.dc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DC', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184761976
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '8.J', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '768.1089093', 'aut_weyl_index': 8, 'centralizer': '1536.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.F', '4.H'], 'contains': ['16.K', '16.L', '16.O', '24.FA', '32.H'], 'core': '48.B', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [79855142625594763233847, 25903229681844523013167, 566444897749485959875336, 404159831259638948150382, 79804308125641822294440, 1313941673647, 79804429413572684637382, 53952035291802302422343], 'label': '3072.bgb.8.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.H', 'old_label': '8.j1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.J', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 184761977
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.DD', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.H', '24.EW'], 'contains': ['96.EI', '96.EL', '96.EM', '96.FK', '96.FL', '96.FP', '96.FW'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 324355644776280741499582, 162121547575114918571536, 25903229683158464676480, 134021272934136496216343, 242089752359655799966096], 'label': '3072.bgb.48.DD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.dd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DD', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184761978
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.DE', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.I', '24.EW'], 'contains': ['96.EJ', '96.EM', '96.EO', '96.FP', '96.FR', '96.FX', '96.GA'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 242089752358354392177983, 162121547575114918571536, 25903229683158464676480, 134021272934136496216343, 324355644777594682437137], 'label': '3072.bgb.48.DE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.de1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DE', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184761979
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.DF', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.J', '24.EW'], 'contains': ['96.EL', '96.EN', '96.EO', '96.FQ', '96.FR', '96.FV', '96.FW'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 162121547575114918571536, 25903229683158464676480, 134021272934136496216343, 324355644777594682437137, 242089752359655799966096], 'label': '3072.bgb.48.DF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '48.df1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DF', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184761980
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.DG', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '768.I', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.GA'], 'contains': ['96.GL', '96.GR', '96.GV', '96.GZ', '96.HB', '96.HD', '96.HF', '96.HN', '96.HT', '96.ID', '96.IK', '96.IR', '96.IT', '96.JF', '96.JY'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922473375925652905521, 162121669227129588479873, 187973685961890096441600, 1313941673647, 25852017101492540879976, 162070456272950954131199], 'label': '3072.bgb.48.DG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '48.dg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DG', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184761981
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.DH', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '768.I', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.GA'], 'contains': ['96.GM', '96.GS', '96.GW', '96.GZ', '96.HC', '96.HE', '96.HF', '96.HO', '96.HU', '96.ID', '96.IL', '96.IS', '96.IU', '96.JF', '96.JZ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922473021741077083393, 187922473375925652905521, 1313941673647, 25852017101492540879976, 162070456272950954131199, 162070456280045573438767], 'label': '3072.bgb.48.DH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '48.dh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DH', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184761982
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.DI', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '768.I', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.GA'], 'contains': ['96.GL', '96.GM', '96.GX', '96.HA', '96.HB', '96.HC', '96.HG', '96.HN', '96.HO', '96.IE', '96.IJ', '96.IR', '96.IS', '96.JO', '96.JX'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922473021741077083393, 187922473375925652905521, 51212594192254410823, 1313941673647, 162070456272950954131199, 162070456280045573438767], 'label': '3072.bgb.48.DI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '48.di1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DI', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184761983
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.DJ', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '768.I', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.GA'], 'contains': ['96.GR', '96.GS', '96.GY', '96.HA', '96.HD', '96.HE', '96.HG', '96.HT', '96.HU', '96.IJ', '96.IM', '96.IT', '96.IU', '96.JX', '96.KA'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922473021741077083393, 187922473375925652905521, 51212594192254410823, 187973685961890096441600, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.48.DJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '48.dj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DJ', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184761984
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.DK', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.K', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.GO'], 'contains': ['96.IG', '96.II', '96.IO', '96.IQ', '96.IV', '96.JU', '96.JW'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [133970303627361494479417, 378307558065813088567696, 54003382328928594643200, 25903229683158464676480, 25852017102974698844878, 242089752359655799966096], 'label': '3072.bgb.48.DK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GO', 'old_label': '48.dk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DK', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184761985
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.DL', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.K', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.GO'], 'contains': ['96.IH', '96.II', '96.IP', '96.IQ', '96.IV', '96.JV', '96.JW'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [242089752358354392177983, 133970303627361494479417, 378307558065813088567696, 54003382328928594643200, 25903229683158464676480, 25852017102974698844878], 'label': '3072.bgb.48.DL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GO', 'old_label': '48.dl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DL', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184761986
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.DM', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.C', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.K', '24.L', '24.T'], 'contains': ['96.B', '96.C', '96.D', '96.E', '96.KF', '96.KG', '96.KL', '96.KX', '96.LG', '96.MJ', '96.MK', '96.NE', '96.NF'], 'core': '192.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229337376182892926, 25903229681844523013167, 51212588579793007921, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.DM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.dm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DM', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184761987
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '8.K', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '384.17949', 'aut_weyl_index': 16, 'centralizer': '1536.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.G', '4.H'], 'contains': ['16.L', '16.M', '16.N', '24.FC', '32.I'], 'core': '48.C', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [486427128437815115841359, 378307814169184473345982, 25903229681844523013167, 53952412691500576681559, 79804308125641822294440, 1313941673647, 79804429413572684637382, 378358649363678452761737], 'label': '3072.bgb.8.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.H', 'old_label': '8.k1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.K', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 184761988
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.DN', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.M', '24.R', '24.U'], 'contains': ['96.KF', '96.KH', '96.KI', '96.KN', '96.KQ', '96.KZ', '96.LE', '96.ML', '96.MM', '96.MO', '96.MP', '96.NG', '96.NI', '96.NK', '96.NM'], 'core': '192.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 51212588579793007921, 122002101738321960, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.48.DN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.dn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DN', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184761989
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.DO', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.K', '24.M', '24.U'], 'contains': ['96.KF', '96.KI', '96.KP', '96.LF', '96.LH', '96.MR', '96.MS', '96.MW', '96.NS', '96.NT', '96.NW'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 79855398717732338388456, 25903229681844523013167, 51212588579793007921, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.DO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.do1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DO', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 184761990
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.DP', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.C', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.K', '24.P', '24.T'], 'contains': ['96.KF', '96.LI', '96.LJ', '96.MU', '96.NU'], 'core': '192.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 162121669227129588479873, 51212588579793007921, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.DP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.dp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DP', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184761991
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.DQ', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.6407063', 'aut_weyl_index': 12, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.L', '24.N', '24.O', '24.P', '24.Q', '24.R', '24.U'], 'contains': ['96.F', '96.G', '96.KF', '96.KH', '96.KM', '96.KT', '96.LL', '96.MN', '96.MQ', '96.MY', '96.NH'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.DQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.dq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DQ', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 184761992
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.DR', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.M', '24.S', '24.U'], 'contains': ['96.KF', '96.KI', '96.KO', '96.KS', '96.LK', '96.MV', '96.MX', '96.MZ', '96.NR'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229691554491852799, 108118165248982343710201, 25903229681844523013167, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.DR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '48.dr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DR', 'subgroup_fusion': None, 'weyl_group': '128.1578'}
  • id: 184761993
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.DS', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '384.20100', 'aut_weyl_index': 16, 'centralizer': '384.FW', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.B', '24.T', '24.U'], 'contains': ['96.KF', '96.KR', '96.LM', '96.MT', '96.NA', '96.NB', '96.NV'], 'core': '192.A', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 122002101738321960, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.48.DS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '48.ds1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DS', 'subgroup_fusion': None, 'weyl_group': '192.1538'}
  • id: 184761994
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.DT', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.C', '24.W'], 'contains': ['96.L', '96.M', '96.N', '96.O', '96.Z', '96.BA', '96.BB', '96.BC', '96.KG', '96.KJ', '96.KK', '96.KV', '96.KW', '96.LU', '96.LW'], 'core': '192.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 378307680063817574222641, 25852272837936812846761, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.DT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '48.dt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DT', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184761995
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.DU', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.L', '24.V', '24.W', '24.X', '24.Y', '24.Z', '24.BA'], 'contains': ['96.H', '96.I', '96.J', '96.K', '96.P', '96.T', '96.KG', '96.KH', '96.KU', '96.KY', '96.LX', '96.NC', '96.ND'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 25852017095880079467006, 25903107685154153232142, 122002101738321960, 1313941673647, 51090958997032170942], 'label': '3072.bgb.48.DU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.du1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DU', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184761996
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.DV', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.6407063', 'aut_weyl_index': 12, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.M', '24.R', '24.V', '24.BB', '24.BC', '24.BD', '24.BE'], 'contains': ['96.KH', '96.KI', '96.LA', '96.LS', '96.MB', '96.NJ', '96.NL', '96.NN'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [53952291033879672806278, 79855398717732338388456, 25903229681844523013167, 51212588579793007921, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.DV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.dv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DV', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 184761997
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '48.DW', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.A', '24.N', '24.W', '24.X', '24.BB', '24.BF', '24.BG'], 'contains': ['96.Q', '96.R', '96.S', '96.KH', '96.KJ', '96.LB', '96.LV', '96.MA'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 51212588579793007921, 79804308125641822294440, 122002101738321960, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.48.DW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.dw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DW', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184761998
    {'ambient': '3072.bgb', 'aut_centralizer_order': 1, 'aut_label': '8.L', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '3072.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.A', '4.I'], 'contains': ['16.A', '24.FZ', '32.K', '32.L', '32.M', '32.N'], 'core': '16.A', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 133970303627361494479417, 404159831259638948150382, 1313941673647, 486427128433516595381056, 162070456272950954131199], 'label': '3072.bgb.8.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '8.l1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.L', 'subgroup_fusion': None, 'weyl_group': '1536.408640541'}
  • id: 184761999
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.DX', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.O', '24.W', '24.Y', '24.BC', '24.BF', '24.BH', '24.BJ'], 'contains': ['96.U', '96.V', '96.W', '96.KH', '96.KK', '96.LC', '96.LZ', '96.MC'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 324406870523993839248121], 'label': '3072.bgb.48.DX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.dx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DX', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184762000
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.DY', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.Q', '24.V', '24.BA', '24.BF', '24.BG', '24.BH', '24.BI'], 'contains': ['96.KH', '96.MD', '96.MG', '96.NO'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 25852017095880079467006, 53952412691500576681559, 25903107685154153232142, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.DY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.dy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DY', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184762001
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.DZ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.N', '24.Y', '24.Z', '24.BB', '24.BH', '24.BI', '24.BK'], 'contains': ['96.X', '96.KH', '96.ME', '96.MI'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108169512287410083283217, 25903229681844523013167, 51212588579793007921, 79804308125641822294440, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.DZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.dz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DZ', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184762002
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.EA', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.O', '24.X', '24.Z', '24.BE', '24.BG', '24.BI', '24.BJ'], 'contains': ['96.Y', '96.KH', '96.MF', '96.MH'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 324406991811924875755576, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.48.EA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.ea1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EA', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184762003
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.EB', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.S', '24.BC', '24.BL'], 'contains': ['96.KI', '96.KK', '96.LN', '96.LP', '96.LY'], 'core': '192.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 216237613974362780043017, 122002101738321960, 1313941673647, 134021272934136496216343, 216288705272228144236816], 'label': '3072.bgb.48.EB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.F', 'old_label': '48.eb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EB', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762004
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.EC', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.S', '24.BD', '24.BL'], 'contains': ['96.KI', '96.LQ', '96.LR'], 'core': '192.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [242089631075849093539192, 25903229681844523013167, 242140721662339602266753, 122002101738321960, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.48.EC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.F', 'old_label': '48.ec1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EC', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762005
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.ED', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '384.20100', 'aut_weyl_index': 16, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.E', '24.M', '24.BL'], 'contains': ['96.KI', '96.LO', '96.LT', '96.NX', '96.NY'], 'core': '192.A', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 51212588579793007921, 122002101738321960, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.48.ED', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.C', 'old_label': '48.ed1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ED', 'subgroup_fusion': None, 'weyl_group': '384.20100'}
  • id: 184762006
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.EE', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.G', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.L', '24.BM', '24.CP'], 'contains': ['96.BD', '96.BE', '96.BF', '96.BG', '96.KL', '96.KM', '96.KU', '96.KX', '96.LG', '96.NZ', '96.OA', '96.QI', '96.QJ'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229337376182892926, 122007701746409022, 25903229681844523013167, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.EE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.ee1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EE', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762007
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.EF', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.M', '24.BV', '24.CQ'], 'contains': ['96.KN', '96.KO', '96.KP', '96.KZ', '96.LA', '96.LF', '96.LO', '96.OE', '96.OG', '96.OM', '96.ON', '96.RK', '96.RM', '96.RT', '96.RU'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229691554491852799, 1313941673647, 122002101738321960, 25903229681844523013167, 79855398717732338388456, 108118165248982343710201], 'label': '3072.bgb.48.EF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.ef1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EF', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184762008
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.EG', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.G', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.P', '24.BM', '24.CP'], 'contains': ['96.KM', '96.LI', '96.LJ', '96.OJ', '96.RP'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [122007701746409022, 25903229681844523013167, 162121669227129588479873, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.EG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.eg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EG', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762009
    {'ambient': '3072.bgb', 'aut_centralizer_order': 1, 'aut_label': '8.M', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '3072.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.C', '4.J'], 'contains': ['16.A', '24.HT', '32.R'], 'core': '16.A', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [108118421696801471190456, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 133970303627361494479417, 404159831259638948150382, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.8.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.D', 'old_label': '8.m1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.M', 'subgroup_fusion': None, 'weyl_group': '1536.408550734'}
  • id: 184762010
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.EH', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.U', '24.BM', '24.BV'], 'contains': ['96.KM', '96.KO', '96.KZ', '96.LH', '96.LM', '96.OH', '96.OI', '96.OK', '96.RN', '96.RO', '96.RS'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79855520714221614566521, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.48.EH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.eh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EH', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 184762011
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.EI', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.R', '24.BV', '24.CQ'], 'contains': ['96.KM', '96.KN', '96.KQ', '96.KZ', '96.LA', '96.LD', '96.LE', '96.OS', '96.OT', '96.OU', '96.OW', '96.RX', '96.RZ', '96.SC', '96.SF'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187973685961890096441600, 122002101738321960, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.48.EI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.ei1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EI', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184762012
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.EJ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.M', '24.BV', '24.CR'], 'contains': ['96.KO', '96.KP', '96.KQ', '96.LE', '96.LH', '96.LO', '96.MB', '96.OY', '96.PB', '96.PE', '96.PG', '96.SH', '96.SY', '96.UA', '96.VH'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 162121668858915397667278, 122002101738321960, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.48.EJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.ej1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EJ', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184762013
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.EK', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '384.BC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.T', '24.BT', '24.CP'], 'contains': ['96.KR', '96.KX', '96.LJ', '96.PM', '96.QO'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 162121669227129588479873, 187973685961890096441600, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.EK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.ek1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EK', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184762014
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.EL', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.L', '24.BN', '24.BO', '24.BP', '24.BQ', '24.BR', '24.BS'], 'contains': ['96.BH', '96.BI', '96.BJ', '96.BK', '96.BL', '96.BQ', '96.KL', '96.KT', '96.KY', '96.LX', '96.OB', '96.PN', '96.QW'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903107687970595565937, 25903229681844523013167, 25903107685154153232142, 122002101738321960, 1313941673647, 51090958997032170942], 'label': '3072.bgb.48.EL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.el1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EL', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762015
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.EM', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.U', '24.BV', '24.CQ'], 'contains': ['96.KM', '96.KN', '96.KO', '96.KP', '96.KR', '96.KZ', '96.LK', '96.OC', '96.OD', '96.OP', '96.OQ', '96.PO', '96.PQ', '96.RH', '96.RQ'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187973685961890096441600, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.EM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.em1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EM', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184762016
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.EN', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.M', '24.BU', '24.CQ'], 'contains': ['96.KN', '96.KP', '96.KS', '96.LA', '96.LT', '96.OO', '96.OR', '96.PS', '96.RV'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 187973685961890096441600, 122002101738321960, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.48.EN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '48.en1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EN', 'subgroup_fusion': None, 'weyl_group': '128.1578'}
  • id: 184762017
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.EO', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.6407063', 'aut_weyl_index': 12, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.R', '24.BN', '24.BW', '24.BX', '24.BY', '24.BZ', '24.CQ'], 'contains': ['96.BM', '96.BN', '96.KN', '96.KT', '96.LD', '96.LS', '96.OV', '96.OX', '96.PT', '96.SB'], 'core': '384.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [53952291033879672806278, 79855520714221614566521, 79855398717732338388456, 25903229681844523013167, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.EO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.eo1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EO', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 184762018
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.EP', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '384.BD', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.T', '24.CA', '24.CP'], 'contains': ['96.KR', '96.LG', '96.LI', '96.PU', '96.SQ'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229337376182892926, 25903229681844523013167, 187973685961890096441600, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.EP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.ep1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EP', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184762019
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.EQ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 48, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.U', '24.BT', '24.BV', '24.CA', '24.CB', '24.CC', '24.CR'], 'contains': ['96.KO', '96.KQ', '96.KR', '96.LH', '96.LL', '96.OZ', '96.PJ', '96.PV', '96.PX', '96.SV', '96.TI'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 79804429421968711780537], 'label': '3072.bgb.48.EQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.eq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EQ', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762020
    {'ambient': '3072.bgb', 'aut_centralizer_order': 1, 'aut_label': '8.N', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '3072.bgb', 'aut_weyl_index': 2, 'centralizer': '3072.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.D', '4.I'], 'contains': ['16.A', '24.HU', '32.Q', '32.S'], 'core': '16.A', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 187922473375925652905521, 404159831259638948150382, 133970303627361494479417, 108118165248982343710201, 162070456272950954131199, 53952412691500576681559], 'label': '3072.bgb.8.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '8.n1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.N', 'subgroup_fusion': None, 'weyl_group': '1536.408640541'}
  • id: 184762021
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.ER', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.S', '24.BU', '24.CD'], 'contains': ['96.KS', '96.LN', '96.LQ', '96.PY', '96.TR'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [242089631075849093539192, 25903229681844523013167, 122002101738321960, 1313941673647, 134021272934136496216343, 216288705272228144236816], 'label': '3072.bgb.48.ER', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.F', 'old_label': '48.er1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ER', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184762022
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.ES', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.S', '24.BU', '24.CE'], 'contains': ['96.KS', '96.LP', '96.LR'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 242140721662339602266753, 216237613974362780043017, 122002101738321960, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.48.ES', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.F', 'old_label': '48.es1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ES', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184762023
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.ET', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 48, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.M', '24.CD', '24.CE', '24.CF', '24.CG', '24.CQ', '24.CR'], 'contains': ['96.KP', '96.KQ', '96.KS', '96.LO', '96.LS', '96.PC', '96.PI', '96.PZ', '96.QB', '96.TV', '96.UG'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 79855398717732338388456, 25903229681844523013167, 187973685961890096441600, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.ET', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '48.et1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ET', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762024
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.EU', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.N', '24.BO', '24.BP', '24.BW', '24.CH', '24.CI', '24.CJ'], 'contains': ['96.BO', '96.BP', '96.KT', '96.LV', '96.MI', '96.QC', '96.UM'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 187973685961890096441600, 79804308125641822294440, 122002101738321960, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.48.EU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.eu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EU', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184762025
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.EV', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.O', '24.BO', '24.BQ', '24.BX', '24.CH', '24.CK', '24.CL'], 'contains': ['96.BR', '96.BS', '96.BV', '96.KT', '96.LZ', '96.MF', '96.QD', '96.UZ'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [378358770650295628183080, 270240484111912758504367, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.EV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.ev1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EV', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762026
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '48.EW', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '192.QC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.N', '24.BQ', '24.BR', '24.BW', '24.CK', '24.CM', '24.CN'], 'contains': ['96.BT', '96.BU', '96.KT', '96.MA', '96.ME'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108169512287410083283217, 25903229681844523013167, 187973685961890096441600, 79804308125641822294440, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.EW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.ew1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EW', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762027
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.EX', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.O', '24.BP', '24.BR', '24.BY', '24.CI', '24.CL', '24.CM'], 'contains': ['96.BW', '96.KT', '96.MC', '96.MH'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 378358649363678452761737, 296041409911409376977422], 'label': '3072.bgb.48.EX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.ex1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EX', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762028
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.EY', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.Q', '24.BN', '24.BS', '24.CH', '24.CI', '24.CK', '24.CM'], 'contains': ['96.BX', '96.BY', '96.KT', '96.MD', '96.MG', '96.PK'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903107687970595565937, 25903229681844523013167, 53952412691500576681559, 25903107685154153232142, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.EY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.ey1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EY', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762029
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '48.EZ', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '192.QC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.R', '24.BS', '24.CJ', '24.CL', '24.CN', '24.CO', '24.CR'], 'contains': ['96.A', '96.KQ', '96.KT', '96.MB', '96.PH', '96.PL', '96.QF', '96.VJ'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229681844523013167, 187973685961890096441600, 79804308125641822294440, 122002101738321960, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.48.EZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.ez1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EZ', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762030
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.FA', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '384.FZ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.U', '24.CP', '24.CQ'], 'contains': ['96.KM', '96.KN', '96.KR', '96.KS', '96.LF', '96.OF', '96.OL', '96.PP', '96.PR', '96.QG', '96.RL'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 79855398717732338388456, 25903229681844523013167, 187973685961890096441600, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.FA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.fa1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FA', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762031
    {'ambient': '3072.bgb', 'aut_centralizer_order': 1, 'aut_label': '8.O', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '3072.bga', 'aut_weyl_index': 2, 'centralizer': '3072.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.E', '4.J'], 'contains': ['16.A', '24.HV', '32.T', '32.U'], 'core': '16.A', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [25903229681844523013167, 108118165248982343710201, 187922473375925652905521, 133970303627361494479417, 404159831259638948150382, 1313941673647, 378358649363678452761737, 162070456272950954131199], 'label': '3072.bgb.8.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.D', 'old_label': '8.o1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.O', 'subgroup_fusion': None, 'weyl_group': '1536.408550734'}
  • id: 184762032
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.FB', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.U', '24.CQ', '24.CR'], 'contains': ['96.KO', '96.KP', '96.KQ', '96.KR', '96.KS', '96.KT', '96.LE', '96.PA', '96.PD', '96.PF', '96.PW', '96.QA', '96.QE', '96.QH', '96.SI'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229691554491852799, 108118165248982343710201, 25903229681844523013167, 122002101738321960, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.48.FB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.fb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FB', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184762033
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.FC', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.W'], 'contains': ['96.BZ', '96.CA', '96.CB', '96.CC', '96.DE', '96.DF', '96.DG', '96.DH', '96.KU', '96.KV', '96.KW', '96.LB', '96.LC', '96.LU', '96.LW'], 'core': '384.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 25852272837936812846761, 122002101738321960, 1313941673647, 324406870523993839248121], 'label': '3072.bgb.48.FC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '48.fc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FC', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184762034
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.FD', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BA', '24.BN', '24.CS', '24.CT', '24.CU', '24.CV', '24.DI'], 'contains': ['96.CD', '96.CW', '96.DS', '96.KY', '96.LD', '96.MG', '96.QK'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79855520714221614566521, 25903229681844523013167, 53952412691500576681559, 25903107685154153232142, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.FD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.fd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FD', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184762035
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.FE', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.G', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.K', '24.CP', '24.DM'], 'contains': ['96.KX', '96.LF', '96.LI', '96.QL', '96.QM'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 79855398717732338388456, 25903229681844523013167, 122002101738321960, 1313941673647, 404210922196204071249966], 'label': '3072.bgb.48.FE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.fe1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FE', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762036
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.FF', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.K', '24.BM', '24.BT'], 'contains': ['96.KX', '96.LH', '96.LJ', '96.QP', '96.QQ'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 162121669227129588479873, 122002101738321960, 1313941673647, 187922594658424724202816, 25852017102974698844878], 'label': '3072.bgb.48.FF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.ff1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FF', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762037
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.FG', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.C', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.F', '24.T', '24.BM', '24.DM'], 'contains': ['96.KX', '96.LI', '96.LM', '96.QN', '96.QR'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 378358905093235639407953, 162070456272950954131199], 'label': '3072.bgb.48.FG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.fg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FG', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762038
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.FH', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.V', '24.BN', '24.CW', '24.CX', '24.CY', '24.CZ', '24.DJ'], 'contains': ['96.CF', '96.CY', '96.EQ', '96.KY', '96.LS', '96.MD', '96.QS', '96.RA'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 122002101738321960, 1313941673647, 134021272934136496216343, 404210922196204071249966, 187922594661241166512703], 'label': '3072.bgb.48.FH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.fh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FH', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762039
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.FI', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.W', '24.BO', '24.CS', '24.CW', '24.DA', '24.DC', '24.DK'], 'contains': ['96.CG', '96.CH', '96.CI', '96.CJ', '96.CZ', '96.EV', '96.KV', '96.KY', '96.LV', '96.LZ', '96.QT', '96.QU'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 25852272837936812846761, 79804308125641822294440, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.FI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.fi1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FI', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184762040
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.FJ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.X', '24.BP', '24.CT', '24.CX', '24.DB', '24.DC', '24.DK'], 'contains': ['96.CK', '96.DA', '96.FC', '96.KY', '96.LV', '96.MH', '96.QV'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 53952035291802302422343, 378358649363678452761737], 'label': '3072.bgb.48.FJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.fj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FJ', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184762041
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.FK', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.Y', '24.BQ', '24.CU', '24.CW', '24.DD', '24.DE', '24.DK'], 'contains': ['96.CL', '96.CQ', '96.DB', '96.FT', '96.KY', '96.LZ', '96.ME', '96.QX'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 162070321828715682652927, 79804308125641822294440, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.FK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.fk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FK', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762042
    {'ambient': '3072.bgb', 'aut_centralizer_order': 1, 'aut_label': '2.D', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '3072.a1', 'complements': ['1536.C', '1536.F', '1536.D', '1536.J'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.B', '4.C', '4.E', '4.J', '6.L', '8.H'], 'core': '2.D', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [108118421696801471190456, 25903229681844523013167, 108118165248982343710201, 187922473375925652905521, 566444897749485959875336, 133970303627361494479417, 404159831259638948150382, 1313941673647, 378358649363678452761737, 162070456272950954131199], 'label': '3072.bgb.2.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.B', '4.C', '4.E'], 'normalizer': '1.a1', 'old_label': '2.d1', 'projective_image': '3072.bgb', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.D', 'subgroup_fusion': None, 'weyl_group': '3072.bgb'}
  • id: 184762043
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '12.A', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1536.408610986', 'aut_weyl_index': 4, 'centralizer': '768.A', 'complements': ['256.J'], 'conjugacy_class_count': 1, 'contained_in': ['4.A', '6.A', '6.F', '6.G'], 'contains': ['24.B', '24.M', '24.R', '24.U', '24.BV', '24.CQ', '24.CR', '24.FQ', '24.FX', '24.FY', '24.FZ', '24.GB'], 'core': '12.A', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 133970303627361494479417, 122002101738321960, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.12.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': ['4.A', '6.A'], 'normal_contains': ['24.B', '48.A'], 'normalizer': '1.a1', 'old_label': '12.a1', 'projective_image': '3072.bgb', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.A', 'subgroup_fusion': None, 'weyl_group': '768.1087581'}
  • id: 184762044
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '48.FL', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '192.CX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.W', '24.BR', '24.CT', '24.CY', '24.DD', '24.DG', '24.DL'], 'contains': ['96.CM', '96.CO', '96.DC', '96.GF', '96.KW', '96.KY', '96.MA', '96.MC'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 324406870523993839248121, 404210922196204071249966], 'label': '3072.bgb.48.FL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.fl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FL', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762045
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '48.FM', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '192.CX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.X', '24.BQ', '24.CS', '24.CZ', '24.DF', '24.DG', '24.DL'], 'contains': ['96.CN', '96.CP', '96.KY', '96.MA', '96.MF'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 324406991811924875755576, 1313941673647, 404210922196204071249966], 'label': '3072.bgb.48.FM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.fm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FM', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762046
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.FN', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.V', '24.BS', '24.DA', '24.DB', '24.DD', '24.DF', '24.DI'], 'contains': ['96.KY', '96.MB', '96.MG', '96.RB'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 53952412691500576681559, 25903107685154153232142, 122002101738321960, 1313941673647, 79804429421968711780537], 'label': '3072.bgb.48.FN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.fn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FN', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762047
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.FO', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.Y', '24.BP', '24.CV', '24.CY', '24.DA', '24.DH', '24.DL'], 'contains': ['96.CR', '96.KY', '96.MC', '96.MI'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 296041409911409376977422, 404210922196204071249966], 'label': '3072.bgb.48.FO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.fo1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FO', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762048
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.FP', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.Z', '24.BR', '24.CV', '24.CX', '24.DE', '24.DF', '24.DK'], 'contains': ['96.CS', '96.CV', '96.KY', '96.ME', '96.MH', '96.RC'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108169512287410083283217, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.48.FP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.fp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FP', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762049
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.FQ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.Z', '24.BO', '24.CU', '24.CZ', '24.DB', '24.DH', '24.DL'], 'contains': ['96.CT', '96.CU', '96.KY', '96.MF', '96.MI', '96.QY'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [270240484111912758504367, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 404210922196204071249966], 'label': '3072.bgb.48.FQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.fq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FQ', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762050
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '48.FR', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '192.CX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.G', '24.BA', '24.BS', '24.DC', '24.DE', '24.DG', '24.DH', '24.DJ'], 'contains': ['96.A', '96.KY', '96.MD', '96.QZ', '96.RD'], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 79804429413572684637382, 404210922196204071249966], 'label': '3072.bgb.48.FR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.fr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FR', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762051
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.FS', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 12, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.L', '24.BT', '24.DI', '24.DJ', '24.DK', '24.DL', '24.DM'], 'contains': ['96.CE', '96.CX', '96.DD', '96.KX', '96.KY', '96.LL', '96.RE', '96.RF', '96.RG'], 'core': '384.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 404210922196204071249966], 'label': '3072.bgb.48.FS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.fs1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FS', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 184762052
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.FT', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.M', '24.BV', '24.DN'], 'contains': ['96.KZ', '96.LA', '96.LH', '96.LK', '96.LO', '96.RI', '96.RJ', '96.RR', '96.RW'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 122002101738321960, 1313941673647, 79804429421968711780537, 25852017102974698844878], 'label': '3072.bgb.48.FT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '48.ft1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FT', 'subgroup_fusion': None, 'weyl_group': '128.1578'}
  • id: 184762053
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.FU', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BC', '24.BU', '24.DN'], 'contains': ['96.LA', '96.LC', '96.LN', '96.LP', '96.LY'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 122002101738321960, 1313941673647, 134021272934136496216343, 216288705272228144236816, 296041409911409376977422], 'label': '3072.bgb.48.FU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.F', 'old_label': '48.fu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FU', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762054
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '12.B', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1536.408610986', 'aut_weyl_index': 4, 'centralizer': '768.A', 'complements': ['256.I'], 'conjugacy_class_count': 1, 'contained_in': ['4.C', '6.A', '6.L', '6.N'], 'contains': ['24.B', '24.DW', '24.EE', '24.HN', '24.HT'], 'core': '12.B', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [108118421696801471190456, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 133970303627361494479417, 122002101738321960, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.12.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': ['4.C', '6.A'], 'normal_contains': ['24.B', '48.B'], 'normalizer': '1.a1', 'old_label': '12.b1', 'projective_image': '3072.bgb', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.B', 'subgroup_fusion': None, 'weyl_group': '768.1087581'}
  • id: 184762055
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.FV', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BD', '24.BU', '24.DN'], 'contains': ['96.LA', '96.LQ', '96.LR'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 242140721662339602266753, 270189392822449473928912, 122002101738321960, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.48.FV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.F', 'old_label': '48.fv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FV', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762056
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.FW', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.6407063', 'aut_weyl_index': 12, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.R', '24.BV', '24.DI', '24.DO', '24.DP', '24.DQ', '24.DR'], 'contains': ['96.KZ', '96.LD', '96.LL', '96.MB', '96.RY', '96.SA', '96.SG'], 'core': '384.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 133970303635757521608262], 'label': '3072.bgb.48.FW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.fw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FW', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 184762057
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '48.FX', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.A', '24.BW', '24.CS', '24.CT', '24.DO', '24.DS', '24.DT'], 'contains': ['96.DI', '96.DJ', '96.DK', '96.LB', '96.LD', '96.LV', '96.MA'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79855398709336311235223, 79804308125641822294440, 122002101738321960, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.48.FX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.fx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FX', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184762058
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.FY', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BA', '24.BN', '24.DP', '24.DS', '24.DT', '24.DU', '24.DV'], 'contains': ['96.DL', '96.DM', '96.DQ', '96.LD', '96.LX', '96.MD', '96.SD'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79855520714221614566521, 25903229681844523013167, 25903107685154153232142, 122002101738321960, 1313941673647, 51090958997032170942], 'label': '3072.bgb.48.FY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.fy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FY', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184762059
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.FZ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BJ', '24.BX', '24.CS', '24.CU', '24.DQ', '24.DS', '24.DU'], 'contains': ['96.DN', '96.DO', '96.DP', '96.LD', '96.LZ', '96.MF', '96.SE'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 324406991811924875755576, 1313941673647], 'label': '3072.bgb.48.FZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.fz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FZ', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184762060
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.GA', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BJ', '24.BY', '24.CT', '24.CV', '24.DQ', '24.DT', '24.DV'], 'contains': ['96.DT', '96.LD', '96.MC', '96.MH'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 324406870523993839248121, 378358649363678452761737], 'label': '3072.bgb.48.GA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.ga1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GA', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184762061
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.GB', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BK', '24.BW', '24.CU', '24.CV', '24.DO', '24.DU', '24.DV'], 'contains': ['96.DR', '96.LD', '96.ME', '96.MI'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108169512287410083283217, 25903229681844523013167, 79855398709336311235223, 79804308125641822294440, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.GB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.gb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GB', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184762062
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.GC', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.G', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.K', '24.CP', '24.ER'], 'contains': ['96.LF', '96.LG', '96.LJ', '96.SL', '96.SO'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 25852138389591620222016, 122002101738321960, 1313941673647, 134021272934136496216343, 51090960298439969137], 'label': '3072.bgb.48.GC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.gc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GC', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762063
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.GD', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.K', '24.BM', '24.CA'], 'contains': ['96.LG', '96.LH', '96.LI', '96.SR', '96.SS'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229337376182892926, 25903229681844523013167, 122002101738321960, 1313941673647, 187922594658424724202816, 25852017102974698844878], 'label': '3072.bgb.48.GD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.gd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GD', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762064
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.GE', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.S', '24.DN', '24.EH'], 'contains': ['96.LK', '96.LN', '96.LR', '96.TG', '96.VE'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [242089752358354392177983, 25903229681844523013167, 133970303627361494479417, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.GE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.F', 'old_label': '48.ge1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GE', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762065
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '12.C', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1536.408610986', 'aut_weyl_index': 4, 'centralizer': '768.A', 'complements': ['256.J', '256.I'], 'conjugacy_class_count': 1, 'contained_in': ['4.F', '6.A', '6.M', '6.O'], 'contains': ['24.B', '24.DZ', '24.EF'], 'core': '12.C', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 133970303627361494479417, 122002101738321960, 1313941673647, 187973308217542771509839, 162070456272950954131199], 'label': '3072.bgb.12.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.C', 'normal_contained_in': ['4.F', '6.A'], 'normal_contains': ['24.B', '48.C'], 'normalizer': '1.a1', 'old_label': '12.c1', 'projective_image': '3072.bgb', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.C', 'subgroup_fusion': None, 'weyl_group': '768.1087581'}
  • id: 184762066
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.GF', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.S', '24.DN', '24.EI'], 'contains': ['96.LK', '96.LP', '96.LQ'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 133970303627361494479417, 122002101738321960, 1313941673647, 134021529040297499210286], 'label': '3072.bgb.48.GF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.F', 'old_label': '48.gf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GF', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762067
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '48.GG', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.B', '24.R', '24.CR', '24.DJ', '24.DW', '24.DX', '24.DY', '24.DZ', '24.EA', '24.EB', '24.EC', '24.ED', '24.EE', '24.EF', '24.EG'], 'contains': ['96.A', '96.LE', '96.LL', '96.LS', '96.SJ', '96.TA', '96.TN', '96.UJ', '96.VI'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.48.GG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.gg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GG', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762068
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.GH', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.B', '24.M', '24.CQ', '24.EH', '24.EI', '24.EJ', '24.EK'], 'contains': ['96.LE', '96.LF', '96.LK', '96.LS', '96.LT', '96.SM', '96.SN', '96.TC', '96.TH', '96.TZ', '96.UF'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 187922473375925652905521, 133970303627361494479417, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.GH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '48.gh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GH', 'subgroup_fusion': None, 'weyl_group': '128.1578'}
  • id: 184762069
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.GI', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.N', '24.DK', '24.DO', '24.DW', '24.EL', '24.EM', '24.EN'], 'contains': ['96.DU', '96.DV', '96.LL', '96.LV', '96.ME', '96.TD', '96.UP'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.48.GI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.gi1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GI', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184762070
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.GJ', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 12, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.L', '24.CA', '24.DP', '24.DX', '24.EL', '24.EO', '24.ER'], 'contains': ['96.DW', '96.DX', '96.DY', '96.LG', '96.LL', '96.LX', '96.ST', '96.TE', '96.UY'], 'core': '384.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25852138757799544092222, 25903229681844523013167, 25852138389591620222016, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.GJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.gj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GJ', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 184762071
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.GK', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.O', '24.DK', '24.DQ', '24.DY', '24.EM', '24.EO', '24.EP'], 'contains': ['96.DZ', '96.EA', '96.ED', '96.LL', '96.LZ', '96.MH', '96.TF', '96.VB'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.48.GK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.gk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GK', 'subgroup_fusion': None, 'weyl_group': '128.2264'}
  • id: 184762072
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '48.GL', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.N', '24.DL', '24.DO', '24.DZ', '24.EO', '24.EP', '24.EQ'], 'contains': ['96.EB', '96.EC', '96.LL', '96.MA', '96.MI'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 25903364135789722998960], 'label': '3072.bgb.48.GL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.gl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GL', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184762073
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.GM', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.O', '24.DL', '24.DQ', '24.EA', '24.EL', '24.EN', '24.EQ'], 'contains': ['96.EE', '96.LL', '96.MC', '96.MF'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804052047512561508433, 25852138389591620222016, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.GM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.gm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GM', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762074
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.GN', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.53387', 'aut_weyl_index': 24, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.P', '24.CA', '24.CB', '24.DM', '24.DR', '24.EB', '24.ES'], 'contains': ['96.LI', '96.LL', '96.SW', '96.TJ'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 378358905093235639407953], 'label': '3072.bgb.48.GN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.gn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GN', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762075
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.GO', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.53387', 'aut_weyl_index': 24, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.P', '24.BT', '24.CC', '24.DR', '24.EC', '24.ER', '24.ET'], 'contains': ['96.LJ', '96.LL', '96.SX', '96.TK'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [162070577934876685646657, 25903229681844523013167, 25852138389591620222016, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.GO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.go1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GO', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762076
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.D', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B'], 'contains': ['24.C', '24.D', '24.E', '24.F', '24.L', '24.N', '24.O', '24.W', '24.X', '24.Y', '24.Z', '24.BO', '24.BP', '24.BQ', '24.BR', '24.DK', '24.DL', '24.EL', '24.EO'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 53952035291802302422343, 378358649363678452761737, 296041409911409376977422], 'label': '3072.bgb.12.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.d1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.D', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184762077
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.GP', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 12, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.Q', '24.CC', '24.DJ', '24.DP', '24.EM', '24.EQ', '24.ES'], 'contains': ['96.LL', '96.MD', '96.TL', '96.VO'], 'core': '384.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 404211043484134973872583, 187922473375925652905521, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.GP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.gp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GP', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 184762078
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.GQ', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 12, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.Q', '24.CB', '24.DI', '24.DX', '24.EN', '24.EP', '24.ET'], 'contains': ['96.LL', '96.MG', '96.TM', '96.VP'], 'core': '384.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229681844523013167, 53952412691500576681559, 25852138389591620222016, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.GQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.gq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GQ', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 184762079
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.GR', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.C', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.H', '24.T', '24.BM', '24.ER'], 'contains': ['96.LG', '96.LJ', '96.LM', '96.SP', '96.TP'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 162121669227129588479873, 122002101738321960, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.48.GR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.gr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GR', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762080
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.GS', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.B', '24.U', '24.BV', '24.DM', '24.ER', '24.ES', '24.ET'], 'contains': ['96.LE', '96.LF', '96.LK', '96.LL', '96.LM', '96.SK', '96.SU', '96.SZ', '96.TB', '96.TO', '96.TQ'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 133970303627361494479417, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.GS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.gs1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GS', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 184762081
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.GT', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BL', '24.CD', '24.DN'], 'contains': ['96.LN', '96.LO', '96.LQ', '96.TS', '96.TT'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 270189392822449473928912, 122002101738321960, 1313941673647, 134021272934136496216343, 216288705272228144236816], 'label': '3072.bgb.48.GT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.F', 'old_label': '48.gt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GT', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184762082
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.GU', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BL', '24.CE', '24.DN'], 'contains': ['96.LO', '96.LP', '96.LR'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 242140721662339602266753, 122002101738321960, 1313941673647, 134021272934136496216343, 296041409911409376977422], 'label': '3072.bgb.48.GU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.F', 'old_label': '48.gu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GU', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184762083
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.GV', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BB', '24.BW', '24.CW', '24.CX', '24.DW', '24.EU', '24.EV'], 'contains': ['96.EF', '96.EG', '96.LS', '96.LV', '96.ME', '96.UB', '96.UO'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 79855398717732338388456, 25903229681844523013167, 256460345499052777, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.GV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.gv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GV', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184762084
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.GW', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.V', '24.BN', '24.DX', '24.EU', '24.EV', '24.EW', '24.EX'], 'contains': ['96.EH', '96.EI', '96.EO', '96.LS', '96.LX', '96.MG', '96.UC', '96.UV'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 79855398717732338388456, 25903229681844523013167, 53952412691500576681559, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.GW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.gw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GW', 'subgroup_fusion': None, 'weyl_group': '128.2264'}
  • id: 184762085
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.GX', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 12, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BC', '24.BX', '24.CD', '24.CW', '24.DY', '24.EH', '24.EW'], 'contains': ['96.EJ', '96.EK', '96.EL', '96.LN', '96.LS', '96.LZ', '96.TU', '96.UE', '96.VG'], 'core': '384.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [242089752358354392177983, 25903229681844523013167, 122002101738321960, 1313941673647, 134021272934136496216343, 187922594661241166512703], 'label': '3072.bgb.48.GX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.gx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GX', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 184762086
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '48.GY', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BB', '24.BW', '24.CY', '24.CZ', '24.DZ', '24.EW', '24.EX'], 'contains': ['96.EM', '96.EN', '96.LS', '96.MA', '96.MI'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 79855142978471449905233, 79855398717732338388456, 25903229681844523013167, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.GY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.gy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GY', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184762087
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.E', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B', '6.C', '6.F'], 'contains': ['24.L', '24.Q', '24.R', '24.V', '24.BA', '24.BN', '24.BS', '24.DI', '24.DJ', '24.DP', '24.DX', '24.FI', '24.FJ', '24.FK', '24.FL'], 'core': '48.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 53952412691500576681559, 51212588579793007921, 122002101738321960, 1313941673647, 79804429413572684637382, 25852017102974698844878], 'label': '3072.bgb.12.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.e1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.E', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184762088
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.GZ', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 12, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BC', '24.BY', '24.CE', '24.CY', '24.EA', '24.EI', '24.EU'], 'contains': ['96.LP', '96.LS', '96.MC'], 'core': '384.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [53952291033879672806278, 79855398717732338388456, 25903229681844523013167, 79804052047512561508433, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.GZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.gz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GZ', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 184762089
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.HA', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.53387', 'aut_weyl_index': 24, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BD', '24.BZ', '24.CD', '24.CF', '24.ED', '24.EI', '24.EJ'], 'contains': ['96.LQ', '96.LS', '96.TW', '96.UH'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 79855398717732338388456, 25903229681844523013167, 122002101738321960, 1313941673647, 134021529040297499210286], 'label': '3072.bgb.48.HA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '48.ha1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HA', 'subgroup_fusion': None, 'weyl_group': '128.1758'}
  • id: 184762090
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.HB', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 12, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BE', '24.BX', '24.CG', '24.CZ', '24.EA', '24.EJ', '24.EV'], 'contains': ['96.EP', '96.LS', '96.MF', '96.TX'], 'core': '384.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [53952291033879672806278, 25903363795619943623743, 79855398717732338388456, 25903229681844523013167, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.HB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.hb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HB', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 184762091
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.HC', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 12, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BE', '24.BY', '24.CF', '24.CX', '24.DY', '24.EK', '24.EX'], 'contains': ['96.LS', '96.MH', '96.UI', '96.VM'], 'core': '384.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229681844523013167, 122002101738321960, 1313941673647, 134021272934136496216343, 378358649363678452761737, 187922594661241166512703], 'label': '3072.bgb.48.HC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.hc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HC', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 184762092
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.HD', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.53387', 'aut_weyl_index': 24, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BD', '24.BZ', '24.CE', '24.CG', '24.EG', '24.EH', '24.EK'], 'contains': ['96.LR', '96.LS', '96.TY', '96.VN'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 122002101738321960, 1313941673647, 134021272934136496216343, 216237613982764859689536, 187922594661241166512703], 'label': '3072.bgb.48.HD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '48.hd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HD', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762093
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.HE', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.I', '24.BL', '24.BU', '24.EH'], 'contains': ['96.LN', '96.LR', '96.LT', '96.UD', '96.VF'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 296092500497899884979223, 25903229681844523013167, 122002101738321960, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.48.HE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.F', 'old_label': '48.he1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HE', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762094
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.HF', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.J', '24.BL', '24.BU', '24.EI'], 'contains': ['96.LP', '96.LQ', '96.LT'], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 187922217292190117815823, 25903229681844523013167, 122002101738321960, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.48.HF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.F', 'old_label': '48.hf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HF', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762095
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.HG', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.W', '24.BP', '24.DT', '24.EL', '24.EU', '24.EY', '24.FA'], 'contains': ['96.ES', '96.ET', '96.EZ', '96.LU', '96.LV', '96.LX', '96.MC'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952156579733379227566, 25903229681844523013167, 54003247541513762671313, 25903107685154153232142, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.HG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.hg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HG', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184762096
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.HH', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.X', '24.BO', '24.DS', '24.EL', '24.EV', '24.EZ', '24.FA'], 'contains': ['96.ER', '96.EU', '96.FA', '96.LV', '96.LX', '96.MF', '96.UK'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952156579733379227566, 25903229681844523013167, 79855264629178445030417, 25903107685154153232142, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.HH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.hh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HH', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184762097
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.HI', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BF', '24.CH', '24.CW', '24.DC', '24.DS', '24.EM', '24.EY'], 'contains': ['96.EW', '96.EX', '96.EY', '96.LV', '96.LZ', '96.MD', '96.UL'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.48.HI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.hi1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HI', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184762098
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.F', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.6536092', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.G'], 'contains': ['24.M', '24.S', '24.BC', '24.BD', '24.BL', '24.BU', '24.CD', '24.CE', '24.DN', '24.EH', '24.EI'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 1313941673647, 122002101738321960, 25903229681844523013167, 242089752358354392177983, 133970303627361494479417, 296041409911409376977422, 25852017102974698844878], 'label': '3072.bgb.12.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '12.f1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.F', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 184762099
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.HJ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BB', '24.CJ', '24.DA', '24.DB', '24.DO', '24.EY', '24.EZ'], 'contains': ['96.LV', '96.MB', '96.MI', '96.UN'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 133970303635757521608262, 53952035291802302422343], 'label': '3072.bgb.48.HJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.hj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HJ', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184762100
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.HK', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BF', '24.CI', '24.CT', '24.DA', '24.EN', '24.EU', '24.FA'], 'contains': ['96.FD', '96.LV', '96.MC', '96.MG'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [51347406816160329727, 53952156579733379227566, 25903229681844523013167, 25903107685154153232142, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.HK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.hk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HK', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184762101
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.HL', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BG', '24.CI', '24.CX', '24.DC', '24.DT', '24.EM', '24.EZ'], 'contains': ['96.LV', '96.MD', '96.MH', '96.UQ'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 25852272837936812846761, 79804308125641822294440, 122002101738321960, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.48.HL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.hl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HL', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184762102
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.HM', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BG', '24.CH', '24.CS', '24.DB', '24.EN', '24.EV', '24.FA'], 'contains': ['96.FB', '96.LV', '96.MF', '96.MG'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952156579733379227566, 25903363795619943623743, 25903229681844523013167, 25903107685154153232142, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.HM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.hm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HM', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184762103
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '48.HN', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '384.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.W', '24.BQ', '24.DS', '24.EO', '24.EW', '24.FB', '24.FC'], 'contains': ['96.FE', '96.FL', '96.FM', '96.FV', '96.FX', '96.LW', '96.LX', '96.LZ', '96.MA'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 324355523485385682622200], 'label': '3072.bgb.48.HN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.hn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HN', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184762104
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.HO', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.Y', '24.BO', '24.DU', '24.EO', '24.EW', '24.EY', '24.FD'], 'contains': ['96.FF', '96.FI', '96.FK', '96.FR', '96.LX', '96.LZ', '96.MI', '96.UT'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 270189649267478943569286], 'label': '3072.bgb.48.HO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.ho1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HO', 'subgroup_fusion': None, 'weyl_group': '128.2264'}
  • id: 184762105
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '48.HP', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '384.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.X', '24.BR', '24.DT', '24.EO', '24.EX', '24.FC', '24.FE'], 'contains': ['96.FG', '96.FH', '96.LX', '96.MA', '96.MH'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 324355523485385682622200, 378358649363678452761737], 'label': '3072.bgb.48.HP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.hp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HP', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184762106
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.HQ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.V', '24.BS', '24.DP', '24.EY', '24.EZ', '24.FB', '24.FE'], 'contains': ['96.LX', '96.MB', '96.MD', '96.UW'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 25903107685154153232142, 122002101738321960, 1313941673647, 79804429421968711780537, 51090958997032170942], 'label': '3072.bgb.48.HQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.hq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HQ', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762107
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.HR', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.Y', '24.BR', '24.DV', '24.EL', '24.EU', '24.FB', '24.FF'], 'contains': ['96.FJ', '96.LX', '96.MC', '96.ME'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [51347406816160329727, 25903229681844523013167, 256460345499052777, 25903107685154153232142, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.HR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.hr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HR', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762108
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.HS', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.Z', '24.BQ', '24.DU', '24.EL', '24.EV', '24.FE', '24.FF'], 'contains': ['96.FN', '96.GB', '96.LX', '96.ME', '96.MF'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903363795619943623743, 25903229681844523013167, 256460345499052777, 25903107685154153232142, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.HS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.hs1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HS', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762109
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.G', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.6536092', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.G'], 'contains': ['24.M', '24.BD', '24.BE', '24.CF', '24.CG', '24.EJ', '24.EK'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 1313941673647, 122002101738321960, 25903229681844523013167, 324406991811924875755576, 133970303627361494479417, 25852017102974698844878, 378358649363678452761737], 'label': '3072.bgb.12.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '12.g1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.G', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 184762110
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.HT', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.Z', '24.BP', '24.DV', '24.EO', '24.EX', '24.EZ', '24.FD'], 'contains': ['96.FO', '96.GC', '96.LX', '96.MH', '96.MI'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 270189649267478943569286, 378358649363678452761737], 'label': '3072.bgb.48.HT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.ht1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HT', 'subgroup_fusion': None, 'weyl_group': '128.2264'}
  • id: 184762111
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '48.HU', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '384.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.L', '24.BA', '24.BS', '24.DX', '24.FA', '24.FC', '24.FD', '24.FF'], 'contains': ['96.A', '96.LX', '96.MG', '96.UU', '96.UX'], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 53952412691500576681559, 79804308125641822294440, 122002101738321960, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.48.HU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.hu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HU', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184762112
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '48.HV', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '384.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BF', '24.CK', '24.CS', '24.DD', '24.EP', '24.EW', '24.FC'], 'contains': ['96.FP', '96.FQ', '96.LZ', '96.MA', '96.MG'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [324355644776280741499582, 378358770650295628183080, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.HV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.hv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HV', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184762113
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.HW', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BC', '24.CL', '24.DA', '24.DD', '24.DQ', '24.EY', '24.FB'], 'contains': ['96.LY', '96.LZ', '96.MB', '96.MC'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 296041409911409376977422], 'label': '3072.bgb.48.HW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.hw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HW', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762114
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.HX', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BH', '24.CK', '24.CW', '24.DE', '24.DU', '24.EM', '24.FB'], 'contains': ['96.FS', '96.FU', '96.LZ', '96.MD', '96.ME', '96.VC'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [378358770650295628183080, 108169512287410083283217, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.HX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.hx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HX', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762115
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.HY', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BH', '24.CH', '24.CU', '24.DA', '24.EP', '24.EW', '24.FD'], 'contains': ['96.FW', '96.GA', '96.LZ', '96.MG', '96.MI'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 296092756945739609872576], 'label': '3072.bgb.48.HY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.hy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HY', 'subgroup_fusion': None, 'weyl_group': '128.2264'}
  • id: 184762116
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '48.HZ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '384.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.M', '24.BJ', '24.CL', '24.DC', '24.DE', '24.DY', '24.FC', '24.FD'], 'contains': ['96.A', '96.LZ', '96.MH', '96.VA', '96.VD'], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 79804429413572684637382, 378358649363678452761737], 'label': '3072.bgb.48.HZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.hz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HZ', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184762117
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '48.IA', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '192.QC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BB', '24.CN', '24.DD', '24.DF', '24.DO', '24.FB', '24.FE'], 'contains': ['96.MA', '96.MB', '96.ME'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108169512287410083283217, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 133970303635757521608262], 'label': '3072.bgb.48.IA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.ia1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IA', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762118
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '48.IB', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '192.CX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BF', '24.CM', '24.CY', '24.DG', '24.DT', '24.EQ', '24.FB'], 'contains': ['96.MA', '96.MC', '96.MD'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 122002101738321960, 324406870523993839248121, 79804308125641822294440, 404211043484134973872583], 'label': '3072.bgb.48.IB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.ib1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IB', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762119
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '48.IC', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '192.CX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BG', '24.CK', '24.CZ', '24.DG', '24.DS', '24.EQ', '24.FE'], 'contains': ['96.FY', '96.FZ', '96.MA', '96.MD', '96.MF'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 122002101738321960, 324406991811924875755576, 79804308125641822294440, 404211043484134973872583], 'label': '3072.bgb.48.IC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.ic1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IC', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762120
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.H', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B'], 'contains': ['24.N', '24.O', '24.Q', '24.BF', '24.BG', '24.BH', '24.BI', '24.CH', '24.CI', '24.CK', '24.CM', '24.EM', '24.EN', '24.EP', '24.EQ'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 122002101738321960, 187922473375925652905521, 296041409911409376977422, 108118165248982343710201, 378358649363678452761737, 25852272837936812846761], 'label': '3072.bgb.12.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.h1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.H', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184762121
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '48.ID', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '384.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BG', '24.CM', '24.CT', '24.DF', '24.EP', '24.EX', '24.FC'], 'contains': ['96.GG', '96.MA', '96.MG', '96.MH'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [324355644776280741499582, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.48.ID', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.id1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ID', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184762122
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.IE', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BE', '24.CL', '24.DB', '24.DF', '24.DQ', '24.EZ', '24.FE'], 'contains': ['96.MB', '96.MF', '96.MH'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [270240484111912758504367, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.48.IE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.ie1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IE', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762123
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.IF', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BH', '24.CI', '24.CY', '24.DH', '24.DV', '24.EQ', '24.EY'], 'contains': ['96.MC', '96.MD', '96.MI'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 404211043484134973872583, 79804308125641822294440, 122002101738321960, 1313941673647, 296041409911409376977422], 'label': '3072.bgb.48.IF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.if1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IF', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762124
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.IG', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BH', '24.CM', '24.CV', '24.DD', '24.EN', '24.EU', '24.FF'], 'contains': ['96.MC', '96.ME', '96.MG'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 256460345499052777, 54003247541513762671313, 25903107685154153232142, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.IG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.ig1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IG', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762125
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.IH', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BI', '24.CM', '24.CX', '24.DE', '24.DV', '24.EM', '24.FE'], 'contains': ['96.MD', '96.ME', '96.MH', '96.VQ'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 162070321828715682652927, 79804308125641822294440, 122002101738321960, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.48.IH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.ih1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IH', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762126
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.II', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BI', '24.CH', '24.CZ', '24.DH', '24.DU', '24.EQ', '24.EZ'], 'contains': ['96.GD', '96.MD', '96.MF', '96.MI'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [270240484111912758504367, 25903229681844523013167, 404211043484134973872583, 79804308125641822294440, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.II', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.ii1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.II', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762127
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.IJ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BI', '24.CK', '24.CU', '24.DF', '24.EN', '24.EV', '24.FF'], 'contains': ['96.GE', '96.ME', '96.MF', '96.MG'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 256460345499052777, 79855264629178445030417, 25903107685154153232142, 122002101738321960, 1313941673647], 'label': '3072.bgb.48.IJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.ij1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IJ', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762128
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.IK', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BI', '24.CI', '24.CV', '24.DB', '24.EP', '24.EX', '24.FD'], 'contains': ['96.MG', '96.MH', '96.MI'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 378358649363678452761737, 296092756945739609872576], 'label': '3072.bgb.48.IK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.ik1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IK', 'subgroup_fusion': None, 'weyl_group': '128.2264'}
  • id: 184762129
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '48.IL', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '192.CX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.O', '24.BJ', '24.CL', '24.DG', '24.DH', '24.EA', '24.FA', '24.FF'], 'contains': ['96.A', '96.MC', '96.MF'], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79855142625594763233847, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.48.IL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.il1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IL', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762130
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '48.IM', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '192.QC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BK', '24.CN', '24.CO', '24.DE', '24.DW', '24.EE', '24.FF'], 'contains': ['96.A', '96.ME', '96.VK', '96.VR'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118421696801471190456, 25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.48.IM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.im1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IM', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762131
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '12.I', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.6407063', 'aut_weyl_index': 12, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.A', '6.B', '6.D'], 'contains': ['24.A', '24.N', '24.R', '24.BB', '24.BK', '24.BW', '24.CJ', '24.CN', '24.DO', '24.DW', '24.DZ'], 'core': '24.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 122002101738321960, 1313941673647, 79804429413572684637382, 53952035291802302422343], 'label': '3072.bgb.12.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.i1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.I', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 184762132
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '48.IN', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BK', '24.CJ', '24.CO', '24.DH', '24.DZ', '24.EF', '24.FD'], 'contains': ['96.A', '96.MI', '96.VL'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 79804429413572684637382, 187973308217542771509839], 'label': '3072.bgb.48.IN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.in1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IN', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762133
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.IO', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '768.I', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.K', '24.FG', '24.GA'], 'contains': ['96.GL', '96.GM', '96.GR', '96.GS', '96.MJ', '96.MR', '96.MU', '96.QL', '96.QP', '96.SL', '96.SR'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 162121669227129588479873, 51212588579793007921, 1313941673647, 162070456274433112077942, 25852017102974698844878], 'label': '3072.bgb.48.IO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.io1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IO', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 184762134
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.IP', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.K', '24.FR', '24.FU'], 'contains': ['96.MJ', '96.MS', '96.MU', '96.QM', '96.QQ', '96.SO', '96.SS'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 51212588579793007921, 1313941673647, 25852017102974698844878, 187922594661241166512703, 51090960298439969137], 'label': '3072.bgb.48.IP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.ip1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IP', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762135
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.IQ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.C', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.T', '24.FG', '24.FR'], 'contains': ['96.MJ', '96.MT', '96.MU', '96.QN', '96.QO', '96.SP', '96.SQ'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922594664024732247801, 25903229337376182892926, 25903229681844523013167, 51212588579793007921, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.IQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.iq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IQ', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762136
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.IR', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.L', '24.FG', '24.FH', '24.FI', '24.FJ', '24.FT', '24.FU'], 'contains': ['96.GH', '96.GI', '96.GN', '96.GO', '96.MJ', '96.MN', '96.ND', '96.NE', '96.NZ', '96.OB', '96.QI', '96.RF', '96.TE'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25852138757799544092222, 25903229681844523013167, 51212588579793007921, 25852138389591620222016, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.IR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.ir1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IR', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762137
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.IS', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.V', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.L', '24.FK', '24.FL'], 'contains': ['96.GJ', '96.GK', '96.GP', '96.GQ', '96.MK', '96.MQ', '96.ND', '96.NF', '96.OA', '96.OB', '96.QJ', '96.RG', '96.UY'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 25852017095880079467006, 25903107685154153232142, 1313941673647, 25852017101492540879976, 51090958997032170942], 'label': '3072.bgb.48.IS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '48.is1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IS', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762138
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.IT', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.U', '24.FQ', '24.FX'], 'contains': ['96.ML', '96.MT', '96.MV', '96.NH', '96.NM', '96.NR', '96.NW', '96.OC', '96.OL', '96.OZ', '96.PF', '96.RN', '96.RQ', '96.SI', '96.SZ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 133970182339249961095537, 133970303635757521608262, 25852017102974698844878, 108118165248982343710201], 'label': '3072.bgb.48.IT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.it1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IT', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184762139
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.IU', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.U', '24.FG', '24.FM', '24.FQ', '24.FY'], 'contains': ['96.MN', '96.MR', '96.MT', '96.NK', '96.NR', '96.OD', '96.PD', '96.RL', '96.RO', '96.TB', '96.TI'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 133970182339249961095537, 25903229681844523013167, 187922473375925652905521, 1313941673647, 79804429421968711780537], 'label': '3072.bgb.48.IU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.iu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IU', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 184762140
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.IV', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.M', '24.FQ', '24.GB'], 'contains': ['96.ML', '96.MR', '96.MV', '96.NG', '96.NJ', '96.NS', '96.NX', '96.OE', '96.OO', '96.OY', '96.PC', '96.RK', '96.RR', '96.SH', '96.TC'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804308122845802507662, 108118165248982343710201, 25903229681844523013167, 1313941673647, 79804429421968711780537, 25852017102974698844878], 'label': '3072.bgb.48.IV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.iv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IV', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184762141
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.IW', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.M', '24.FX', '24.FZ'], 'contains': ['96.MM', '96.MS', '96.MV', '96.NI', '96.NN', '96.NT', '96.NY', '96.OG', '96.OR', '96.PB', '96.PI', '96.RM', '96.RR', '96.SY', '96.TH'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 133970303627361494479417, 1313941673647], 'label': '3072.bgb.48.IW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.iw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IW', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184762142
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.J', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B', '6.E', '6.G'], 'contains': ['24.O', '24.R', '24.BC', '24.BE', '24.BJ', '24.BX', '24.BY', '24.CL', '24.DQ', '24.DY', '24.EA'], 'core': '48.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 79804429413572684637382, 378358649363678452761737, 296041409911409376977422], 'label': '3072.bgb.12.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.j1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.J', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184762143
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.IX', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.P', '24.FG', '24.FN', '24.FO', '24.FP', '24.FU', '24.FV'], 'contains': ['96.MN', '96.MU', '96.RP', '96.TJ', '96.TK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [162070577934876685646657, 25903229681844523013167, 51212588579793007921, 25852138389591620222016, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.IX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.ix1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IX', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762144
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.IY', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.P', '24.FH', '24.FM', '24.FO', '24.FP', '24.FT', '24.FW'], 'contains': ['96.MN', '96.NU', '96.OJ', '96.TJ', '96.TK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 51212588579793007921, 25852138389591620222016, 1313941673647, 25852017102974698844878, 108169256203674548203560], 'label': '3072.bgb.48.IY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.ix2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IY', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762145
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.IZ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.Q', '24.FI', '24.FJ', '24.FM', '24.FN', '24.FV', '24.FW'], 'contains': ['96.MN', '96.NO', '96.PK', '96.TL', '96.TM'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 53952412691500576681559, 51212588579793007921, 25852138389591620222016, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.IZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.iy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IZ', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762146
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.JA', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.U', '24.FH', '24.FN', '24.FQ', '24.FZ'], 'contains': ['96.MN', '96.MV', '96.NI', '96.NT', '96.NV', '96.OF', '96.OK', '96.PA', '96.RQ', '96.TI', '96.TQ'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 133970303627361494479417, 1313941673647], 'label': '3072.bgb.48.JA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.iz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.JA', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 184762147
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.JB', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.M', '24.FX'], 'contains': ['96.MP', '96.MW', '96.MX', '96.NJ', '96.NM', '96.NW', '96.NY', '96.OM', '96.OR', '96.PC', '96.PG', '96.RT', '96.RW', '96.TZ', '96.VH'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 79804429416356250372480, 79855520714221614566521, 25903229681844523013167, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.48.JB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.ja1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.JB', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184762148
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.JC', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.M', '24.FX', '24.FY'], 'contains': ['96.MO', '96.MW', '96.MX', '96.NK', '96.NN', '96.NW', '96.NX', '96.ON', '96.OO', '96.PE', '96.PI', '96.RU', '96.RW', '96.UA', '96.UF'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 187922594664024732247801, 79855398717732338388456, 25903229681844523013167, 187973685961890096441600, 1313941673647], 'label': '3072.bgb.48.JC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.jb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.JC', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184762149
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.JD', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.V', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.Q', '24.FK', '24.FL'], 'contains': ['96.MQ', '96.NO', '96.PK', '96.VO', '96.VP'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107687970595565937, 25903229681844523013167, 53952412691500576681559, 25903107685154153232142, 1313941673647, 25852017101492540879976], 'label': '3072.bgb.48.JD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '48.jc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.JD', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762150
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.JE', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.R', '24.FI', '24.FO', '24.FQ', '24.GB'], 'contains': ['96.ML', '96.MN', '96.NG', '96.NL', '96.NP', '96.OS', '96.OV', '96.PH', '96.RX', '96.SA', '96.TA'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79804308122845802507662, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 1313941673647], 'label': '3072.bgb.48.JE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.jd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.JE', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762151
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.JF', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.R', '24.FJ', '24.FP', '24.FY', '24.FZ'], 'contains': ['96.MM', '96.MN', '96.NI', '96.NN', '96.NQ', '96.OT', '96.OX', '96.PL', '96.RZ', '96.SA', '96.TN'], 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.48.JF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.je1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.JF', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 184762152
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.JG', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.R', '24.FK', '24.FY'], 'contains': ['96.MO', '96.MQ', '96.NK', '96.NL', '96.NQ', '96.OU', '96.OV', '96.PL', '96.SC', '96.SG', '96.UJ'], 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 187973685961890096441600, 79804308125641822294440, 1313941673647, 108118287251071627990321, 79804429413572684637382], 'label': '3072.bgb.48.JG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.jf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.JG', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 184762153
    {'ambient': '3072.bgb', 'aut_centralizer_order': 1, 'aut_label': '2.E', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '3072.a1', 'complements': ['1536.I', '1536.C', '1536.F', '1536.D', '1536.K', '1536.J'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.B', '4.F', '4.G', '6.M', '8.I'], 'core': '2.E', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [25903229681844523013167, 134021529040297499210286, 1313941673647, 187922473375925652905521, 404159831259638948150382, 133970303627361494479417, 566444897749485959875336, 378358905093235639407953, 162070456272950954131199, 108118165248982343710201], 'label': '3072.bgb.2.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.B', '4.F', '4.G'], 'normalizer': '1.a1', 'old_label': '2.e1', 'projective_image': '3072.bgb', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.E', 'subgroup_fusion': None, 'weyl_group': '3072.bgb'}
  • id: 184762154
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.K', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.D', '6.E', '6.F'], 'contains': ['24.P', '24.R', '24.DR', '24.EB', '24.EC', '24.FO', '24.FP'], 'core': '48.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 51212588579793007921, 122002101738321960, 1313941673647, 79804429413572684637382, 25852017102974698844878, 108169256203674548203560], 'label': '3072.bgb.12.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.k1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.K', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184762155
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.JH', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '384.GJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.R', '24.FL', '24.FX'], 'contains': ['96.MP', '96.MQ', '96.NM', '96.NN', '96.NP', '96.OW', '96.OX', '96.PH', '96.SF', '96.SG', '96.VI'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 79804429416356250372480, 79855398717732338388456, 25903229681844523013167, 51212588579793007921, 1313941673647], 'label': '3072.bgb.48.JH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.jg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.JH', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762156
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.JI', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.Z', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.T', '24.FS', '24.FT'], 'contains': ['96.NA', '96.NE', '96.NU', '96.PM', '96.PU', '96.QN', '96.SP'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922594664024732247801, 25903229337376182892926, 25903229681844523013167, 187973685961890096441600, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.JI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.jh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.JI', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184762157
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.JJ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.I', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.L', '24.FR', '24.GA'], 'contains': ['96.GT', '96.GU', '96.GV', '96.GW', '96.GX', '96.GY', '96.MJ', '96.MK', '96.MY', '96.NC', '96.NZ', '96.OA', '96.PN', '96.RE', '96.ST'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229337376182892926, 25903229681844523013167, 51212588579793007921, 1313941673647, 25852017101492540879976, 25852017102974698844878], 'label': '3072.bgb.48.JJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.ji1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.JJ', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 184762158
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.JK', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.U', '24.FX', '24.FY'], 'contains': ['96.MM', '96.MQ', '96.MT', '96.MX', '96.MZ', '96.NK', '96.NW', '96.OH', '96.OP', '96.PA', '96.PJ', '96.PR', '96.QA', '96.RH', '96.SK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229691554491852799, 134021272934136496216343, 1313941673647, 25903229681844523013167, 25852138393689126932998, 108118165248982343710201], 'label': '3072.bgb.48.JK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.jj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.JK', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184762159
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.JL', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.U', '24.FX', '24.FY'], 'contains': ['96.MO', '96.MQ', '96.MW', '96.MX', '96.NA', '96.NI', '96.NR', '96.OL', '96.OQ', '96.PD', '96.PJ', '96.PO', '96.PW', '96.RN', '96.SK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 25852138393689126932998, 25903229681844523013167, 51212588579793007921, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.48.JL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.jj2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.JL', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184762160
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.JM', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.M', '24.FX', '24.GB'], 'contains': ['96.ML', '96.MP', '96.MS', '96.MW', '96.MZ', '96.NJ', '96.NX', '96.OG', '96.ON', '96.OY', '96.PG', '96.PS', '96.PZ', '96.RI', '96.SM'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 162121668858915397667278, 162070578272437343706839, 79855398717732338388456, 108118165248982343710201], 'label': '3072.bgb.48.JM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.jk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.JM', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184762161
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.JN', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.M', '24.FY', '24.GB'], 'contains': ['96.MM', '96.MO', '96.MR', '96.MW', '96.MZ', '96.NL', '96.NX', '96.OE', '96.OM', '96.PB', '96.PE', '96.PS', '96.QB', '96.RJ', '96.SN'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [162070578272437343706839, 108118165248982343710201, 25903229681844523013167, 162121668858915397667278, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.48.JN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.jl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.JN', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184762162
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.JO', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.U', '24.FR', '24.FX'], 'contains': ['96.MS', '96.MT', '96.MX', '96.MY', '96.NM', '96.OF', '96.OI', '96.OQ', '96.QE', '96.SU', '96.SV'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [187922594664024732247801, 108118165248982343710201, 79855398717732338388456, 25903229681844523013167, 187973685961890096441600, 1313941673647], 'label': '3072.bgb.48.JO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.jm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.JO', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 184762163
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.JP', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 48, 'centralizer': '384.GI', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.U', '24.FS', '24.FX'], 'contains': ['96.MP', '96.MX', '96.NA', '96.NH', '96.NT', '96.OP', '96.PF', '96.PP', '96.PV', '96.RO', '96.SU'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [187922594664024732247801, 108118165248982343710201, 79855398717732338388456, 25903229681844523013167, 51212588579793007921, 1313941673647], 'label': '3072.bgb.48.JP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.jm2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.JP', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762164
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.JQ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.I', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.P', '24.FR', '24.GA'], 'contains': ['96.GZ', '96.HA', '96.MU', '96.MY', '96.OJ', '96.SW', '96.SX'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 162121669227129588479873, 51212588579793007921, 1313941673647, 25852017101492540879976, 25852017102974698844878], 'label': '3072.bgb.48.JQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.jn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.JQ', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 184762165
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.L', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.C', '6.D', '6.G'], 'contains': ['24.R', '24.BD', '24.BZ', '24.ED', '24.EG'], 'core': '48.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 404210787739267985320182, 187922473375925652905521, 296092500500710274860657, 122002101738321960, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.12.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.l1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.L', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184762166
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.JR', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.R', '24.FX', '24.GB'], 'contains': ['96.ML', '96.MM', '96.MO', '96.MP', '96.MY', '96.NJ', '96.NP', '96.OS', '96.OT', '96.OU', '96.OW', '96.PT', '96.QF', '96.RY', '96.SJ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [187922594664024732247801, 108118165248982343710201, 25903229681844523013167, 187973685961890096441600, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.48.JR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.jo1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.JR', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184762167
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.JS', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.X', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.P', '24.T', '24.FU', '24.GA'], 'contains': ['96.HB', '96.HC', '96.HD', '96.HE', '96.MJ', '96.MU', '96.NB', '96.PM', '96.PU', '96.QR', '96.TP'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 162121669227129588479873, 187973685961890096441600, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.48.JS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.jp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.JS', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762168
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.JT', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.U', '24.FX', '24.GB'], 'contains': ['96.MP', '96.MV', '96.MW', '96.MY', '96.MZ', '96.NA', '96.NG', '96.OD', '96.OH', '96.OZ', '96.PQ', '96.PR', '96.QE', '96.QH', '96.SZ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229691554491852799, 1313941673647, 25903229681844523013167, 133970182339249961095537, 25852017102974698844878, 108118165248982343710201], 'label': '3072.bgb.48.JT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.jq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.JT', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184762169
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.JU', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.U', '24.FT', '24.FV', '24.FY', '24.GB'], 'contains': ['96.MN', '96.MO', '96.MZ', '96.NA', '96.NS', '96.OC', '96.OI', '96.PX', '96.QA', '96.QG', '96.TB'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 133970182339249961095537, 25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 1313941673647], 'label': '3072.bgb.48.JU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.jr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.JU', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762170
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.JV', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.U', '24.FU', '24.FW', '24.FZ', '24.GB'], 'contains': ['96.MM', '96.MN', '96.MS', '96.MV', '96.NB', '96.PP', '96.PQ', '96.PW', '96.PX', '96.RS', '96.TQ'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.48.JV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.js1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.JV', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762171
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '48.JW', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '192.NQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.U', '24.GA', '24.GB'], 'contains': ['96.HF', '96.HG', '96.ML', '96.MR', '96.MY', '96.MZ', '96.NB', '96.OK', '96.PO', '96.PV', '96.QG', '96.QH', '96.TO'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 1313941673647, 108118287251071627990321, 162070456272950954131199], 'label': '3072.bgb.48.JW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.jt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.JW', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762172
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.JX', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.V', '24.FI', '24.FK'], 'contains': ['96.ND', '96.NL', '96.NO', '96.QS', '96.RB', '96.UC', '96.UW'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 25852017095880079467006, 25903107685154153232142, 1313941673647, 53952291036675691857216, 51090958997032170942], 'label': '3072.bgb.48.JX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '48.ju1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.JX', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762173
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.JY', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.V', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.V', '24.FJ', '24.FL'], 'contains': ['96.ND', '96.NN', '96.NO', '96.RA', '96.RB', '96.UV', '96.UW'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [53952291033879672806278, 79855398717732338388456, 25903229681844523013167, 53952412691500576681559, 51212588579793007921, 1313941673647], 'label': '3072.bgb.48.JY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '48.jv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.JY', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762174
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.JZ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.C', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.BA', '24.FI', '24.FL'], 'contains': ['96.ND', '96.NO', '96.NP', '96.QK', '96.QZ', '96.SD', '96.UU'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79855520714221614566521, 79804429415054842584367, 25903229681844523013167, 25903107685154153232142, 1313941673647, 51090958997032170942], 'label': '3072.bgb.48.JZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '48.jw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.JZ', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184762175
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.KA', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.Q', '24.BA', '24.FJ', '24.FK'], 'contains': ['96.ND', '96.NO', '96.NQ', '96.QK', '96.RD', '96.SD', '96.UX'], 'core': '192.B', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79855520714221614566521, 25903229681844523013167, 53952412691500576681559, 79804308125641822294440, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.48.KA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '48.jx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.KA', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762176
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '12.M', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.6407063', 'aut_weyl_index': 12, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.A', '6.C', '6.E'], 'contains': ['24.R', '24.BK', '24.CO', '24.EE', '24.EF'], 'core': '48.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118421696801471190456, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 187973685961890096441600, 122002101738321960, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.12.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.m1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.M', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 184762177
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.KB', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.K', '24.FT', '24.GC'], 'contains': ['96.NE', '96.NS', '96.NU', '96.QL', '96.QQ', '96.SL', '96.SS'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 162121669227129588479873, 1313941673647, 162070456274433112077942, 187922594658424724202816, 25852017102974698844878], 'label': '3072.bgb.48.KB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.jy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.KB', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762178
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.KC', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.U', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.K', '24.FH', '24.FS'], 'contains': ['96.NE', '96.NT', '96.NU', '96.QM', '96.QP', '96.SO', '96.SR'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25852017094578671678641, 25903229681844523013167, 25852138389591620222016, 1313941673647, 134021272934136496216343, 51090960298439969137], 'label': '3072.bgb.48.KC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.jz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.KC', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762179
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.KD', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.C', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.R', '24.T', '24.FH', '24.GC'], 'contains': ['96.NE', '96.NU', '96.NV', '96.QO', '96.QR', '96.SQ', '96.TP'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 51212588579793007921, 133970303627361494479417, 1313941673647, 108118286902479131308678], 'label': '3072.bgb.48.KD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.ka1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.KD', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762180
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.KE', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.U', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.L', '24.FS', '24.GC'], 'contains': ['96.HH', '96.HI', '96.HJ', '96.HK', '96.HL', '96.HM', '96.NC', '96.NE', '96.NF', '96.NH', '96.QI', '96.QJ', '96.QW', '96.RE', '96.ST'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229337376182892926, 122007701746409022, 25903229681844523013167, 1313941673647, 25852017101492540879976, 25852017102974698844878], 'label': '3072.bgb.48.KE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.kb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.KE', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762181
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.KF', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.M', '24.FQ', '24.FX'], 'contains': ['96.NG', '96.NJ', '96.NM', '96.NR', '96.NT', '96.NW', '96.NX', '96.RJ', '96.RM', '96.RU', '96.RV', '96.SH', '96.SM', '96.TV', '96.VH'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [162070578272437343706839, 108118165248982343710201, 79855398717732338388456, 25903229681844523013167, 51212588579793007921, 1313941673647], 'label': '3072.bgb.48.KF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.kc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.KF', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184762182
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.KG', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.M', '24.FQ', '24.FY'], 'contains': ['96.NI', '96.NK', '96.NL', '96.NR', '96.NS', '96.NW', '96.NX', '96.RI', '96.RK', '96.RT', '96.RV', '96.SN', '96.SY', '96.UA', '96.UG'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [162070578272437343706839, 108118165248982343710201, 25903229681844523013167, 51212588579793007921, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.48.KG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.kd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.KG', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184762183
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.KH', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.U', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.P', '24.FS', '24.GC'], 'contains': ['96.NH', '96.NU', '96.RP', '96.SW', '96.SX'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [122007701746409022, 25903229681844523013167, 162121669227129588479873, 1313941673647, 25852017101492540879976, 25852017102974698844878], 'label': '3072.bgb.48.KH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.ke1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.KH', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762184
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.KI', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.U', '24.FQ', '24.GC'], 'contains': ['96.NG', '96.NH', '96.NR', '96.NS', '96.NV', '96.RH', '96.RL', '96.RS', '96.SI', '96.SV', '96.TO'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79855520714221614566521, 25903229681844523013167, 187922473375925652905521, 1313941673647, 108118287251071627990321, 162070456272950954131199], 'label': '3072.bgb.48.KI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.kf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.KI', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 184762185
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.KJ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.R', '24.FQ', '24.FX'], 'contains': ['96.NG', '96.NH', '96.NI', '96.NJ', '96.NK', '96.NM', '96.NP', '96.RX', '96.RY', '96.RZ', '96.SB', '96.SC', '96.SF', '96.SJ', '96.VJ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [187922594664024732247801, 108118165248982343710201, 25903229681844523013167, 51212588579793007921, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.48.KJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.kg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.KJ', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184762186
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.KK', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.G', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.CP', '24.FH', '24.FR'], 'contains': ['96.NZ', '96.OF', '96.OJ', '96.QM', '96.QO', '96.SO', '96.SQ'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 25852138389591620222016, 108169377837562135992360, 1313941673647, 134021272934136496216343, 51090960298439969137], 'label': '3072.bgb.48.KK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.kh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.KK', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762187
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.N', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.6536092', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.F'], 'contains': ['24.K', '24.L', '24.P', '24.T', '24.U', '24.BM', '24.BT', '24.CA', '24.CP', '24.DM', '24.ER', '24.FG', '24.FH', '24.FR', '24.FS', '24.FT', '24.FU', '24.GA', '24.GC'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 51212588579793007921, 133970303627361494479417, 122002101738321960, 1313941673647, 25852017102974698844878, 108169256203674548203560], 'label': '3072.bgb.12.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.n1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.N', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 184762188
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.KL', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.BM', '24.FR', '24.FT'], 'contains': ['96.NZ', '96.OI', '96.OJ', '96.QN', '96.QQ', '96.SP', '96.SS'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922594664024732247801, 25903229337376182892926, 25903229681844523013167, 1313941673647, 187922594658424724202816, 25852017102974698844878], 'label': '3072.bgb.48.KL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.ki1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.KL', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762189
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.KM', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '768.I', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.BM', '24.FH', '24.GA'], 'contains': ['96.HN', '96.HO', '96.HT', '96.HU', '96.NZ', '96.OJ', '96.OK', '96.QP', '96.QR', '96.SR', '96.TP'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229691554491852799, 108118165248982343710201, 25903229681844523013167, 133970303627361494479417, 1313941673647, 108118286902479131308678], 'label': '3072.bgb.48.KM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.kj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.KM', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 184762190
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.KN', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.BN', '24.FI', '24.FK'], 'contains': ['96.HP', '96.HQ', '96.HV', '96.HW', '96.OB', '96.OV', '96.PK', '96.QK', '96.QS', '96.SD', '96.UC'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107687970595565937, 25903229681844523013167, 25903107685154153232142, 1313941673647, 53952291036675691857216, 51090958997032170942], 'label': '3072.bgb.48.KN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '48.kk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.KN', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762191
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.KO', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.V', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.BN', '24.FJ', '24.FL'], 'contains': ['96.HR', '96.HS', '96.HX', '96.HY', '96.OB', '96.OX', '96.PK', '96.QK', '96.RA', '96.SD', '96.UV'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [53952291033879672806278, 79855520714221614566521, 79855398717732338388456, 25903229681844523013167, 53952412691500576681559, 1313941673647], 'label': '3072.bgb.48.KO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '48.kl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.KO', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762192
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.KP', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.BY', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.BS', '24.FI', '24.FL'], 'contains': ['96.OB', '96.PH', '96.PK', '96.QZ', '96.RB', '96.UU', '96.UW'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804429415054842584367, 25903107687970595565937, 25903229681844523013167, 25903107685154153232142, 1313941673647, 51090958997032170942], 'label': '3072.bgb.48.KP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '48.km1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.KP', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762193
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.KQ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.BS', '24.FJ', '24.FK'], 'contains': ['96.OB', '96.PK', '96.PL', '96.RB', '96.RD', '96.UW', '96.UX'], 'core': '192.B', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229691554491852799, 25903229681844523013167, 53952412691500576681559, 79804308125641822294440, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.48.KQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '48.kn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.KQ', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 184762194
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.KR', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BV', '24.FX', '24.FY'], 'contains': ['96.OD', '96.OI', '96.OM', '96.OP', '96.OT', '96.PE', '96.PJ', '96.RI', '96.RN', '96.RU', '96.RW', '96.SC', '96.SG', '96.SK', '96.SY'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 25852138393689126932998, 25903229681844523013167, 187973685961890096441600, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.48.KR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.ko1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.KR', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184762195
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.KS', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BV', '24.FX', '24.FY'], 'contains': ['96.OC', '96.OH', '96.ON', '96.OQ', '96.OU', '96.PB', '96.PJ', '96.RJ', '96.RO', '96.RT', '96.RW', '96.RZ', '96.SG', '96.SK', '96.UA'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 134021272934136496216343, 1313941673647, 162121668858915397667278, 25852138393689126932998, 108118165248982343710201], 'label': '3072.bgb.48.KS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.ko2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.KS', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184762328
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.PI', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.26539', 'aut_weyl_index': 24, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ED', '24.GL', '24.HW'], 'contains': ['96.UH', '96.UJ'], 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952413035981411118158, 25903229681844523013167, 79804308125641822294440, 1313941673647, 79804429413572684637382, 134021529040297499210286], 'label': '3072.bgb.48.PI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.K', 'old_label': '48.pc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.PI', 'subgroup_fusion': None, 'weyl_group': '128.931'}
  • id: 184762196
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.KT', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CQ', '24.FQ', '24.FX'], 'contains': ['96.OD', '96.OF', '96.OL', '96.OO', '96.OS', '96.PC', '96.PF', '96.RH', '96.RM', '96.RT', '96.RV', '96.SB', '96.SF', '96.SI', '96.SM'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [162070578272437343706839, 108118165248982343710201, 79855398717732338388456, 25903229681844523013167, 187973685961890096441600, 1313941673647], 'label': '3072.bgb.48.KT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.kp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.KT', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184762197
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.KU', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CQ', '24.FQ', '24.FY'], 'contains': ['96.OC', '96.OE', '96.OL', '96.OO', '96.OV', '96.PA', '96.PD', '96.RH', '96.RL', '96.RU', '96.RV', '96.RZ', '96.SC', '96.SN', '96.UG'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [162070578272437343706839, 25903229691554491852799, 108118165248982343710201, 25903229681844523013167, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.48.KU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.kq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.KU', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184762198
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.O', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.6536092', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.F'], 'contains': ['24.P', '24.Q', '24.U', '24.CB', '24.CC', '24.ES', '24.ET', '24.FM', '24.FN', '24.FV', '24.FW'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 53952412691500576681559, 51212588579793007921, 133970303627361494479417, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.12.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.o1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.O', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 184762199
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.KV', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BV', '24.FX'], 'contains': ['96.OG', '96.OH', '96.OP', '96.OQ', '96.OW', '96.OZ', '96.PG', '96.RM', '96.RN', '96.RW', '96.RY', '96.SF', '96.SU', '96.VH'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229691554491852799, 1313941673647, 25903229681844523013167, 79855398717732338388456, 108118165248982343710201, 187922594664024732247801], 'label': '3072.bgb.48.KV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.kr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.KV', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184762200
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.KW', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BV', '24.FQ', '24.GB'], 'contains': ['96.OC', '96.OD', '96.OE', '96.OK', '96.OS', '96.OY', '96.OZ', '96.RI', '96.RJ', '96.RK', '96.RS', '96.RX', '96.RY', '96.SH', '96.TO'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 1313941673647, 108118287251071627990321, 79804429421968711780537, 162070456272950954131199], 'label': '3072.bgb.48.KW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.ks1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.KW', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184762201
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.KX', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CR', '24.FQ', '24.FX'], 'contains': ['96.OY', '96.OZ', '96.PA', '96.PC', '96.PD', '96.PF', '96.PH', '96.SI', '96.SJ', '96.SV', '96.SY', '96.TV', '96.UA', '96.VH', '96.VJ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [187922594664024732247801, 25903229691554491852799, 108118165248982343710201, 25903229681844523013167, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.48.KX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.kt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.KX', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184762202
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.KY', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.BS', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.CP', '24.FS', '24.FU'], 'contains': ['96.PM', '96.PP', '96.PU', '96.QI', '96.QM', '96.RP', '96.SO'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 187973685961890096441600, 1313941673647, 25852017102974698844878, 187922594661241166512703, 51090960298439969137], 'label': '3072.bgb.48.KY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.ku1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.KY', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184762203
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '48.KZ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BO'], 'contains': ['96.HZ', '96.IA', '96.IB', '96.IC', '96.PN', '96.QC', '96.QD', '96.QT', '96.QY', '96.UK', '96.UT'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804429416356250372480, 378358770650295628183080, 25903229681844523013167, 25852272837936812846761, 1313941673647, 242140721658215271465607], 'label': '3072.bgb.48.KZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BO', 'old_label': '48.kv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.KZ', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 184762204
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.LA', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '384.DP', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BT', '24.FS', '24.GA'], 'contains': ['96.ID', '96.IE', '96.IM', '96.PM', '96.PV', '96.QP', '96.RE', '96.SX'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 162121669227129588479873, 187973685961890096441600, 1313941673647, 25852017101492540879976, 25852017102974698844878], 'label': '3072.bgb.48.LA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.kw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.LA', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762205
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.LB', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '384.CG', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.BT', '24.FT', '24.FU', '24.GD', '24.GE', '24.GF', '24.GN'], 'contains': ['96.PM', '96.PX', '96.QQ', '96.RF', '96.TK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [162070577934876685646657, 25903229681844523013167, 187973685961890096441600, 25852138389591620222016, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.LB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.kx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.LB', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184762206
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.LC', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BV', '24.FX', '24.GB'], 'contains': ['96.OH', '96.OI', '96.OM', '96.ON', '96.OS', '96.OW', '96.OY', '96.PG', '96.PO', '96.PQ', '96.PV', '96.RJ', '96.RR', '96.RY', '96.SZ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 133970182339249961095537, 25903229681844523013167, 187973685961890096441600, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.LC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.ky1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.LC', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184762207
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.LD', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BV', '24.FY', '24.GB', '24.GD', '24.GG'], 'contains': ['96.OE', '96.OH', '96.OU', '96.PE', '96.PO', '96.PX', '96.RI', '96.SA', '96.TB'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229691554491852799, 1313941673647, 25903229681844523013167, 187922473375925652905521, 133970182339249961095537, 108118165248982343710201], 'label': '3072.bgb.48.LD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.kz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.LD', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762208
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.LE', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CQ', '24.FX', '24.FZ'], 'contains': ['96.OF', '96.OG', '96.OR', '96.OT', '96.OX', '96.PA', '96.PI', '96.PP', '96.PQ', '96.PW', '96.RM', '96.RQ', '96.RZ', '96.TH'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 25903229691554491852799, 25903229681844523013167, 187922473375925652905521, 133970303627361494479417, 1313941673647], 'label': '3072.bgb.48.LE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.la1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.LE', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184762209
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.P', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B'], 'contains': ['24.V', '24.W', '24.Y', '24.BB', '24.BC', '24.BF', '24.BH', '24.CW', '24.CY', '24.DA', '24.DD', '24.EU', '24.EW', '24.EY', '24.FB'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [242089752358354392177983, 25903229681844523013167, 122002101738321960, 1313941673647, 134021272934136496216343, 53952035291802302422343, 296041409911409376977422, 187922594661241166512703], 'label': '3072.bgb.12.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.p1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.P', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184762210
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.LF', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BV', '24.FZ', '24.GB', '24.GE', '24.GH'], 'contains': ['96.OG', '96.OK', '96.OT', '96.PB', '96.PQ', '96.PX', '96.RR', '96.SA', '96.TQ'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229691554491852799, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 133970303627361494479417, 1313941673647], 'label': '3072.bgb.48.LF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.lb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.LF', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762211
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.LG', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.K', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BX', '24.GJ', '24.GO'], 'contains': ['96.IF', '96.IG', '96.IH', '96.PT', '96.QD', '96.SE', '96.TU', '96.TX'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 54003382330230002441647, 378307558065813088567696, 1313941673647, 134021272934136496216343, 216288705272228144236816], 'label': '3072.bgb.48.LG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BA', 'old_label': '48.lc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.LG', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762212
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.LH', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.K', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BZ', '24.GJ', '24.GO'], 'contains': ['96.II', '96.PT', '96.TW', '96.TY'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 242140721662339602266753, 54003382330230002441647, 404159575154785525538638, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.48.LH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BA', 'old_label': '48.ld1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.LH', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762213
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.LI', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 48, 'centralizer': '384.GH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CQ', '24.FX', '24.GI'], 'contains': ['96.OQ', '96.OR', '96.OW', '96.PF', '96.PR', '96.PZ', '96.RU', '96.SB', '96.TZ'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 79804429416356250372480, 25903229681844523013167, 108169377837562135992360, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.48.LI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '48.le1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.LI', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762214
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.LJ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CQ', '24.FX', '24.GJ'], 'contains': ['96.OL', '96.ON', '96.OP', '96.OR', '96.PT', '96.QE', '96.SF', '96.TV', '96.TZ'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 79804429416356250372480, 25903229681844523013167, 187973685961890096441600, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.48.LJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '48.le2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.LJ', 'subgroup_fusion': None, 'weyl_group': '128.1578'}
  • id: 184762215
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.LK', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CQ', '24.FX', '24.FY'], 'contains': ['96.OL', '96.OM', '96.OP', '96.OQ', '96.OU', '96.OX', '96.PD', '96.PI', '96.PR', '96.PS', '96.QA', '96.RT', '96.RV', '96.SC', '96.UF'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 187922594664024732247801, 79855520714221614566521, 79855398717732338388456, 25903229681844523013167, 1313941673647], 'label': '3072.bgb.48.LK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.lf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.LK', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184762216
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.LL', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '384.DQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CA', '24.FS', '24.GA'], 'contains': ['96.IJ', '96.IK', '96.IL', '96.PU', '96.PV', '96.SR', '96.ST', '96.SW'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229337376182892926, 25903229681844523013167, 187973685961890096441600, 1313941673647, 25852017101492540879976, 25852017102974698844878], 'label': '3072.bgb.48.LL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.lg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.LL', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762217
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.LM', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '384.CH', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.CA', '24.FT', '24.FU', '24.GG', '24.GH', '24.GK', '24.GQ'], 'contains': ['96.PU', '96.PX', '96.SS', '96.TE', '96.TJ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25852138757799544092222, 25903229681844523013167, 187973685961890096441600, 25852138389591620222016, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.LM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.lh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.LM', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184762218
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.LN', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '384.CH', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.CB', '24.FV', '24.FW', '24.GD', '24.GE', '24.GK', '24.GQ'], 'contains': ['96.PX', '96.TJ', '96.TM'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 53952412691500576681559, 187973685961890096441600, 25852138389591620222016, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.LN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.li1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.LN', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184762219
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.LO', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '384.CG', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.CC', '24.FV', '24.FW', '24.GF', '24.GG', '24.GH', '24.GN'], 'contains': ['96.PX', '96.TK', '96.TL'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 187973685961890096441600, 25852138389591620222016, 1313941673647, 25852017102974698844878, 108169256203674548203560], 'label': '3072.bgb.48.LO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.lj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.LO', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184762220
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.Q', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B'], 'contains': ['24.V', '24.X', '24.Z', '24.BB', '24.BE', '24.BG', '24.BI', '24.CX', '24.CZ', '24.DB', '24.DF', '24.EV', '24.EX', '24.EZ', '24.FE'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 134021272934136496216343, 1313941673647, 122002101738321960, 53952035291802302422343, 324406991811924875755576, 187922594661241166512703, 378358649363678452761737], 'label': '3072.bgb.12.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.q1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.Q', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184762221
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.LP', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 48, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CR', '24.FY', '24.FZ', '24.GF', '24.GK'], 'contains': ['96.PA', '96.PB', '96.PI', '96.PL', '96.PW', '96.PX', '96.SY', '96.TI', '96.TN'], 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229691554491852799, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.48.LP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.lk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.LP', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762222
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.LQ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '384.EC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CD', '24.GI', '24.GO'], 'contains': ['96.IN', '96.IO', '96.IP', '96.PY', '96.PZ', '96.TS', '96.TU', '96.TW'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 54003382330230002441647, 404159575154785525538638, 1313941673647, 134021272934136496216343, 216288705272228144236816], 'label': '3072.bgb.48.LQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BA', 'old_label': '48.ll1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.LQ', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 184762223
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.LR', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '384.EB', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CG', '24.GI', '24.GO'], 'contains': ['96.IQ', '96.PZ', '96.TX', '96.TY'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 242140721662339602266753, 54003382330230002441647, 378307558065813088567696, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.48.LR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BA', 'old_label': '48.lm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.LR', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762224
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.LS', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CD', '24.GL', '24.GR'], 'contains': ['96.PY', '96.QB', '96.TT', '96.UE', '96.UH'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [324355779217738848775558, 378358770650295628183080, 25903229681844523013167, 79804308125641822294440, 134021394933610431760703, 1313941673647], 'label': '3072.bgb.48.LS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BE', 'old_label': '48.ln1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.LS', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184762225
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.LT', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CF', '24.GL', '24.GR'], 'contains': ['96.QB', '96.UH', '96.UI'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 134021394933610431760703, 1313941673647, 378358649363678452761737, 324355901222623977942343], 'label': '3072.bgb.48.LT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BE', 'old_label': '48.lo1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.LT', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184762226
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.LU', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 48, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CR', '24.FY', '24.GL'], 'contains': ['96.PD', '96.PE', '96.PJ', '96.PL', '96.QA', '96.QB', '96.UA', '96.UG', '96.UJ'], 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229691554491852799, 25903229681844523013167, 79804308125641822294440, 1313941673647, 108118287251071627990321, 79804429413572684637382], 'label': '3072.bgb.48.LU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '48.lp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.LU', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762227
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.LV', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CJ', '24.GM', '24.GP'], 'contains': ['96.QC', '96.QF', '96.UN', '96.UR', '96.VL'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804308122845802507662, 25903229681844523013167, 162121668858915397667278, 79804308125641822294440, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.48.LV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BC', 'old_label': '48.lq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.LV', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762228
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.LW', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 48, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CR', '24.FX', '24.GM'], 'contains': ['96.PF', '96.PG', '96.PI', '96.PJ', '96.QE', '96.QF', '96.VH', '96.VI', '96.VJ'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 79804429416356250372480, 79855398717732338388456, 25903229681844523013167, 187973685961890096441600, 1313941673647], 'label': '3072.bgb.48.LW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '48.lr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.LW', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762229
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.LX', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CO', '24.GM', '24.GP'], 'contains': ['96.QF', '96.VK', '96.VL'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108169512287410083283217, 79804308122845802507662, 25903229691554491852799, 25903229681844523013167, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.48.LX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BC', 'old_label': '48.ls1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.LX', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762230
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.LY', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.BM', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.CP', '24.FT', '24.GA'], 'contains': ['96.IR', '96.IS', '96.IT', '96.IU', '96.NZ', '96.OJ', '96.PM', '96.PU', '96.QG', '96.QL', '96.SL'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 162121669227129588479873, 187973685961890096441600, 1313941673647, 162070456274433112077942, 25852017102974698844878], 'label': '3072.bgb.48.LY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.lt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.LY', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762231
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '12.R', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.H', '6.B'], 'contains': ['24.A', '24.W', '24.X', '24.BA', '24.BF', '24.BG', '24.BJ', '24.CS', '24.CT', '24.DC', '24.DG', '24.DS', '24.DT', '24.FA', '24.FC'], 'core': '24.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 122002101738321960, 79804429413572684637382, 53952035291802302422343, 378307558065813088567696, 79804308125641822294440, 378358649363678452761737], 'label': '3072.bgb.12.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.r1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.R', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 184762232
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.LZ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CQ', '24.FX', '24.GB'], 'contains': ['96.OC', '96.OG', '96.OM', '96.OO', '96.OW', '96.PC', '96.PO', '96.PP', '96.PR', '96.PS', '96.PT', '96.QE', '96.QH', '96.RX', '96.SM'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229691554491852799, 1313941673647, 25903229681844523013167, 162070578272437343706839, 79855398717732338388456, 108118165248982343710201], 'label': '3072.bgb.48.LZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.lu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.LZ', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184762233
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.MA', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CQ', '24.FY', '24.GB'], 'contains': ['96.OD', '96.ON', '96.OO', '96.OT', '96.OU', '96.OV', '96.PO', '96.PR', '96.PS', '96.PW', '96.QA', '96.QB', '96.QG', '96.RK', '96.SN'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [162070578272437343706839, 108118165248982343710201, 25903229681844523013167, 187973685961890096441600, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.48.MA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.lv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.MA', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184762234
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '48.MB', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '192.NJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CR', '24.FX', '24.GB'], 'contains': ['96.OZ', '96.PB', '96.PC', '96.PE', '96.PG', '96.PH', '96.PV', '96.PW', '96.PZ', '96.QA', '96.QE', '96.QF', '96.QH', '96.SH', '96.SJ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [187922594664024732247801, 108118165248982343710201, 25903229681844523013167, 162121668858915397667278, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.48.MB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.lw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.MB', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762235
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '48.MC', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '192.NR', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CQ', '24.GB', '24.GO'], 'contains': ['96.IV', '96.IW', '96.OE', '96.OS', '96.PQ', '96.PS', '96.PT', '96.PZ', '96.QG', '96.QH', '96.TC'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79804308122845802507662, 108118165248982343710201, 25903229681844523013167, 187973685961890096441600, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.MC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '48.lx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.MC', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184762236
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '48.MD', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '192.NS', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CR', '24.GB', '24.GN', '24.GP', '24.GQ', '24.GR'], 'contains': ['96.OY', '96.PX', '96.QB', '96.QF', '96.QH', '96.TA'], 'core': '768.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [79804308122845802507662, 25903229691554491852799, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647], 'label': '3072.bgb.48.MD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.ly1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.MD', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184762237
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.ME', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.G', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.CP', '24.FG', '24.GC'], 'contains': ['96.QI', '96.QL', '96.QO', '96.RL', '96.RP', '96.SL', '96.SQ'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [122007701746409022, 25903229681844523013167, 162121669227129588479873, 1313941673647, 162070456274433112077942, 25852017102974698844878], 'label': '3072.bgb.48.ME', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.lz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ME', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762238
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.MF', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.U', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.BM', '24.FG', '24.FS'], 'contains': ['96.QI', '96.QN', '96.QP', '96.RO', '96.RP', '96.SP', '96.SR'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922594664024732247801, 25903229337376182892926, 122007701746409022, 25903229681844523013167, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.MF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.ma1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.MF', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762239
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.MG', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.BM', '24.FU', '24.GC'], 'contains': ['96.QI', '96.QQ', '96.QR', '96.RP', '96.RS', '96.SS', '96.TP'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 162121669227129588479873, 1313941673647, 187922594658424724202816, 162070456272950954131199], 'label': '3072.bgb.48.MG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.mb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.MG', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762240
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '48.MH', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.CW', '24.GU', '24.HC'], 'contains': ['96.JG', '96.JH', '96.KB', '96.KC', '96.QS', '96.QU', '96.QX', '96.UB', '96.UE', '96.UL', '96.VC'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 79804308125641822294440, 134021394933610431760703, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.48.MH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '48.mc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.MH', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762241
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '48.MI', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.CX', '24.GU', '24.HC'], 'contains': ['96.QS', '96.QV', '96.RC', '96.UB', '96.UI', '96.UQ', '96.VQ'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 134021394933610431760703, 1313941673647, 53952035291802302422343, 378358649363678452761737], 'label': '3072.bgb.48.MI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '48.md1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.MI', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762242
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.S', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B'], 'contains': ['24.Y', '24.Z', '24.BA', '24.BH', '24.BI', '24.BJ', '24.BK', '24.CU', '24.CV', '24.DE', '24.DH', '24.DU', '24.DV', '24.FD', '24.FF'], 'core': '48.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 378307558065813088567696, 79804308125641822294440, 122002101738321960, 1313941673647, 79804429413572684637382, 378358649363678452761737, 162070200540784685681302], 'label': '3072.bgb.12.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.s1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.S', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184762243
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '48.MJ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BO'], 'contains': ['96.IZ', '96.JA', '96.JB', '96.JD', '96.QT', '96.QW', '96.QY', '96.UK', '96.UM', '96.UT', '96.UZ'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804429416356250372480, 378358770650295628183080, 270240484111912758504367, 25903229681844523013167, 25852272837936812846761, 1313941673647], 'label': '3072.bgb.48.MJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BO', 'old_label': '48.me1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.MJ', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 184762244
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '48.MK', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.CW', '24.GY', '24.HD'], 'contains': ['96.JI', '96.JJ', '96.KD', '96.KE', '96.QU', '96.QX', '96.RA', '96.UL', '96.UO', '96.VC', '96.VG'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [242089752358354392177983, 25903229681844523013167, 1313941673647, 134021272934136496216343, 53952035291802302422343, 187922594661241166512703], 'label': '3072.bgb.48.MK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '48.mf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.MK', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762245
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '48.ML', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.CX', '24.GY', '24.HD'], 'contains': ['96.QV', '96.RA', '96.RC', '96.UO', '96.UQ', '96.VM', '96.VQ'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 134021272934136496216343, 53952035291802302422343, 378358649363678452761737, 187922594661241166512703], 'label': '3072.bgb.48.ML', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '48.mg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ML', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762246
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.MM', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.DC', '24.GU', '24.HD'], 'contains': ['96.QU', '96.QV', '96.QZ', '96.UL', '96.UQ', '96.UR', '96.VA'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804308122845802507662, 25903229681844523013167, 25852272837936812846761, 79804308125641822294440, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.48.MM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '48.mh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.MM', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762247
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.MN', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.S', '24.DC', '24.GY', '24.HC'], 'contains': ['96.QU', '96.QV', '96.RD', '96.UL', '96.UQ', '96.US', '96.VD'], 'core': '192.B', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 1313941673647, 79804429413572684637382, 53952035291802302422343, 378358649363678452761737], 'label': '3072.bgb.48.MN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '48.mi1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.MN', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762248
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.MO', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.FO', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.DE', '24.GU', '24.HD'], 'contains': ['96.QX', '96.QZ', '96.RC', '96.VA', '96.VC', '96.VK', '96.VQ'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 79804308122845802507662, 25903229681844523013167, 162070321828715682652927, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.48.MO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '48.mj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.MO', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762249
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.MP', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.DE', '24.GY', '24.HC'], 'contains': ['96.QX', '96.RC', '96.RD', '96.VC', '96.VD', '96.VQ', '96.VR'], 'core': '192.B', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 1313941673647, 79804429413572684637382, 378358649363678452761737, 162070200540784685681302], 'label': '3072.bgb.48.MP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '48.mk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.MP', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 184762250
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.MQ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.DI', '24.FI', '24.FJ', '24.GD', '24.GE', '24.GS', '24.GT'], 'contains': ['96.QK', '96.RB', '96.RF', '96.SA', '96.TM'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855520714221614566521, 25903229681844523013167, 53952412691500576681559, 25852138389591620222016, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.MQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.ml1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.MQ', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762251
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.MR', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.V', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.DI', '24.FK', '24.FL'], 'contains': ['96.QK', '96.RB', '96.RG', '96.SG', '96.VP'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855520714221614566521, 25903229681844523013167, 53952412691500576681559, 25903107685154153232142, 1313941673647, 25852017101492540879976], 'label': '3072.bgb.48.MR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '48.mm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.MR', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762252
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.MS', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.U', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.DM', '24.FR', '24.FS'], 'contains': ['96.QM', '96.QN', '96.RE', '96.SU', '96.SW'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [187922594664024732247801, 108118165248982343710201, 79855398717732338388456, 25903229681844523013167, 1313941673647, 404210922196204071249966], 'label': '3072.bgb.48.MS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.mn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.MS', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762253
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.T', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B'], 'contains': ['24.G', '24.H', '24.I', '24.J', '24.BN', '24.BO', '24.BQ', '24.BW', '24.BX', '24.CH', '24.CK', '24.CS', '24.CU', '24.CW', '24.CZ', '24.DS', '24.DU', '24.EV', '24.EW'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [242089752358354392177983, 25903229681844523013167, 122002101738321960, 324406991811924875755576, 1313941673647, 134021272934136496216343, 53952035291802302422343, 187922594661241166512703], 'label': '3072.bgb.12.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.t1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.T', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184762254
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.MT', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BT', '24.FR', '24.GC'], 'contains': ['96.QO', '96.QQ', '96.RE', '96.SV', '96.SX'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 162121669227129588479873, 1313941673647, 25852017101492540879976, 187922594658424724202816, 25852017102974698844878], 'label': '3072.bgb.48.MT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.mo1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.MT', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762255
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.MU', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '384.CG', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.DJ', '24.FI', '24.GN', '24.GU', '24.GV', '24.GW', '24.HA'], 'contains': ['96.QS', '96.QZ', '96.RF', '96.TA', '96.TL'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79804308122845802507662, 108118165248982343710201, 25903229681844523013167, 404211043484134973872583, 187922473375925652905521, 1313941673647], 'label': '3072.bgb.48.MU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.mp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.MU', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 184762256
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.MV', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.DM', '24.FG', '24.FT', '24.GD', '24.GS', '24.GX', '24.HA'], 'contains': ['96.QL', '96.QN', '96.RF', '96.TB', '96.TJ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 133970182339249961095537, 25903229681844523013167, 187922473375925652905521, 1313941673647, 404210922196204071249966], 'label': '3072.bgb.48.MV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.mq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.MV', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762257
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '48.MW', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.DK', '24.GU', '24.GY'], 'contains': ['96.IX', '96.IY', '96.JK', '96.JL', '96.QU', '96.QV', '96.QX', '96.RC', '96.RF', '96.TD', '96.TF'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647, 53952035291802302422343, 378358649363678452761737], 'label': '3072.bgb.48.MW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '48.mr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.MW', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762258
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.MX', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.BT', '24.FG', '24.FH', '24.GF', '24.GS', '24.GT', '24.GV'], 'contains': ['96.QO', '96.QP', '96.RF', '96.TI', '96.TK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 133970182343548561347240, 25852138389591620222016, 1313941673647, 25852017102974698844878, 108169256203674548203560], 'label': '3072.bgb.48.MX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.ms1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.MX', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762259
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.MY', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.DJ', '24.FJ', '24.GF', '24.GX', '24.GY', '24.GZ', '24.HB'], 'contains': ['96.RA', '96.RD', '96.RF', '96.TL', '96.TN'], 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647, 79804429413572684637382, 404210922196204071249966], 'label': '3072.bgb.48.MY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.mt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.MY', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 184762260
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.MZ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.I', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.DM', '24.GA', '24.GC'], 'contains': ['96.JF', '96.JO', '96.KA', '96.QL', '96.QR', '96.RE', '96.SW', '96.TO'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 1313941673647, 108118287251071627990321, 378358905093235639407953, 162070456272950954131199], 'label': '3072.bgb.48.MZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.mu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.MZ', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 184762261
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.NA', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.DM', '24.FH', '24.FU', '24.GE', '24.GT', '24.HA', '24.HB'], 'contains': ['96.QM', '96.QR', '96.RF', '96.TJ', '96.TQ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 133970303627361494479417, 1313941673647, 404210922196204071249966], 'label': '3072.bgb.48.NA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.mv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.NA', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762262
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.NB', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.DJ', '24.FK', '24.HC'], 'contains': ['96.QS', '96.RD', '96.RG', '96.UJ', '96.VO'], 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 1313941673647, 108118287251071627990321, 79804429413572684637382, 404210922196204071249966], 'label': '3072.bgb.48.NB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.mw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.NB', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762263
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '48.NC', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.DK', '24.HC', '24.HD'], 'contains': ['96.JC', '96.JE', '96.JM', '96.JN', '96.QU', '96.QV', '96.QX', '96.RC', '96.RG', '96.UP', '96.VB'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922594664024732247801, 378358770650295628183080, 25903229681844523013167, 25852272837936812846761, 79804308125641822294440, 1313941673647], 'label': '3072.bgb.48.NC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '48.mx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.NC', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762264
    {'ambient': '3072.bgb', 'aut_centralizer_order': 1, 'aut_label': '2.F', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '3072.a1', 'complements': ['1536.C', '1536.F', '1536.D', '1536.E', '1536.K'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.C', '4.D', '4.G', '6.N', '8.J'], 'core': '2.F', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [108118421696801471190456, 25903229681844523013167, 108118165248982343710201, 187922473375925652905521, 566444897749485959875336, 133970303627361494479417, 404159831259638948150382, 1313941673647, 134021529040297499210286, 162070456272950954131199], 'label': '3072.bgb.2.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.C', '4.D', '4.G'], 'normalizer': '1.a1', 'old_label': '2.f1', 'projective_image': '3072.bgb', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.F', 'subgroup_fusion': None, 'weyl_group': '3072.bgb'}
  • id: 184762265
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.U', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B'], 'contains': ['24.BN', '24.BP', '24.BR', '24.BW', '24.BY', '24.CI', '24.CM', '24.CT', '24.CV', '24.CX', '24.CY', '24.DT', '24.DV', '24.EU', '24.EX'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 134021272934136496216343, 1313941673647, 122002101738321960, 53952035291802302422343, 187922594661241166512703, 296041409911409376977422, 378358649363678452761737], 'label': '3072.bgb.12.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.u1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.U', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184762266
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.ND', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '384.FB', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.DJ', '24.FL', '24.HD'], 'contains': ['96.QZ', '96.RA', '96.RG', '96.VI', '96.VO'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [187922594664024732247801, 25903229681844523013167, 1313941673647, 134021272934136496216343, 404210922196204071249966, 187922594661241166512703], 'label': '3072.bgb.48.ND', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.my1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ND', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762267
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.NE', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BV', '24.FQ', '24.FX'], 'contains': ['96.RH', '96.RI', '96.RN', '96.RO', '96.RQ', '96.RR', '96.RT', '96.RU', '96.RX', '96.RY', '96.SF', '96.SH', '96.SV', '96.SZ', '96.VH'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 133970182339249961095537, 25852017102974698844878, 108118165248982343710201, 79804429421968711780537], 'label': '3072.bgb.48.NE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.mz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.NE', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 184762268
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.NF', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BV', '24.FQ', '24.FY', '24.GS', '24.HE'], 'contains': ['96.RH', '96.RJ', '96.RK', '96.RN', '96.SA', '96.SC', '96.TB', '96.TI', '96.UA'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 187922473375925652905521, 133970182339249961095537, 133970303635757521608262, 108118165248982343710201], 'label': '3072.bgb.48.NF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.na1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.NF', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 184762269
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.NG', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CQ', '24.FQ', '24.HF'], 'contains': ['96.RK', '96.RL', '96.RQ', '96.RV', '96.RX', '96.SB', '96.SI', '96.TC', '96.TV'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79804308122845802507662, 108118165248982343710201, 25903229681844523013167, 1313941673647, 133970303635757521608262, 25852017102974698844878], 'label': '3072.bgb.48.NG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '48.nb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.NG', 'subgroup_fusion': None, 'weyl_group': '128.1578'}
  • id: 184762270
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.NH', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.DP', '24.FI', '24.FJ', '24.GG', '24.GH', '24.HE', '24.HG'], 'contains': ['96.SA', '96.SD', '96.TE', '96.TL', '96.UW'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855520714221614566521, 25852138757799544092222, 25903229681844523013167, 25852138389591620222016, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.NH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.nc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.NH', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762271
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.NI', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.DR', '24.FO', '24.FP', '24.GD', '24.GH', '24.GT', '24.HE'], 'contains': ['96.SA', '96.TJ', '96.TK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855520714221614566521, 25903229681844523013167, 25852138389591620222016, 1313941673647, 25852017102974698844878, 108169256203674548203560], 'label': '3072.bgb.48.NI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.nd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.NI', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762272
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.NJ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.DR', '24.FO', '24.FP', '24.GE', '24.GG', '24.GS', '24.HG'], 'contains': ['96.SA', '96.TJ', '96.TK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855520714221614566521, 162070577934876685646657, 25903229681844523013167, 25852138389591620222016, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.NJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.nd2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.NJ', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762273
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.NK', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BV', '24.FQ', '24.FZ', '24.GT', '24.HG'], 'contains': ['96.RM', '96.RQ', '96.RR', '96.RS', '96.RZ', '96.SA', '96.SY', '96.TI', '96.TQ'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647, 79804429421968711780537, 162070456272950954131199], 'label': '3072.bgb.48.NK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.ne1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.NK', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 184762274
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.NL', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.T', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BX', '24.GI', '24.HF'], 'contains': ['96.JP', '96.JQ', '96.JR', '96.SB', '96.SE', '96.TU', '96.TX', '96.UZ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 350207796319225162214423, 54003382330230002441647, 1313941673647, 134021272934136496216343, 216288705272228144236816], 'label': '3072.bgb.48.NL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BA', 'old_label': '48.nf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.NL', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762275
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.NM', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.T', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.BZ', '24.GI', '24.HF'], 'contains': ['96.JS', '96.SB', '96.TW', '96.TY'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [324355779217738848775558, 25903229681844523013167, 242140721662339602266753, 54003382330230002441647, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.48.NM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BA', 'old_label': '48.ng1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.NM', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762276
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.V', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B'], 'contains': ['24.BO', '24.BP', '24.BS', '24.CH', '24.CI', '24.CJ', '24.CL', '24.DA', '24.DB', '24.DC', '24.DH', '24.EY', '24.EZ', '24.FA', '24.FD'], 'core': '48.B', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 122002101738321960, 79804429413572684637382, 53952035291802302422343, 79804308125641822294440, 296041409911409376977422, 378358649363678452761737], 'label': '3072.bgb.12.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.v1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.V', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184762277
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.NN', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.V', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.DP', '24.FK', '24.FL'], 'contains': ['96.SD', '96.SG', '96.UW', '96.UY', '96.VO'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 25903107685154153232142, 1313941673647, 25852017101492540879976, 79804429421968711780537, 51090958997032170942], 'label': '3072.bgb.48.NN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '48.nh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.NN', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762278
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.NO', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.U', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ER', '24.FR', '24.FS'], 'contains': ['96.SO', '96.SP', '96.ST', '96.SU', '96.SX'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 25852138389591620222016, 1313941673647, 108118287251071627990321, 134021272934136496216343, 51090960298439969137], 'label': '3072.bgb.48.NO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.ni1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.NO', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762279
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.NP', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CA', '24.FR', '24.GC'], 'contains': ['96.SQ', '96.SS', '96.ST', '96.SV', '96.SW'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229337376182892926, 25903229681844523013167, 1313941673647, 187922594658424724202816, 25852017101492540879976, 25852017102974698844878], 'label': '3072.bgb.48.NP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.nj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.NP', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762280
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.NQ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.DW', '24.GP', '24.GU', '24.HH', '24.HI'], 'contains': ['96.TA', '96.TD', '96.UB', '96.UR', '96.VK'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79804308122845802507662, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.48.NQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '48.nk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.NQ', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762281
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.NR', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '384.CH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.DX', '24.FI', '24.GQ', '24.HJ', '24.HS'], 'contains': ['96.TA', '96.TE', '96.TM', '96.UC', '96.UU'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 53952412691500576681559, 25852138389591620222016, 54003382328928594643200, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.NR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.nl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.NR', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184762282
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.NS', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.ER', '24.FG', '24.FT', '24.GG', '24.HE', '24.HO', '24.HS'], 'contains': ['96.SL', '96.SP', '96.TB', '96.TE', '96.TK'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 25852138389591620222016, 1313941673647, 108118287251071627990321, 25852017102974698844878, 108169256203674548203560], 'label': '3072.bgb.48.NS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.nm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.NS', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762283
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.NT', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.DY', '24.GR', '24.GU', '24.HL', '24.HM'], 'contains': ['96.TA', '96.TF', '96.UE', '96.UI', '96.VA'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79804308122845802507662, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.48.NT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '48.nn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.NT', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 184762284
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.NU', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.B', '24.FX', '24.HK'], 'contains': ['96.SJ', '96.SK', '96.SM', '96.SU', '96.SZ', '96.TH', '96.TZ', '96.UF', '96.VI'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 162070578272437343706839, 25903229681844523013167, 187922473375925652905521, 133970303627361494479417, 1313941673647], 'label': '3072.bgb.48.NU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '48.no1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.NU', 'subgroup_fusion': None, 'weyl_group': '128.1578'}
  • id: 184762285
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '48.NV', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CR', '24.FQ', '24.GV', '24.HH', '24.HJ', '24.HL'], 'contains': ['96.SH', '96.SI', '96.TA', '96.TI', '96.UG', '96.VJ'], 'core': '768.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [79804308122845802507662, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647, 79804429421968711780537], 'label': '3072.bgb.48.NV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.np1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.NV', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762286
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.NW', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '384.CH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.EB', '24.FO', '24.GQ', '24.HA', '24.HJ'], 'contains': ['96.TA', '96.TJ'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79804308122845802507662, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647, 378358905093235639407953], 'label': '3072.bgb.48.NW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.nq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.NW', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184762287
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '12.W', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 24, 'centralizer': '768.R', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B'], 'contains': ['24.BQ', '24.BR', '24.BS', '24.CK', '24.CL', '24.CM', '24.CN', '24.DD', '24.DE', '24.DF', '24.DG', '24.FB', '24.FC', '24.FE', '24.FF'], 'core': '48.C', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 79804429413572684637382, 378358649363678452761737, 296041409911409376977422, 162070200540784685681302], 'label': '3072.bgb.12.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.w1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.W', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762288
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.NX', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '384.CG', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.EC', '24.FO', '24.GN', '24.GV', '24.HI', '24.HM', '24.HS'], 'contains': ['96.TA', '96.TK'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [162070577934876685646657, 25903229681844523013167, 25852138389591620222016, 54003382328928594643200, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.NX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.nr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.NX', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 184762289
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.NY', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ED', '24.GR', '24.GW', '24.HI', '24.HL'], 'contains': ['96.TA', '96.UH'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 25852138389591620222016, 54003382328928594643200, 1313941673647, 134021529040297499210286, 25852017102974698844878], 'label': '3072.bgb.48.NY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '48.ns1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.NY', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 184762290
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.NZ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.EF', '24.GP', '24.GW', '24.HH', '24.HM'], 'contains': ['96.TA', '96.VL'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [79804308122845802507662, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647, 187973308217542771509839], 'label': '3072.bgb.48.NZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '48.nt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.NZ', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762291
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.OA', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.ES', '24.FM', '24.FV', '24.GG', '24.GX', '24.HA', '24.HE'], 'contains': ['96.TB', '96.TJ', '96.TL'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 133970182339249961095537, 25903229681844523013167, 187922473375925652905521, 1313941673647, 378358905093235639407953], 'label': '3072.bgb.48.OA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.nu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.OA', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762292
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.OB', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.ET', '24.FM', '24.FV', '24.GD', '24.GS', '24.HO', '24.HS'], 'contains': ['96.TB', '96.TK', '96.TM'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 53952412691500576681559, 25852138389591620222016, 1313941673647, 108118287251071627990321, 25852017102974698844878], 'label': '3072.bgb.48.OB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.nv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.OB', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762293
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.OC', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.K', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.EH', '24.GO', '24.HF'], 'contains': ['96.JT', '96.JU', '96.JV', '96.TC', '96.TG', '96.TU', '96.TY', '96.UD'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [242089752358354392177983, 25903229681844523013167, 133970303627361494479417, 54003382328928594643200, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.OC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BA', 'old_label': '48.nw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.OC', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762294
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.OD', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.K', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.EJ', '24.GO', '24.HF'], 'contains': ['96.JW', '96.TC', '96.TW', '96.TX'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952413035981411118158, 79855142625594763233847, 25903229681844523013167, 187922473375925652905521, 133970303627361494479417, 1313941673647], 'label': '3072.bgb.48.OD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BA', 'old_label': '48.nx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.OD', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762295
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.OE', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.6407063', 'aut_weyl_index': 12, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.B', '24.FY', '24.GX', '24.HN', '24.HO', '24.HP'], 'contains': ['96.SK', '96.SN', '96.TB', '96.TN', '96.UF', '96.UJ'], 'core': '192.B', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [162070578272437343706839, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.48.OE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.ny1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.OE', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 184762296
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '48.OF', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.EM', '24.GU', '24.GY'], 'contains': ['96.TD', '96.TF', '96.TL', '96.UL', '96.UQ', '96.VC', '96.VQ'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 25852272837936812846761, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.48.OF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '48.nz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.OF', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762297
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.OG', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.DW', '24.GY', '24.HN', '24.HQ', '24.HT'], 'contains': ['96.TD', '96.TN', '96.UO', '96.US', '96.VR'], 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647, 79804429413572684637382, 53952035291802302422343], 'label': '3072.bgb.48.OG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '48.oa1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.OG', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762298
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.X', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.6536092', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.F'], 'contains': ['24.BT', '24.BV', '24.CB', '24.DI', '24.DM', '24.DR', '24.ET', '24.GD', '24.GE', '24.GS', '24.GT'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 53952412691500576681559, 187973685961890096441600, 133970303627361494479417, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.12.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.x1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.X', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 184762299
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.OH', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.CA', '24.FG', '24.FH', '24.GK', '24.HE', '24.HG', '24.HJ'], 'contains': ['96.SQ', '96.SR', '96.TE', '96.TI', '96.TJ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25852138757799544092222, 25903229681844523013167, 133970182343548561347240, 25852138389591620222016, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.OH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.ob1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.OH', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762300
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.OI', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.DX', '24.FJ', '24.GK', '24.HO', '24.HU'], 'contains': ['96.TE', '96.TM', '96.TN', '96.UV', '96.UX'], 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 53952412691500576681559, 1313941673647, 79804429413572684637382, 25852017102974698844878], 'label': '3072.bgb.48.OI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.oc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.OI', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762301
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.OJ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.EH', '24.HK', '24.HV'], 'contains': ['96.TG', '96.TH', '96.VF', '96.VG', '96.VN'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [242089752358354392177983, 53952291033879672806278, 25903229681844523013167, 133970303627361494479417, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.OJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.CB', 'old_label': '48.od1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.OJ', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762302
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.OK', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.DY', '24.GY', '24.HP', '24.HR', '24.HV'], 'contains': ['96.TF', '96.TN', '96.VD', '96.VG', '96.VM'], 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647, 79804429413572684637382, 378358649363678452761737], 'label': '3072.bgb.48.OK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '48.oe1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.OK', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 184762303
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.OL', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.EK', '24.HK', '24.HV'], 'contains': ['96.TH', '96.VM', '96.VN'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 133970303627361494479417, 1313941673647, 378358649363678452761737, 25852017102974698844878], 'label': '3072.bgb.48.OL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.CB', 'old_label': '48.of1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.OL', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762304
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.OM', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.CB', '24.FM', '24.FN', '24.GK', '24.GS', '24.GT', '24.HJ'], 'contains': ['96.TI', '96.TJ', '96.TM'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 53952412691500576681559, 133970182343548561347240, 25852138389591620222016, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.OM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.og1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.OM', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762305
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.ON', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.CC', '24.FM', '24.FN', '24.GF', '24.GV', '24.HE', '24.HG'], 'contains': ['96.TI', '96.TK', '96.TL'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [162070577934876685646657, 25903229681844523013167, 133970182343548561347240, 25852138389591620222016, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.ON', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.oh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ON', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762306
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.OO', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.26539', 'aut_weyl_index': 24, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.EB', '24.FP', '24.GK', '24.GX', '24.HB', '24.HQ', '24.HR'], 'contains': ['96.TJ', '96.TN'], 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647, 79804429413572684637382, 378358905093235639407953], 'label': '3072.bgb.48.OO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.oi1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.OO', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 184762307
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.OP', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.26539', 'aut_weyl_index': 24, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.EC', '24.FP', '24.GF', '24.HO', '24.HU'], 'contains': ['96.TK', '96.TN'], 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 1313941673647, 79804429413572684637382, 25852017102974698844878, 108169256203674548203560], 'label': '3072.bgb.48.OP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.oj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.OP', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762308
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.OQ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.EE', '24.GZ', '24.HN', '24.HR', '24.HT'], 'contains': ['96.TN', '96.VR'], 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118421696801471190456, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.48.OQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '48.ok1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.OQ', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184762309
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.Y', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.6536092', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.F'], 'contains': ['24.BV', '24.CA', '24.CC', '24.DP', '24.DR', '24.ER', '24.ES', '24.GG', '24.GH', '24.HE', '24.HG'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187973685961890096441600, 133970303627361494479417, 122002101738321960, 1313941673647, 25852017102974698844878, 108169256203674548203560], 'label': '3072.bgb.12.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.y1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.Y', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 184762310
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.OR', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.26539', 'aut_weyl_index': 24, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.EG', '24.GZ', '24.HP', '24.HQ', '24.HV'], 'contains': ['96.TN', '96.VN'], 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 404210787739267985320182, 187922473375925652905521, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.48.OR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '48.ol1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.OR', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 184762311
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.OS', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.I', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ER', '24.GA', '24.GC'], 'contains': ['96.JX', '96.JY', '96.JZ', '96.SL', '96.ST', '96.SX', '96.TO', '96.TP'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 162121669227129588479873, 1313941673647, 25852017101492540879976, 162070456272950954131199], 'label': '3072.bgb.48.OS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '48.om1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.OS', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 184762312
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.OT', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '384.FX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.B', '24.FQ', '24.GB', '24.HA', '24.HS'], 'contains': ['96.SJ', '96.SM', '96.SN', '96.SZ', '96.TA', '96.TB', '96.TC', '96.TO', '96.TQ'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [162070578272437343706839, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 133970303627361494479417, 1313941673647], 'label': '3072.bgb.48.OT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.on1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.OT', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762313
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.OU', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.ER', '24.FH', '24.FU', '24.GH', '24.HG', '24.HS', '24.HU'], 'contains': ['96.SO', '96.TE', '96.TK', '96.TP', '96.TQ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 133970303627361494479417, 1313941673647, 25852017102974698844878, 108169256203674548203560], 'label': '3072.bgb.48.OU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.oo1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.OU', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762314
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.OV', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.ES', '24.FN', '24.FW', '24.GH', '24.HA', '24.HB', '24.HG'], 'contains': ['96.TJ', '96.TL', '96.TQ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 133970303627361494479417, 1313941673647, 378358905093235639407953], 'label': '3072.bgb.48.OV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.op1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.OV', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762315
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.OW', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.ET', '24.FN', '24.FW', '24.GE', '24.GT', '24.HS', '24.HU'], 'contains': ['96.TK', '96.TM', '96.TQ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 53952412691500576681559, 133970303627361494479417, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.48.OW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.oq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.OW', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762316
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.OX', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CD', '24.GJ', '24.HF'], 'contains': ['96.TR', '96.TT', '96.TU', '96.TV', '96.TW'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [324355779217738848775558, 25903229681844523013167, 54003382330230002441647, 1313941673647, 134021272934136496216343, 216288705272228144236816], 'label': '3072.bgb.48.OX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BA', 'old_label': '48.or1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.OX', 'subgroup_fusion': None, 'weyl_group': '64.215'}
  • id: 184762317
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.OY', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.T', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.EH', '24.GI', '24.GJ'], 'contains': ['96.TU', '96.TY', '96.TZ', '96.VE', '96.VF'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 79804429416356250372480, 296092500497899884979223, 25903229681844523013167, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.48.OY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BA', 'old_label': '48.os1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.OY', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762318
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.OZ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CG', '24.GJ', '24.HF'], 'contains': ['96.TV', '96.TX', '96.TY'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903229681844523013167, 242140721662339602266753, 350207796319225162214423, 54003382330230002441647, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.48.OZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BA', 'old_label': '48.ot1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.OZ', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762319
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.PA', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.T', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.EJ', '24.GI', '24.GJ'], 'contains': ['96.TW', '96.TX', '96.TZ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 1313941673647, 108118287251071627990321, 134021272934136496216343, 134021529040297499210286], 'label': '3072.bgb.48.PA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BA', 'old_label': '48.ou1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.PA', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762320
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '12.Z', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 12, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.F', '6.H', '6.I'], 'contains': ['24.BT', '24.CC', '24.CR', '24.DJ', '24.EC', '24.GF', '24.GN', '24.GV'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 187973685961890096441600, 122002101738321960, 1313941673647, 79804429413572684637382, 25852017102974698844878, 108169256203674548203560], 'label': '3072.bgb.12.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.z1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.Z', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 184762321
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.PB', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.DW', '24.HC', '24.HN'], 'contains': ['96.UB', '96.UJ', '96.UP', '96.US', '96.VR'], 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 1313941673647, 108118287251071627990321, 79804429413572684637382, 53952035291802302422343], 'label': '3072.bgb.48.PB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '48.ov1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.PB', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762322
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.PC', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.DX', '24.FK', '24.HW'], 'contains': ['96.UC', '96.UJ', '96.UX', '96.UY', '96.VP'], 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952413035981411118158, 25903229681844523013167, 53952412691500576681559, 79804308125641822294440, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.48.PC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.C', 'old_label': '48.ow1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.PC', 'subgroup_fusion': None, 'weyl_group': '128.850'}
  • id: 184762323
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.PD', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.EH', '24.HK', '24.HP'], 'contains': ['96.UD', '96.UF', '96.VE', '96.VG', '96.VN'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25852138393689126932998, 25903229681844523013167, 404210787739267985320182, 1313941673647, 134021272934136496216343, 187922594661241166512703], 'label': '3072.bgb.48.PD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.CB', 'old_label': '48.ox1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.PD', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762324
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.PE', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CD', '24.GL', '24.HL'], 'contains': ['96.TR', '96.TS', '96.UE', '96.UG', '96.UH'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 79804308125641822294440, 134021394933610431760703, 1313941673647, 324355901222623977942343], 'label': '3072.bgb.48.PE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BE', 'old_label': '48.oy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.PE', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184762325
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.PF', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.DY', '24.GL', '24.HC'], 'contains': ['96.UE', '96.UI', '96.UJ', '96.VB', '96.VD'], 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 1313941673647, 108118287251071627990321, 79804429413572684637382, 378358649363678452761737], 'label': '3072.bgb.48.PF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '48.oz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.PF', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 184762326
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.PG', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.EK', '24.HK', '24.HP'], 'contains': ['96.UF', '96.VM', '96.VN'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25852138393689126932998, 25903229681844523013167, 1313941673647, 134021272934136496216343, 378358649363678452761737, 187922594661241166512703], 'label': '3072.bgb.48.PG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.CB', 'old_label': '48.pa1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.PG', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762327
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.PH', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CF', '24.GL', '24.HL'], 'contains': ['96.UG', '96.UH', '96.UI'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [324355779217738848775558, 25903229681844523013167, 79804308125641822294440, 134021394933610431760703, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.48.PH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BE', 'old_label': '48.pb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.PH', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184762329
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.PJ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.EE', '24.HN', '24.HW'], 'contains': ['96.UJ', '96.VR'], 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [108118421696801471190456, 25903229681844523013167, 79804308125641822294440, 1313941673647, 108118287251071627990321, 79804429413572684637382], 'label': '3072.bgb.48.PJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.N', 'old_label': '48.pd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.PJ', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 184762330
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '48.PK', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.EM', '24.HC', '24.HD'], 'contains': ['96.UL', '96.UP', '96.UQ', '96.VB', '96.VC', '96.VO', '96.VQ'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922594664024732247801, 25903229681844523013167, 25852272837936812846761, 79804308125641822294440, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.48.PK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '48.pe1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.PK', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 184762331
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.BA', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.6536092', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.G'], 'contains': ['24.BX', '24.BZ', '24.CD', '24.CG', '24.CQ', '24.EH', '24.EJ', '24.GI', '24.GJ', '24.GO', '24.HF'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 1313941673647, 122002101738321960, 25903229681844523013167, 324406991811924875755576, 242089752358354392177983, 133970303627361494479417, 25852017102974698844878], 'label': '3072.bgb.12.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '12.ba1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BA', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 184762332
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.PL', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.DW', '24.GM', '24.HD'], 'contains': ['96.UO', '96.UP', '96.UR', '96.VI', '96.VK'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 79804429416356250372480, 79855398717732338388456, 25903229681844523013167, 256460345499052777, 1313941673647], 'label': '3072.bgb.48.PL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '48.pf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.PL', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762333
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.PM', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 48, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CJ', '24.GM', '24.HH'], 'contains': ['96.UM', '96.UN', '96.UR', '96.VJ', '96.VL'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804308122845802507662, 25903229681844523013167, 79804308125641822294440, 1313941673647, 134021272925740469097576, 53952035291802302422343], 'label': '3072.bgb.48.PM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BC', 'old_label': '48.pg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.PM', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 184762334
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.PN', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '384.FH', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.DX', '24.FL', '24.HX'], 'contains': ['96.UU', '96.UV', '96.UY', '96.VI', '96.VP'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 79804429416356250372480, 79855398717732338388456, 25903229681844523013167, 53952412691500576681559, 1313941673647], 'label': '3072.bgb.48.PN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.C', 'old_label': '48.ph1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.PN', 'subgroup_fusion': None, 'weyl_group': '64.32'}
  • id: 184762335
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.PO', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.DY', '24.HD', '24.HK'], 'contains': ['96.VA', '96.VB', '96.VG', '96.VI', '96.VM'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [187922594664024732247801, 25903229681844523013167, 1313941673647, 134021272934136496216343, 378358649363678452761737, 187922594661241166512703], 'label': '3072.bgb.48.PO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '48.pi1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.PO', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 184762336
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '48.PP', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 24, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.EF', '24.GM', '24.HX'], 'contains': ['96.VI', '96.VL'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 79804429416356250372480, 79855398717732338388456, 25903229681844523013167, 1313941673647, 187973308217542771509839], 'label': '3072.bgb.48.PP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.J', 'old_label': '48.pj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.PP', 'subgroup_fusion': None, 'weyl_group': '128.753'}
  • id: 184762337
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.PQ', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.EG', '24.HK', '24.HX'], 'contains': ['96.VI', '96.VN'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [187922594664024732247801, 25903229681844523013167, 1313941673647, 134021272934136496216343, 216237613982764859689536, 187922594661241166512703], 'label': '3072.bgb.48.PQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.O', 'old_label': '48.pk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.PQ', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 184762338
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '48.PR', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.CO', '24.GM', '24.HH'], 'contains': ['96.VJ', '96.VK', '96.VL'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108169512287410083283217, 79804308122845802507662, 25903229681844523013167, 79804308125641822294440, 1313941673647, 79804429421968711780537], 'label': '3072.bgb.48.PR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BC', 'old_label': '48.pl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.PR', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762339
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '64.A', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '768.Z', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.B', '16.D', '16.E', '32.A', '32.B', '32.C'], 'contains': ['128.A', '128.B', '192.A', '256.B'], 'core': '192.A', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [25903229681844523013167, 216288570480689195210176, 1313941673647, 486427128433516595381056, 486478219730068018627222], 'label': '3072.bgb.64.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.C', 'old_label': '64.a1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.A', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 184762340
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '64.B', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '384.GM', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.F', '16.G', '32.A', '32.D', '32.E'], 'contains': ['128.A', '128.C', '192.MI', '256.C'], 'core': '384.A', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [25903229681844523013167, 566444897749485959875336, 404159831259638948150382, 1313941673647, 404210922196204071249966], 'label': '3072.bgb.64.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.C', 'old_label': '64.b1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.B', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 184762341
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '64.C', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '768.BC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.K', '32.B', '32.D', '32.H'], 'contains': ['128.A', '128.D', '192.MM', '256.D'], 'core': '384.A', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [566495989041738862713598, 25903229681844523013167, 296041666021875301271736, 1313941673647, 53952035291802302422343], 'label': '3072.bgb.64.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.C', 'old_label': '64.c1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.C', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 184762342
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.BB', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.6536092', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.G'], 'contains': ['24.BY', '24.BZ', '24.CE', '24.CF', '24.CQ', '24.EI', '24.EK'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [53952291033879672806278, 1313941673647, 122002101738321960, 25903229681844523013167, 133970303627361494479417, 296041409911409376977422, 25852017102974698844878, 378358649363678452761737], 'label': '3072.bgb.12.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '12.bb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BB', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 184762343
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '64.D', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '768.Z', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.H', '16.L', '32.A', '32.H', '32.I'], 'contains': ['128.A', '128.E', '192.MN', '256.E'], 'core': '384.A', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [566495989041738862713598, 25903229681844523013167, 296041666021875301271736, 1313941673647, 51212962568394582352], 'label': '3072.bgb.64.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.C', 'old_label': '64.d1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.D', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 184762344
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '64.E', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '768.BC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.I', '16.M', '32.C', '32.D', '32.I'], 'contains': ['128.A', '128.F', '192.MO', '256.F'], 'core': '384.A', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [378358770650295628183080, 25903229681844523013167, 566444897749485959875336, 404159831259638948150382, 1313941673647], 'label': '3072.bgb.64.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.C', 'old_label': '64.e1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.E', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 184762345
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '64.F', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '768.BG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.N', '32.B', '32.E', '32.I'], 'contains': ['128.A', '192.MQ', '256.G'], 'core': '384.A', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [25903229681844523013167, 486426872699855848892862, 324406614437468765763120, 458326854504114162364782, 1313941673647], 'label': '3072.bgb.64.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.C', 'old_label': '64.f1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.F', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 184762346
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '64.G', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '768.BG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.J', '16.O', '32.C', '32.E', '32.H'], 'contains': ['128.A', '192.MS', '256.H'], 'core': '384.A', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [51347406816160329727, 25903229681844523013167, 216288570480689195210176, 1313941673647, 486478219730068018627222], 'label': '3072.bgb.64.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.C', 'old_label': '64.g1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.G', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 184762347
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '64.H', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '768.Z', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.P', '16.Q', '16.R', '32.A'], 'contains': ['128.B', '128.C', '128.E', '192.MV', '256.I'], 'core': '768.A', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [121659103022301503, 25903229681844523013167, 216288570480689195210176, 1313941673647, 486427128433516595381056], 'label': '3072.bgb.64.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.A', 'old_label': '64.h1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.H', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 184762349
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '64.J', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '384.5678', 'aut_weyl_index': 16, 'centralizer': '1536.C', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.A', '32.F', '32.K', '32.M', '32.O', '32.Q'], 'contains': ['192.PC', '256.A', '256.K'], 'core': '768.A', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [25903229681844523013167, 187922473375925652905521, 404159831259638948150382, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.64.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.C', 'old_label': '64.j1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.J', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 184762350
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '64.K', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '192.956', 'aut_weyl_index': 32, 'centralizer': '768.BG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.A', '32.J', '32.L', '32.P', '32.R', '32.S', '32.T'], 'contains': ['192.B', '256.A'], 'core': '192.B', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [25903229681844523013167, 404159831259638948150382, 79804308125641822294440, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.64.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.H', 'old_label': '64.k1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.K', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 184762351
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '64.L', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '384.5677', 'aut_weyl_index': 16, 'centralizer': '3072.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.A', '32.G', '32.N', '32.U'], 'contains': ['192.QP', '256.A'], 'core': '768.A', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 404159831259638948150382, 1313941673647, 134021272934136496216343], 'label': '3072.bgb.64.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.G', 'old_label': '64.l1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.L', 'subgroup_fusion': None, 'weyl_group': '384.5677'}
  • id: 184762352
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '64.M', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '48.51', 'aut_weyl_index': 128, 'centralizer': '1536.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.C'], 'contains': ['128.G', '128.H', '128.I', '128.J', '128.K', '128.L', '128.M', '192.QS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [378358905460129661894279, 51347406816160329727, 378358770650295628183080, 25852272837936812846761, 620448401365031515454761], 'label': '3072.bgb.64.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.M', 'old_label': '64.m1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.M', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 184762353
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '12.BC', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.6407063', 'aut_weyl_index': 12, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.A', '6.H', '6.J'], 'contains': ['24.CJ', '24.CO', '24.CR', '24.DW', '24.EF', '24.GM', '24.GP', '24.HH'], 'core': '48.B', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229691554491852799, 1313941673647, 122002101738321960, 25903229681844523013167, 79804429413572684637382, 53952035291802302422343, 187922473375925652905521, 108118165248982343710201], 'label': '3072.bgb.12.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BC', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 184762354
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '64.N', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '1536.C', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.P'], 'contains': ['128.N', '128.O', '128.P', '192.QW', '256.I'], 'core': '3072.a1', 'coset_action_label': None, 'count': 128, 'diagramx': None, 'generators': [162070456271649546332752, 162121668867311424773041, 378359026753640149313262, 486427128433516595381056, 187973564325206449322177], 'label': '3072.bgb.64.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.N', 'old_label': '64.n1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.N', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 184762355
    {'ambient': '3072.bgb', 'aut_centralizer_order': 128, 'aut_label': '96.A', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '48.C', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.J', '48.A', '48.B', '48.C', '48.EZ', '48.FR', '48.GG', '48.HU', '48.HZ', '48.IL', '48.IM', '48.IN'], 'contains': ['192.B', '192.MP', '192.QC'], 'core': '96.A', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [25903229681844523013167, 79804308125641822294440, 122002101738321960, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.96.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.A', 'normal_contained_in': ['24.B', '48.A', '48.B', '48.C'], 'normal_contains': ['192.B', '384.A'], 'normalizer': '1.a1', 'old_label': '96.a1', 'projective_image': '3072.bgb', 'quotient_action_image': '48.48', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '96.A', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 184762356
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.B', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.BI', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.E', '48.F', '48.DM'], 'contains': ['192.C', '192.D', '192.M', '192.P', '192.T', '192.X', '192.BU', '192.DU', '192.DX', '192.EH', '192.EK', '192.EU', '192.EV', '192.FG', '192.FI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [368207923870206, 51212588579793007921, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.b1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.B', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762357
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.C', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.BB', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.E', '48.G', '48.DM'], 'contains': ['192.C', '192.D', '192.K', '192.O', '192.T', '192.X', '192.BV', '192.DV', '192.DW', '192.EG', '192.EK', '192.ET', '192.EW', '192.FG', '192.FH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229337376182892926, 25852017095880079467006, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.c1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.C', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762358
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.D', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.BH', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.F', '48.H', '48.DM'], 'contains': ['192.C', '192.D', '192.F', '192.P', '192.Q', '192.BI', '192.BU', '192.DV', '192.DX', '192.DZ', '192.EA', '192.EU', '192.EW', '192.EZ', '192.FB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [368207923870206, 25852017095880079467006, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.d1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.D', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762359
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.E', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.BA', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.G', '48.H', '48.DM'], 'contains': ['192.C', '192.D', '192.E', '192.O', '192.Q', '192.BI', '192.BV', '192.DU', '192.DW', '192.DY', '192.EA', '192.ET', '192.EV', '192.EZ', '192.FA'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229337376182892926, 51212588579793007921, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.e1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.E', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762360
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.F', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.FY', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.F', '48.G', '48.I', '48.J', '48.K', '48.L', '48.DQ'], 'contains': ['192.C', '192.G', '192.R', '192.U', '192.BW', '192.ED', '192.EE', '192.EL', '192.FC'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [108118165248982343710201, 187922473375925652905521, 187973685961890096441600, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.96.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.f1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.F', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184762361
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.G', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.GD', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.E', '48.H', '48.DQ'], 'contains': ['192.C', '192.H', '192.R', '192.V', '192.BX', '192.ED', '192.EE', '192.EM', '192.FD'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 108118165248982343710201, 187922473375925652905521, 187973685961890096441600, 25903229683158464676480], 'label': '3072.bgb.96.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.g1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.G', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762362
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.H', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.F', '48.G', '48.M', '48.N', '48.S', '48.T', '48.DU'], 'contains': ['192.D', '192.G', '192.W', '192.BD', '192.CN', '192.EP', '192.ER', '192.EY', '192.FF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25852017095880079467006, 122004885304085057, 122002101738321960, 1313941673647, 51090958997032170942], 'label': '3072.bgb.96.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.h1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.H', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184762363
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.I', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.L', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.E', '48.H', '48.DU'], 'contains': ['192.D', '192.H', '192.W', '192.BF', '192.CO', '192.EQ', '192.ES', '192.EX', '192.FE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25852017095880079467006, 25903107685154153232142, 122002101738321960, 1313941673647, 51090958997032170942], 'label': '3072.bgb.96.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.i1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.I', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762364
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '12.BD', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 12, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.F', '6.J', '6.K'], 'contains': ['24.CA', '24.CB', '24.CR', '24.DX', '24.EB', '24.GK', '24.GQ', '24.HJ'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 53952412691500576681559, 187973685961890096441600, 122002101738321960, 1313941673647, 79804429413572684637382, 25852017102974698844878], 'label': '3072.bgb.12.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BD', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 184762365
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.J', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '384.E', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.G', '48.O', '48.P', '48.U', '48.DU'], 'contains': ['192.E', '192.G', '192.K', '192.Z', '192.BE', '192.BO', '192.CR', '192.EP', '192.EQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 25852138757799544092222, 25852017095880079467006, 25903107685154153232142, 1313941673647], 'label': '3072.bgb.96.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.j1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.J', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762366
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.K', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '384.T', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.F', '48.Q', '48.R', '48.V', '48.DU'], 'contains': ['192.F', '192.G', '192.M', '192.BA', '192.BE', '192.BQ', '192.DA', '192.ER', '192.ES'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 25852017095880079467006, 25903107685154153232142, 1313941673647, 51090958997032170942], 'label': '3072.bgb.96.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.k1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.K', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762367
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.L', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '384.E', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.O', '48.W', '48.DT'], 'contains': ['192.E', '192.I', '192.L', '192.BB', '192.BG', '192.CC', '192.CM', '192.QS', '192.QT'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 25852272837936812846761, 122002101738321960, 25903229683158464676480, 378307680062503632549246], 'label': '3072.bgb.96.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '96.l1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.L', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762368
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.M', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.P', '48.W', '48.DT'], 'contains': ['192.E', '192.J', '192.N', '192.BC', '192.BH', '192.CD', '192.CQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [51469042011382569606, 378358770648994141276807, 378307680063817574222641, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.96.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '96.m1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.M', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184762369
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.N', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.Q', '48.W', '48.DT'], 'contains': ['192.F', '192.J', '192.L', '192.BB', '192.BH', '192.CG', '192.CV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 378307680063817574222641, 25852272837936812846761, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.96.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '96.n1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.N', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184762370
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.O', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '384.T', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.R', '48.W', '48.DT'], 'contains': ['192.F', '192.I', '192.N', '192.BC', '192.BG', '192.CH', '192.DS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [51469042011382569606, 378358770648994141276807, 122002101738321960, 25903229683158464676480, 378307680062503632549246], 'label': '3072.bgb.96.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '96.o1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.O', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762371
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.P', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '384.M', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.H', '48.W', '48.DU'], 'contains': ['192.E', '192.F', '192.H', '192.Z', '192.BA', '192.BJ', '192.CP', '192.EX', '192.EY'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 122004885304085057, 51212588579793007921, 1313941673647, 51090958997032170942], 'label': '3072.bgb.96.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.p1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.P', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762372
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '96.Q', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.MI', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.I', '48.M', '48.O', '48.R', '48.DW'], 'contains': ['192.G', '192.I', '192.BK', '192.CI', '192.CX'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 54003503618341535825287, 51212588579793007921, 25903229683158464676480, 79855264262271969233416], 'label': '3072.bgb.96.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.q1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.Q', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184762373
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.R', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.J', '48.N', '48.P', '48.Q', '48.DW'], 'contains': ['192.G', '192.J', '192.BM', '192.CI', '192.CY'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 54003503618341535825287, 25852017095880079467006, 25903229683158464676480, 79855264262271969233416], 'label': '3072.bgb.96.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.r1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.R', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762374
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.S', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.W', '48.X', '48.DW'], 'contains': ['192.H', '192.I', '192.J', '192.BK', '192.BM', '192.CK', '192.DK'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 51212588579793007921, 79804308125641822294440, 25903229683158464676480, 53952035291802302422343], 'label': '3072.bgb.96.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '96.s1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.S', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762375
    {'ambient': '3072.bgb', 'aut_centralizer_order': 1, 'aut_label': '2.G', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '3072.a1', 'complements': ['1536.E', '1536.I', '1536.C', '1536.F', '1536.D'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.D', '4.E', '4.F', '6.O', '8.K'], 'core': '2.G', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 187922473375925652905521, 404159831259638948150382, 133970303627361494479417, 566444897749485959875336, 108118165248982343710201, 162070456272950954131199, 378358649363678452761737, 53952412691500576681559], 'label': '3072.bgb.2.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.D', '4.E', '4.F'], 'normalizer': '1.a1', 'old_label': '2.g1', 'projective_image': '3072.bgb', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.G', 'subgroup_fusion': None, 'weyl_group': '3072.bgb'}
  • id: 184762376
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '12.BE', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 12, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.G', '6.H', '6.K'], 'contains': ['24.CD', '24.CF', '24.CR', '24.DY', '24.ED', '24.GL', '24.GR', '24.HL'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 296092500500710274860657, 122002101738321960, 1313941673647, 79804429413572684637382, 378358649363678452761737], 'label': '3072.bgb.12.BE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.be1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BE', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 184762377
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.T', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '384.V', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.E', '48.X', '48.DU'], 'contains': ['192.H', '192.K', '192.M', '192.BO', '192.BQ', '192.CP', '192.DL', '192.FE', '192.FF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 25852017095880079467006, 122004885304085057, 1313941673647, 51090958997032170942], 'label': '3072.bgb.96.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.t1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.T', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762378
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.U', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.W', '48.X', '48.DX'], 'contains': ['192.H', '192.L', '192.N', '192.BP', '192.BR', '192.CT', '192.DM'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 54003503618341535825287, 122002101738321960, 324406870525295326154166, 25903229683158464676480], 'label': '3072.bgb.96.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '96.u1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.U', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184762379
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.V', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '384.E', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.K', '48.O', '48.Q', '48.S', '48.DX'], 'contains': ['192.G', '192.L', '192.BP', '192.CW', '192.DB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770650295628183080, 79804308125641822294440, 122002101738321960, 25903229683158464676480, 324406870523993839248121], 'label': '3072.bgb.96.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.v1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.V', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762380
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.W', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '384.T', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.L', '48.P', '48.R', '48.T', '48.DX'], 'contains': ['192.G', '192.N', '192.BR', '192.CZ', '192.DB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770648994141276807, 79804308125641822294440, 122002101738321960, 25903229683158464676480, 324406870523993839248121], 'label': '3072.bgb.96.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.w1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.W', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762381
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.X', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.FY', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.I', '48.J', '48.S', '48.T', '48.U', '48.V', '48.DZ'], 'contains': ['192.G', '192.DD', '192.DI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 108169512287410083283217, 54003503618341535825287, 51212588579793007921, 25903229683158464676480], 'label': '3072.bgb.96.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.x1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.X', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184762382
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.Y', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.K', '48.L', '48.M', '48.N', '48.U', '48.V', '48.EA'], 'contains': ['192.G', '192.DE', '192.DH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 54003503618341535825287, 324406991811924875755576, 25903229683158464676480, 378358649363678452761737], 'label': '3072.bgb.96.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.y1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.Y', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184762383
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.Z', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '384.E', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.O', '48.X', '48.DT'], 'contains': ['192.I', '192.K', '192.L', '192.CD', '192.CE', '192.CM', '192.DR'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [51469042011382569606, 378358770650295628183080, 378307680063817574222641, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.96.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '96.z1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.Z', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762384
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.BA', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.P', '48.X', '48.DT'], 'contains': ['192.J', '192.K', '192.N', '192.CC', '192.CF', '192.CQ', '192.DT'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770648994141276807, 25852272837936812846761, 122002101738321960, 25903229683158464676480, 378307680062503632549246], 'label': '3072.bgb.96.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '96.ba1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BA', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184762385
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.BB', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.Q', '48.X', '48.DT'], 'contains': ['192.J', '192.L', '192.M', '192.CE', '192.CH', '192.CV', '192.DT'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [51469042011382569606, 378358770650295628183080, 122002101738321960, 25903229683158464676480, 378307680062503632549246], 'label': '3072.bgb.96.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '96.bb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BB', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184762386
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.BC', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '384.T', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.R', '48.X', '48.DT'], 'contains': ['192.I', '192.M', '192.N', '192.CF', '192.CG', '192.DR', '192.DS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770648994141276807, 378307680063817574222641, 25852272837936812846761, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.96.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '96.bc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BC', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762387
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '12.BF', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.A', '6.I', '6.K'], 'contains': ['24.CN', '24.CO', '24.CR', '24.DZ', '24.EE'], 'core': '48.C', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118421696801471190456, 25903229691554491852799, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.12.BF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BF', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 184762388
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.BD', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.DC', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.E', '48.F', '48.EE'], 'contains': ['192.P', '192.R', '192.T', '192.W', '192.X', '192.BQ', '192.BU', '192.FJ', '192.FM', '192.FW', '192.GA', '192.HK', '192.HL', '192.IU', '192.IW'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [122007701746409022, 368207923870206, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.bd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BD', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762389
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.BE', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.CJ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.E', '48.G', '48.EE'], 'contains': ['192.O', '192.R', '192.T', '192.W', '192.X', '192.BO', '192.BV', '192.FK', '192.FL', '192.FV', '192.GA', '192.HJ', '192.HM', '192.IU', '192.IV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229337376182892926, 25903107687970595565937, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.BE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.be1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BE', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762390
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.BF', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.DB', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.F', '48.H', '48.EE'], 'contains': ['192.P', '192.Q', '192.R', '192.W', '192.BA', '192.BI', '192.BU', '192.FK', '192.FM', '192.FQ', '192.FR', '192.HK', '192.HM', '192.HZ', '192.IB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903107687970595565937, 368207923870206, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.BF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.bf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BF', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762391
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.BG', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.CI', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.G', '48.H', '48.EE'], 'contains': ['192.O', '192.Q', '192.R', '192.W', '192.Z', '192.BI', '192.BV', '192.FJ', '192.FL', '192.FP', '192.FR', '192.HJ', '192.HL', '192.HZ', '192.IA'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229337376182892926, 122007701746409022, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.BG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.bg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BG', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762392
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.BH', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.CP', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.F', '48.G', '48.BA', '48.BB', '48.BG', '48.BH', '48.EL'], 'contains': ['192.Q', '192.T', '192.U', '192.BE', '192.CN', '192.FN', '192.FO', '192.GJ', '192.GK', '192.HS', '192.HT'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107687970595565937, 122004885304085057, 122002101738321960, 1313941673647, 51090958997032170942], 'label': '3072.bgb.96.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.bh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BH', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762393
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.BI', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.EP', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.E', '48.H', '48.EL'], 'contains': ['192.O', '192.P', '192.V', '192.BF', '192.CP', '192.FN', '192.FO', '192.GM', '192.HC', '192.IN', '192.LN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 25903107687970595565937, 122004885304085057, 1313941673647, 51090958997032170942], 'label': '3072.bgb.96.BI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.bi1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BI', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762394
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.BJ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.CU', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.G', '48.Y', '48.BC', '48.BD', '48.BI', '48.BJ', '48.EL'], 'contains': ['192.O', '192.U', '192.BD', '192.CR', '192.FS', '192.GF', '192.GJ', '192.HS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 25903107687970595565937, 25852138757799544092222, 25903107685154153232142, 1313941673647], 'label': '3072.bgb.96.BJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.bj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BJ', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762395
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.BK', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.FI', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.F', '48.Z', '48.BE', '48.BF', '48.BK', '48.BL', '48.EL'], 'contains': ['192.P', '192.U', '192.BD', '192.DA', '192.FT', '192.GG', '192.GK', '192.HT'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 25903107687970595565937, 25903107685154153232142, 1313941673647, 51090958997032170942], 'label': '3072.bgb.96.BK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.bk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BK', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762396
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.BL', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.ET', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.H', '48.BM', '48.EL'], 'contains': ['192.Q', '192.V', '192.BJ', '192.CO', '192.FS', '192.FT', '192.GM', '192.IN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107687970595565937, 25903107685154153232142, 122002101738321960, 1313941673647, 51090958997032170942], 'label': '3072.bgb.96.BL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '96.bl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BL', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762397
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.BM', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.Y', '48.Z', '48.BN', '48.BO', '48.BQ', '48.BR', '48.EO'], 'contains': ['192.S', '192.U', '192.BS', '192.CA', '192.GD', '192.GE', '192.GQ', '192.IX'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 53952291033879672806278, 79855520714221614566521, 79855398717732338388456, 1313941673647], 'label': '3072.bgb.96.BM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.bm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BM', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762398
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '12.BG', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 12, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.G', '6.I', '6.J'], 'contains': ['24.CE', '24.CG', '24.CR', '24.EA', '24.EG'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 404210787739267985320182, 187922473375925652905521, 122002101738321960, 1313941673647, 79804429413572684637382, 296041409911409376977422], 'label': '3072.bgb.12.BG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BG', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 184762399
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.BN', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BM', '48.BP', '48.EO'], 'contains': ['192.S', '192.V', '192.BT', '192.CB', '192.GD', '192.GE', '192.GR', '192.IY'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [53952291033879672806278, 79855520714221614566521, 79855398717732338388456, 122002101738321960, 1313941673647], 'label': '3072.bgb.96.BN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BN', 'old_label': '96.bn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BN', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762400
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.BO', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.FY', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.I', '48.J', '48.BA', '48.BB', '48.BD', '48.BF', '48.EU'], 'contains': ['192.U', '192.CI', '192.DI', '192.HB', '192.LH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 54003503618341535825287, 187973685961890096441600, 25903229683158464676480, 79855264262271969233416], 'label': '3072.bgb.96.BO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.bo1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BO', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184762401
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.BP', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BC', '48.BE', '48.BN', '48.BO', '48.BS', '48.BT', '48.EU'], 'contains': ['192.U', '192.CJ', '192.DJ', '192.HB', '192.LH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187973685961890096441600, 79804308125641822294440, 122002101738321960, 25903229683158464676480, 53952035291802302422343], 'label': '3072.bgb.96.BP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.bo2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BP', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762402
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.BQ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.FM', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.E', '48.BP', '48.EL'], 'contains': ['192.T', '192.V', '192.CO', '192.DL', '192.GF', '192.GG', '192.HC', '192.LN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [122007701746409022, 25903107685154153232142, 122002101738321960, 1313941673647, 51090958997032170942], 'label': '3072.bgb.96.BQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '96.bp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BQ', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762403
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.BR', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.FN', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BC', '48.BE', '48.BQ', '48.BR', '48.BU', '48.BV', '48.EV'], 'contains': ['192.U', '192.CS', '192.DF', '192.HD', '192.HE', '192.LW', '192.MB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 378358770650295628183080, 54003503618341535825287, 25903229683158464676480, 270240484110598816830720], 'label': '3072.bgb.96.BR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.bq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BR', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762404
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.BS', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.CU', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.K', '48.BA', '48.BI', '48.BK', '48.BR', '48.BS', '48.EV'], 'contains': ['192.U', '192.CW', '192.DE', '192.HD', '192.LW'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770650295628183080, 270240484111912758504367, 79804308125641822294440, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.96.BS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.br1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BS', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762405
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '96.BT', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.QZ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.I', '48.BG', '48.BI', '48.BL', '48.BN', '48.BU', '48.EW'], 'contains': ['192.U', '192.CX', '192.DD'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 108169512287410083283217, 54003503618341535825287, 25903229683158464676480, 162070456280045573438767], 'label': '3072.bgb.96.BT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.bs1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BT', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184762406
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.BU', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '192.QC', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.J', '48.BH', '48.BJ', '48.BK', '48.BO', '48.BV', '48.EW'], 'contains': ['192.U', '192.CY', '192.DD'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 108169512287410083283217, 54003503618341535825287, 187973685961890096441600, 25903229683158464676480], 'label': '3072.bgb.96.BU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.bt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BU', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762407
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.BV', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.FI', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.L', '48.BB', '48.BJ', '48.BL', '48.BQ', '48.BT', '48.EV'], 'contains': ['192.U', '192.CZ', '192.DE', '192.HE', '192.MB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770648994141276807, 270240484111912758504367, 79804308125641822294440, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.96.BV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.bu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BV', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762408
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.BW', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.CP', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.K', '48.L', '48.BD', '48.BF', '48.BG', '48.BH', '48.EX'], 'contains': ['192.U', '192.DB', '192.DH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 54003503618341535825287, 25903229683158464676480, 378358649363678452761737, 296041409911409376977422], 'label': '3072.bgb.96.BW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.bv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BW', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762409
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.BH', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B'], 'contains': ['24.CS', '24.CT', '24.CU', '24.CV', '24.DA', '24.DB', '24.DD', '24.DF', '24.DI', '24.DK', '24.DL', '24.DO', '24.DQ', '24.EN', '24.EP'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [270240484111912758504367, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 53952035291802302422343, 378358649363678452761737], 'label': '3072.bgb.12.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.bh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BH', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184762410
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.BX', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.FN', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.Y', '48.Z', '48.BS', '48.BT', '48.BU', '48.BV', '48.EY'], 'contains': ['192.U', '192.DC', '192.DG', '192.GH', '192.GI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107687970595565937, 53952412691500576681559, 122004885304085057, 122002101738321960, 1313941673647], 'label': '3072.bgb.96.BX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.bw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BX', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762411
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.BY', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.FP', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BM', '48.BP', '48.EY'], 'contains': ['192.V', '192.DN', '192.DP', '192.GH', '192.GI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 25903107687970595565937, 122004885304085057, 79855399081842795124439, 1313941673647], 'label': '3072.bgb.96.BY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BN', 'old_label': '96.bx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BY', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762412
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.BZ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '384.E', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.O', '48.W', '48.FC'], 'contains': ['192.Z', '192.BB', '192.BG', '192.BK', '192.BP', '192.CD', '192.CM', '192.QU', '192.QV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 25852272837936812846761, 122002101738321960, 324406870525295326154166, 25903229683158464676480], 'label': '3072.bgb.96.BZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '96.by1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BZ', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762413
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.CA', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.P', '48.W', '48.FC'], 'contains': ['192.Z', '192.BC', '192.BH', '192.BM', '192.BR', '192.CC', '192.CQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [51469042011382569606, 378358770648994141276807, 122002101738321960, 25903229683158464676480, 324406870523993839248121], 'label': '3072.bgb.96.CA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '96.bz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CA', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184762414
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.CB', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.Q', '48.W', '48.FC'], 'contains': ['192.BA', '192.BB', '192.BH', '192.BM', '192.BP', '192.CH', '192.CV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 25852272837936812846761, 122002101738321960, 25903229683158464676480, 324406870523993839248121], 'label': '3072.bgb.96.CB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '96.ca1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CB', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184762415
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.CC', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '384.T', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.R', '48.W', '48.FC'], 'contains': ['192.BA', '192.BC', '192.BG', '192.BK', '192.BR', '192.CG', '192.DS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [51469042011382569606, 378358770648994141276807, 122002101738321960, 324406870525295326154166, 25903229683158464676480], 'label': '3072.bgb.96.CC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '96.cb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CC', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762416
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.CD', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.Y', '48.Z', '48.BW', '48.BX', '48.BY', '48.BZ', '48.FD'], 'contains': ['192.BD', '192.BS', '192.DG', '192.IC', '192.JC'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79855520714221614566521, 53952412691500576681559, 122004885304085057, 122002101738321960, 1313941673647], 'label': '3072.bgb.96.CD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.cc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CD', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762417
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.CE', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.FD', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.E', '48.CA', '48.FS'], 'contains': ['192.X', '192.BF', '192.BX', '192.DL', '192.HN', '192.HY', '192.IG', '192.JP'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 108118165248982343710201, 187922473375925652905521, 25903229683158464676480, 404210922196204071249966], 'label': '3072.bgb.96.CE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.cd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CE', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762471
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '96.EB', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.NX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.I', '48.CI', '48.CW', '48.CX', '48.GL'], 'contains': ['192.BW', '192.CX', '192.DI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [377744146017650047, 108118165248982343710201, 187922473375925652905521, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.96.EB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.dz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.EB', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184762418
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.CF', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.FE', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.Y', '48.Z', '48.CB', '48.CC', '48.CD', '48.CE', '48.FH'], 'contains': ['192.BD', '192.CA', '192.DC', '192.IJ', '192.IP', '192.LA', '192.MD'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 404210922197505558871681, 162121547575114918571536, 25903229683158464676480, 134021272934136496216343], 'label': '3072.bgb.96.CF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.ce1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CF', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762419
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.CG', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BC', '48.BE', '48.BW', '48.BX', '48.CB', '48.CC', '48.FI'], 'contains': ['192.Y', '192.BD', '192.CJ', '192.CS', '192.HO', '192.HQ', '192.IL', '192.LF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 378358770650295628183080, 54003503618341535825287, 25852272837936812846761, 25903229683158464676480], 'label': '3072.bgb.96.CG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.cf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CG', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762420
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.BI', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B', '6.H', '6.L'], 'contains': ['24.CW', '24.CX', '24.DC', '24.DE', '24.DJ', '24.DK', '24.DW', '24.DY', '24.EM', '24.GU', '24.GY', '24.HC', '24.HD'], 'core': '48.B', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 79804429413572684637382, 53952035291802302422343, 378358649363678452761737], 'label': '3072.bgb.12.BI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bi1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BI', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184762421
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.CH', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.CA', '48.CL', '48.FI'], 'contains': ['192.Y', '192.BF', '192.CL', '192.CU', '192.HP', '192.HR', '192.IK', '192.LE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 378358770650295628183080, 25852272837936812846761, 79804308125641822294440, 25903229683158464676480], 'label': '3072.bgb.96.CH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.DK', 'old_label': '96.cg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CH', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762422
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.CI', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '384.E', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.O', '48.Q', '48.BA', '48.CG', '48.FI'], 'contains': ['192.BB', '192.BE', '192.CE', '192.CI', '192.CW', '192.HO', '192.HP'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770650295628183080, 25852272837936812846761, 79804308125641822294440, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.96.CI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.ch1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CI', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762423
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.CJ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '384.T', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.P', '48.R', '48.BB', '48.CH', '48.FI'], 'contains': ['192.BC', '192.BE', '192.CF', '192.CI', '192.CZ', '192.HQ', '192.HR'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770648994141276807, 25852272837936812846761, 79804308125641822294440, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.96.CJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.ci1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CJ', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762424
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.CK', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.M', '48.N', '48.BD', '48.BF', '48.CG', '48.CH', '48.FJ'], 'contains': ['192.BD', '192.CI', '192.DH', '192.IM', '192.LJ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 54003503618341535825287, 25903229683158464676480, 378358649363678452761737, 79855264262271969233416], 'label': '3072.bgb.96.CK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.cj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CK', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184762425
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.CL', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.CU', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.S', '48.BI', '48.BK', '48.BY', '48.CC', '48.CG', '48.FK'], 'contains': ['192.BD', '192.CW', '192.DD', '192.IO', '192.LY'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770650295628183080, 162070321828715682652927, 79804308125641822294440, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.96.CL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.ck1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CL', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762426
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '96.CM', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.CM', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.O', '48.R', '48.BG', '48.CI', '48.FL'], 'contains': ['192.BE', '192.BG', '192.CX', '192.DB', '192.DR'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79804308125641822294440, 122002101738321960, 25903229683158464676480, 324406870523993839248121, 404210922196204071249966], 'label': '3072.bgb.96.CM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.cl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CM', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184762427
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '96.CN', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.CN', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.M', '48.BI', '48.BL', '48.BW', '48.CD', '48.CI', '48.FM'], 'contains': ['192.BD', '192.CX', '192.DE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 54003503618341535825287, 404210922197505558871681, 324406991811924875755576, 25903229683158464676480], 'label': '3072.bgb.96.CN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.cm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CN', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184762428
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.CO', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '192.CX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.P', '48.Q', '48.BH', '48.CJ', '48.FL'], 'contains': ['192.BE', '192.BH', '192.CY', '192.DB', '192.DT'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [404210922197505558871681, 79804308125641822294440, 122002101738321960, 25903229683158464676480, 324406870523993839248121], 'label': '3072.bgb.96.CO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.cn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CO', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762429
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.CP', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '192.CX', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.N', '48.BJ', '48.BK', '48.BX', '48.CE', '48.CJ', '48.FM'], 'contains': ['192.BD', '192.CY', '192.DE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 54003503618341535825287, 324406991811924875755576, 25903229683158464676480, 404210922196204071249966], 'label': '3072.bgb.96.CP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.co1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CP', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762430
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.CQ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.FI', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.T', '48.BJ', '48.BL', '48.BZ', '48.CB', '48.CH', '48.FK'], 'contains': ['192.BD', '192.CZ', '192.DD', '192.IQ', '192.ME'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770648994141276807, 162070321828715682652927, 79804308125641822294440, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.96.CQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.cp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CQ', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762431
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '12.BJ', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 12, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B', '6.I', '6.M'], 'contains': ['24.CY', '24.CZ', '24.DG', '24.DH', '24.DJ', '24.DL', '24.DZ', '24.EA', '24.EQ'], 'core': '48.C', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 79804429413572684637382, 296041409911409376977422, 404210922196204071249966], 'label': '3072.bgb.12.BJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BJ', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 184762432
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.CR', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.CO', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.S', '48.T', '48.BD', '48.BF', '48.CI', '48.CJ', '48.FO'], 'contains': ['192.BD', '192.DB', '192.DI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 54003503618341535825287, 25903229683158464676480, 296041409911409376977422, 404210922196204071249966], 'label': '3072.bgb.96.CR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.cq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CR', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762433
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.CS', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.CP', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.U', '48.V', '48.BG', '48.BH', '48.CG', '48.CH', '48.FP'], 'contains': ['192.BE', '192.DD', '192.DH', '192.HW', '192.HX'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 54003503618341535825287, 25903229683158464676480, 133970560084911187416382, 378358649363678452761737], 'label': '3072.bgb.96.CS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.cr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CS', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762434
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.CT', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.CO', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.U', '48.V', '48.BA', '48.BB', '48.CI', '48.CJ', '48.FQ'], 'contains': ['192.BE', '192.DE', '192.DI', '192.HU', '192.HV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [270240484111912758504367, 79804308125641822294440, 122002101738321960, 25903229683158464676480, 404210922196204071249966], 'label': '3072.bgb.96.CT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.cs1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CT', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762435
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.CU', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.FE', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BC', '48.BE', '48.BY', '48.BZ', '48.CD', '48.CE', '48.FQ'], 'contains': ['192.BD', '192.DF', '192.DJ', '192.HU', '192.HV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 54003503618341535825287, 25903229683158464676480, 270240484110598816830720, 404210922196204071249966], 'label': '3072.bgb.96.CU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.cs2', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CU', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762436
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.CV', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.FQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.CA', '48.CL', '48.FP'], 'contains': ['192.BF', '192.DO', '192.DQ', '192.HW', '192.HX'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [108169512287410083283217, 54003503618341535825287, 122002101738321960, 25903229683158464676480, 378358649363678452761737], 'label': '3072.bgb.96.CV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.DK', 'old_label': '96.ct1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CV', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762437
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.CW', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BM', '48.CF', '48.FD'], 'contains': ['192.BJ', '192.BT', '192.DP', '192.IC'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 79855520714221614566521, 122004885304085057, 79855399081842795124439, 1313941673647], 'label': '3072.bgb.96.CW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.U', 'old_label': '96.cu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CW', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762438
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.CX', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.CO', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.F', '48.G', '48.CG', '48.CH', '48.CI', '48.CJ', '48.FS'], 'contains': ['192.X', '192.BD', '192.BE', '192.BI', '192.BW', '192.HN', '192.HY', '192.IE', '192.IF', '192.IR', '192.IS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [108118165248982343710201, 187922473375925652905521, 122002101738321960, 25903229683158464676480, 404210922196204071249966], 'label': '3072.bgb.96.CX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.cv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CX', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762439
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.CY', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.EY', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BM', '48.CK', '48.FH'], 'contains': ['192.BJ', '192.CB', '192.DN', '192.IJ', '192.IP'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [404210922197505558871681, 162121547575114918571536, 122002101738321960, 25903229683158464676480, 134021272934136496216343], 'label': '3072.bgb.96.CY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.cw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CY', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762440
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.CZ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '384.O', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.W', '48.CK', '48.FI'], 'contains': ['192.BB', '192.BC', '192.BJ', '192.CK', '192.CT', '192.IK', '192.IL'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770650295628183080, 54003503618341535825287, 25852272837936812846761, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.96.CZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.P', 'old_label': '96.cx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CZ', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184762441
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.DA', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.CF', '48.CL', '48.FJ'], 'contains': ['192.BJ', '192.CL', '192.DQ', '192.IM'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [54003503618341535825287, 122002101738321960, 25903229683158464676480, 53952035291802302422343, 378358649362364591657542], 'label': '3072.bgb.96.DA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BH', 'old_label': '96.cy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.DA', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762442
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.BK', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.C', '6.H', '6.M'], 'contains': ['24.DJ', '24.ED', '24.EF', '24.GW'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 296092500500710274860657, 122002101738321960, 1313941673647, 79804429413572684637382, 404210922196204071249966], 'label': '3072.bgb.12.BK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BK', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184762443
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.DB', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.EZ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.CK', '48.CL', '48.FK'], 'contains': ['192.BJ', '192.CU', '192.DO', '192.IO', '192.IQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 378358770650295628183080, 187973308220359388001840, 79804308125641822294440, 25903229683158464676480], 'label': '3072.bgb.96.DB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '96.cz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.DB', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762444
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.DC', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '192.CX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.W', '48.CF', '48.FL'], 'contains': ['192.BG', '192.BH', '192.BJ', '192.DK', '192.DM'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [54003503618341535825287, 404210922197505558871681, 122002101738321960, 324406870525295326154166, 25903229683158464676480], 'label': '3072.bgb.96.DC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.R', 'old_label': '96.da1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.DC', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184762445
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.DD', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.ES', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.H', '48.CL', '48.FS'], 'contains': ['192.BF', '192.BI', '192.BJ', '192.BX', '192.IG', '192.IR', '192.IS', '192.IT'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 108118165248982343710201, 187922473375925652905521, 404210922197505558871681, 25903229683158464676480], 'label': '3072.bgb.96.DD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.db1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.DD', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762446
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.DE', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '384.E', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.O', '48.X', '48.FC'], 'contains': ['192.BK', '192.BO', '192.BP', '192.CC', '192.CE', '192.CM', '192.DR'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [51469042011382569606, 378358770650295628183080, 122002101738321960, 25903229683158464676480, 324406870523993839248121], 'label': '3072.bgb.96.DE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '96.dc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.DE', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762447
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.DF', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.P', '48.X', '48.FC'], 'contains': ['192.BM', '192.BO', '192.BR', '192.CD', '192.CF', '192.CQ', '192.DT'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770648994141276807, 25852272837936812846761, 122002101738321960, 324406870525295326154166, 25903229683158464676480], 'label': '3072.bgb.96.DF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '96.dd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.DF', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184762448
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.DG', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.Q', '48.X', '48.FC'], 'contains': ['192.BM', '192.BP', '192.BQ', '192.CE', '192.CG', '192.CV', '192.DT'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [51469042011382569606, 378358770650295628183080, 122002101738321960, 324406870525295326154166, 25903229683158464676480], 'label': '3072.bgb.96.DG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '96.de1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.DG', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184762449
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.DH', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '384.T', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.R', '48.X', '48.FC'], 'contains': ['192.BK', '192.BQ', '192.BR', '192.CF', '192.CH', '192.DR', '192.DS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770648994141276807, 25852272837936812846761, 122002101738321960, 25903229683158464676480, 324406870523993839248121], 'label': '3072.bgb.96.DH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '96.df1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.DH', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762450
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.DI', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BN', '48.BW', '48.CM', '48.CP', '48.FX'], 'contains': ['192.BL', '192.BS', '192.CJ', '192.CX'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952413029067462088376, 79804308125641822294440, 122002101738321960, 25903229683158464676480, 53952035291802302422343], 'label': '3072.bgb.96.DI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.dg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.DI', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 184762451
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.DJ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BO', '48.BX', '48.CN', '48.CO', '48.FX'], 'contains': ['192.BN', '192.BS', '192.CJ', '192.CY'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855398709336311235223, 79804308125641822294440, 122002101738321960, 25903229683158464676480, 53952035291802302422343], 'label': '3072.bgb.96.DJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.dh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.DJ', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 184762452
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.DK', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.CF', '48.CQ', '48.FX'], 'contains': ['192.BL', '192.BN', '192.BT', '192.CL', '192.DK'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [54003503618341535825287, 79855398709336311235223, 122002101738321960, 25903229683158464676480, 79855264262271969233416], 'label': '3072.bgb.96.DK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CT', 'old_label': '96.di1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.DK', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184762453
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '12.BL', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 12, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.C', '6.I', '6.L'], 'contains': ['24.DJ', '24.EE', '24.EG', '24.GZ'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118421696801471190456, 108118165248982343710201, 25903229681844523013167, 404210787739267985320182, 187922473375925652905521, 122002101738321960, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.12.BL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BL', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 184762454
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.DL', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BM', '48.BP', '48.FY'], 'contains': ['192.BT', '192.CO', '192.DN', '192.IZ', '192.JD'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79855520714221614566521, 25903107685154153232142, 122002101738321960, 1313941673647, 51090958997032170942], 'label': '3072.bgb.96.DL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BN', 'old_label': '96.dj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.DL', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762455
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.DM', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.Y', '48.CM', '48.CN', '48.CR', '48.FY'], 'contains': ['192.BS', '192.CR', '192.DC', '192.IZ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 79855520714221614566521, 25852138757799544092222, 25903107685154153232142, 1313941673647], 'label': '3072.bgb.96.DM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.dk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.DM', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184762456
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.DN', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BQ', '48.BR', '48.BW', '48.BX', '48.CR', '48.CS', '48.FZ'], 'contains': ['192.BS', '192.CS', '192.DE', '192.JA', '192.JB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 378358770650295628183080, 324406991810611014641303, 54003503618341535825287, 25903229683158464676480], 'label': '3072.bgb.96.DN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.dl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.DN', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762457
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.DO', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BR', '48.BY', '48.CM', '48.CO', '48.FZ'], 'contains': ['192.BS', '192.CW', '192.DF', '192.JA'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770650295628183080, 79804308125641822294440, 122002101738321960, 324406991811924875755576, 25903229683158464676480], 'label': '3072.bgb.96.DO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.dm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.DO', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184762458
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.DP', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BQ', '48.BZ', '48.CN', '48.CP', '48.FZ'], 'contains': ['192.BS', '192.CZ', '192.DF', '192.JB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770648994141276807, 79804308125641822294440, 122002101738321960, 324406991811924875755576, 25903229683158464676480], 'label': '3072.bgb.96.DP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.dn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.DP', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184762459
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.DQ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.Z', '48.CO', '48.CP', '48.CS', '48.FY'], 'contains': ['192.BS', '192.DA', '192.DC', '192.JD'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 53952291032377091563446, 25903107685154153232142, 1313941673647, 51090958997032170942], 'label': '3072.bgb.96.DQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.do1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.DQ', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184762460
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.DR', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BN', '48.BO', '48.BY', '48.BZ', '48.CR', '48.CS', '48.GB'], 'contains': ['192.BS', '192.DD', '192.DJ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 108169512287410083283217, 54003503618341535825287, 79855398709336311235223, 25903229683158464676480], 'label': '3072.bgb.96.DR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.dp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.DR', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762461
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.DS', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BP', '48.CQ', '48.FD'], 'contains': ['192.BT', '192.DL', '192.DP', '192.JC'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 53952291032377091563446, 122004885304085057, 79855399081842795124439, 1313941673647], 'label': '3072.bgb.96.DS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.U', 'old_label': '96.dq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.DS', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762462
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.DT', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.CF', '48.CQ', '48.GA'], 'contains': ['192.BT', '192.DM', '192.DQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [54003503618341535825287, 122002101738321960, 25903229683158464676480, 324406870523993839248121, 378358649363678452761737], 'label': '3072.bgb.96.DT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CT', 'old_label': '96.dr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.DT', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762463
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.DU', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.FY', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.I', '48.J', '48.CG', '48.CH', '48.CT', '48.CU', '48.GI'], 'contains': ['192.BW', '192.CI', '192.DD', '192.JW', '192.LL'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 187922473375925652905521, 134021394930826866723126, 25903229683158464676480, 79855264262271969233416], 'label': '3072.bgb.96.DU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.ds1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.DU', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184762464
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.BM', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.B', '6.F', '6.L', '6.M'], 'contains': ['24.B', '24.DJ', '24.DM', '24.EB', '24.ES', '24.GX', '24.HA', '24.HB'], 'core': '24.B', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229681844523013167, 108118165248982343710201, 187922473375925652905521, 133970303627361494479417, 122002101738321960, 1313941673647, 378358905093235639407953, 162070456272950954131199], 'label': '3072.bgb.12.BM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BM', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184762465
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.DV', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.CA', '48.CL', '48.GI'], 'contains': ['192.BX', '192.CL', '192.DO', '192.JW', '192.LL'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922473375925652905521, 134021394930826866723126, 122002101738321960, 25903229683158464676480, 53952035291802302422343], 'label': '3072.bgb.96.DV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.DK', 'old_label': '96.dt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.DV', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762466
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.DW', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.FG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.F', '48.CT', '48.CV', '48.CW', '48.GJ'], 'contains': ['192.BU', '192.BW', '192.CN', '192.DA', '192.JH', '192.JM', '192.JX', '192.LO'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25852138757799544092222, 25852138389591620222016, 122002101738321960, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.DW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.du1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.DW', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184762467
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.DX', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.EO', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.E', '48.H', '48.GJ'], 'contains': ['192.BU', '192.BV', '192.BX', '192.CO', '192.CP', '192.JI', '192.JJ', '192.JX', '192.JY', '192.LO', '192.LS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 25852138757799544092222, 25852138389591620222016, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.DX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.dv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.DX', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762468
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.DY', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.CT', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.G', '48.CU', '48.CX', '48.CY', '48.GJ'], 'contains': ['192.BV', '192.BW', '192.CN', '192.CR', '192.JH', '192.JL', '192.JY', '192.LS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25852138389591620222016, 122002101738321960, 1313941673647, 25852017102974698844878, 51090958997032170942], 'label': '3072.bgb.96.DY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.dw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.DY', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184762469
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.DZ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.CA', '48.CL', '48.GK'], 'contains': ['192.BX', '192.CU', '192.DQ', '192.JZ', '192.KB', '192.LZ', '192.MG'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922473375925652905521, 134021394930826866723126, 122002101738321960, 25903229683158464676480, 378358649363678452761737], 'label': '3072.bgb.96.DZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.DK', 'old_label': '96.dx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.DZ', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762470
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.EA', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.CT', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.K', '48.CG', '48.CV', '48.CX', '48.GK'], 'contains': ['192.BW', '192.CW', '192.DH', '192.JZ', '192.LZ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 187922473375925652905521, 134021394930826866723126, 25903229683158464676480, 378358649362364591657542], 'label': '3072.bgb.96.EA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.dy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.EA', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184762472
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.EC', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.J', '48.CJ', '48.CV', '48.CY', '48.GL'], 'contains': ['192.BW', '192.CY', '192.DI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108118165248982343710201, 187922473375925652905521, 122002101738321960, 25903229683158464676480, 25903364135789722998960], 'label': '3072.bgb.96.EC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.ea1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.EC', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762473
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.ED', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.FG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.L', '48.CH', '48.CW', '48.CY', '48.GK'], 'contains': ['192.BW', '192.CZ', '192.DH', '192.KB', '192.MG'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 187922473375925652905521, 134021394930826866723126, 25903229683158464676480, 378358649363678452761737], 'label': '3072.bgb.96.ED', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.eb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ED', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184762474
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.EE', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.CO', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.K', '48.L', '48.CI', '48.CJ', '48.CT', '48.CU', '48.GM'], 'contains': ['192.BW', '192.DB', '192.DE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 79804052047512561508433, 1313941673647, 51091303465372291183, 25852017102974698844878], 'label': '3072.bgb.96.EE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.ec1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.EE', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762475
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.BN', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.8841562', 'aut_weyl_index': 12, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B'], 'contains': ['24.DO', '24.DP', '24.DQ', '24.DS', '24.DT', '24.DU', '24.DV', '24.EL', '24.EM', '24.EO', '24.EQ', '24.EY', '24.EZ', '24.FB', '24.FE'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [270240484111912758504367, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 25852272837936812846761, 122002101738321960, 1313941673647, 378358649363678452761737], 'label': '3072.bgb.12.BN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.bn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BN', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 184762476
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.EF', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BN', '48.BO', '48.CB', '48.CC', '48.CZ', '48.DB', '48.GV'], 'contains': ['192.CA', '192.CJ', '192.DD', '192.KV', '192.LK'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79855398717732338388456, 256460345499052777, 122002101738321960, 1313941673647, 79855520715724195809353], 'label': '3072.bgb.96.EF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.ed1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.EF', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762477
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.EG', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.GE', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.CK', '48.DA', '48.GV'], 'contains': ['192.CB', '192.CK', '192.DO', '192.KV', '192.LK'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 79855398717732338388456, 25903485430815165863622, 1313941673647, 79855520715724195809353], 'label': '3072.bgb.96.EG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '96.ee1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.EG', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184762478
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.EH', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BM', '48.BP', '48.GW'], 'contains': ['192.CB', '192.CO', '192.DP', '192.KW', '192.LB', '192.LR', '192.MF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 79855398717732338388456, 79855399081842795124439, 1313941673647, 79855520715724195809353], 'label': '3072.bgb.96.EH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BN', 'old_label': '96.ef1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.EH', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762479
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.EI', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.Y', '48.CZ', '48.DC', '48.DD', '48.GW'], 'contains': ['192.CA', '192.CR', '192.DG', '192.KW', '192.LR'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855398717732338388456, 53952412691500576681559, 122002101738321960, 1313941673647, 79855520715724195809353], 'label': '3072.bgb.96.EI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.eg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.EI', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762480
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.EJ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BQ', '48.CB', '48.DC', '48.DE', '48.GX'], 'contains': ['192.BY', '192.CA', '192.CS', '192.CZ', '192.KI', '192.KN', '192.KX', '192.LT'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [122002101738321960, 25903229683158464676480, 134021272934136496216343, 187922594661241166512703, 242089752359655799966096], 'label': '3072.bgb.96.EJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.eh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.EJ', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762481
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.EK', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.EV', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.CK', '48.DA', '48.GX'], 'contains': ['192.BY', '192.BZ', '192.CB', '192.CT', '192.CU', '192.KJ', '192.KK', '192.KX', '192.KZ', '192.LT', '192.MA'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 242089752358354392177983, 25903229683158464676480, 134021272934136496216343, 187922594661241166512703], 'label': '3072.bgb.96.EK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '96.ei1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.EK', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184762482
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.EL', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BR', '48.CC', '48.DD', '48.DF', '48.GX'], 'contains': ['192.BZ', '192.CA', '192.CS', '192.CW', '192.KI', '192.KM', '192.KZ', '192.MA'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [242089752358354392177983, 122002101738321960, 25903229683158464676480, 134021272934136496216343, 187922594661241166512703], 'label': '3072.bgb.96.EL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.ej1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.EL', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762483
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '96.EM', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.QA', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BN', '48.CD', '48.DD', '48.DE', '48.GY'], 'contains': ['192.CA', '192.CX', '192.DJ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952156586827744566398, 79855398717732338388456, 122002101738321960, 1313941673647, 79855520715724195809353], 'label': '3072.bgb.96.EM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.ek1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.EM', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184762484
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.EN', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.GF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BO', '48.CE', '48.DC', '48.DF', '48.GY'], 'contains': ['192.CA', '192.CY', '192.DJ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855142978471449905233, 79855398717732338388456, 122002101738321960, 1313941673647, 79855520715724195809353], 'label': '3072.bgb.96.EN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.el1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.EN', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762485
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.EO', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.Z', '48.DB', '48.DE', '48.DF', '48.GW'], 'contains': ['192.CA', '192.DA', '192.DG', '192.LB', '192.MF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855398717732338388456, 79855399081842795124439, 122002101738321960, 1313941673647, 79855520715724195809353], 'label': '3072.bgb.96.EO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.em1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.EO', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762486
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.A', '6.B', '6.C', '6.D', '6.E', '6.F', '6.G', '6.H', '6.I', '6.J', '6.K', '6.L', '6.M', '6.N', '6.O'], 'core': '6.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 122002101738321960, 187922473375925652905521, 133970303627361494479417, 108118421696801471190456, 296041409911409376977422, 108118165248982343710201, 162070456272950954131199, 378358649363678452761737], 'label': '3072.bgb.3.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '3.a1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184762487
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.BO', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B', '6.J', '6.N'], 'contains': ['24.DW', '24.DX', '24.EA', '24.EL', '24.EN', '24.EU', '24.EV', '24.FA', '24.FF'], 'core': '48.B', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 79804052047512561508433, 122002101738321960, 1313941673647, 79804429413572684637382, 54003125882410914585582, 25852017102974698844878], 'label': '3072.bgb.12.BO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bo1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BO', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184762488
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.EP', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.FE', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BQ', '48.BR', '48.CD', '48.CE', '48.CZ', '48.DB', '48.HB'], 'contains': ['192.CA', '192.DE', '192.DF', '192.KP', '192.KQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903363795619943623743, 79855398717732338388456, 122002101738321960, 1313941673647, 79855520715724195809353], 'label': '3072.bgb.96.EP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.en1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.EP', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762489
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.EQ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.FC', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BP', '48.DA', '48.FH'], 'contains': ['192.CB', '192.DL', '192.DN', '192.LA', '192.MD'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [162121547575114918571536, 122002101738321960, 25903229683158464676480, 134021272934136496216343, 404210922196204071249966], 'label': '3072.bgb.96.EQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.eo1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.EQ', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762490
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.ER', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.M', '48.N', '48.BA', '48.BB', '48.CT', '48.CU', '48.HH'], 'contains': ['192.CI', '192.CN', '192.DE', '192.LD', '192.LI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 53952156579733379227566, 53952034948635409649297, 25903107685154153232142, 1313941673647], 'label': '3072.bgb.96.ER', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.ep1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ER', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184762491
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.ES', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.W', '48.X', '48.HG'], 'contains': ['192.CC', '192.CD', '192.CG', '192.CH', '192.CK', '192.CP', '192.DM'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 53952156579733379227566, 79804052047512561508433, 122004885304085057, 1313941673647], 'label': '3072.bgb.96.ES', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '96.eq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ES', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184762492
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.ET', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '384.E', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.O', '48.P', '48.BD', '48.CU', '48.HG'], 'contains': ['192.CC', '192.CD', '192.CI', '192.CR', '192.DB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 54003247541513762671313, 25903107685154153232142, 1313941673647, 79855142971377084566401], 'label': '3072.bgb.96.ET', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.er1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ET', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762493
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.EU', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BC', '48.CM', '48.CN', '48.CZ', '48.HH'], 'contains': ['192.CJ', '192.CR', '192.DF', '192.LD'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [53952156579733379227566, 79855264629178445030417, 122004885304085057, 122002101738321960, 1313941673647], 'label': '3072.bgb.96.EU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.es1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.EU', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184762494
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.EV', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '384.U', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.X', '48.DA', '48.FI'], 'contains': ['192.CE', '192.CF', '192.CK', '192.CT', '192.DL', '192.LE', '192.LF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770648994141276807, 54003503618341535825287, 25852272837936812846761, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.96.EV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.P', 'old_label': '96.et1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.EV', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184762495
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.EW', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '384.N', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.CK', '48.DA', '48.HI'], 'contains': ['192.CK', '192.CU', '192.DN', '192.LG', '192.LM'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 378358770650295628183080, 79804308125641822294440, 25903229683158464676480, 79855264262271969233416], 'label': '3072.bgb.96.EW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '96.eu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.EW', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184762496
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.EX', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BS', '48.CC', '48.CM', '48.CO', '48.HI'], 'contains': ['192.CJ', '192.CW', '192.DC', '192.LG'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770650295628183080, 79804308125641822294440, 122002101738321960, 25903229683158464676480, 53952035291802302422343], 'label': '3072.bgb.96.EX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.ev1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.EX', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184762497
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.EY', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BT', '48.CB', '48.CN', '48.CP', '48.HI'], 'contains': ['192.CJ', '192.CZ', '192.DC', '192.LM'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770648994141276807, 79804308125641822294440, 122002101738321960, 25903229683158464676480, 53952035291802302422343], 'label': '3072.bgb.96.EY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.ew1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.EY', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184762498
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.BP', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.D', '6.J', '6.L'], 'contains': ['24.DW', '24.EB', '24.EG', '24.HQ'], 'core': '48.B', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 122002101738321960, 404210787739267985320182, 79804429413572684637382, 53952035291802302422343, 187922473375925652905521, 108118165248982343710201], 'label': '3072.bgb.12.BP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BP', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184762499
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.EZ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '384.T', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.Q', '48.R', '48.BF', '48.CT', '48.HG'], 'contains': ['192.CG', '192.CH', '192.CI', '192.DA', '192.DB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 53952156579733379227566, 54003247541513762671313, 25903107685154153232142, 1313941673647], 'label': '3072.bgb.96.EZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.ex1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.EZ', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762500
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.FA', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BE', '48.CO', '48.CP', '48.DB', '48.HH'], 'contains': ['192.CJ', '192.DA', '192.DF', '192.LI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [79855264629178445030417, 122004885304085057, 122002101738321960, 1313941673647, 79855142971377084566401], 'label': '3072.bgb.96.FA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.ey1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.FA', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184762501
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.FB', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BS', '48.BT', '48.BW', '48.BX', '48.CZ', '48.DB', '48.HM'], 'contains': ['192.CJ', '192.DE', '192.DG'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [53952156579733379227566, 25903363795619943623743, 122004885304085057, 122002101738321960, 1313941673647], 'label': '3072.bgb.96.FB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.ez1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.FB', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762502
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.FC', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.CA', '48.CQ', '48.FJ'], 'contains': ['192.CL', '192.DL', '192.DQ', '192.LJ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [54003503618341535825287, 122002101738321960, 25903229683158464676480, 53952035291802302422343, 378358649363678452761737], 'label': '3072.bgb.96.FC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BH', 'old_label': '96.fa1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.FC', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762503
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.FD', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '768.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.CF', '48.CQ', '48.HK'], 'contains': ['192.CL', '192.DM', '192.DP'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [51347406816160329727, 53952156579733379227566, 25903107685154153232142, 122002101738321960, 1313941673647], 'label': '3072.bgb.96.FD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CT', 'old_label': '96.fb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.FD', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762504
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.FE', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.W', '48.X', '48.HN'], 'contains': ['192.CM', '192.CP', '192.CQ', '192.CT', '192.CV', '192.DK', '192.DS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 324355523484084195000247, 54003503618341535825287, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.96.FE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '96.fc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.FE', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762505
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.FF', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.CT', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.S', '48.BA', '48.CV', '48.CX', '48.HO'], 'contains': ['192.CN', '192.CW', '192.DI', '192.LP', '192.LX'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770650295628183080, 79804308125641822294440, 122002101738321960, 25903229683158464676480, 270189649267478943569286], 'label': '3072.bgb.96.FF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.fd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.FF', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184762506
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '96.FG', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.BF', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.M', '48.BG', '48.CW', '48.CX', '48.HP'], 'contains': ['192.CN', '192.CX', '192.DH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 54003503618341535825287, 25903229683158464676480, 324355523485385682622200, 378358649362364591657542], 'label': '3072.bgb.96.FG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.fe1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.FG', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184762507
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.FH', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.N', '48.BH', '48.CV', '48.CY', '48.HP'], 'contains': ['192.CN', '192.CY', '192.DH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 54003503618341535825287, 25903229683158464676480, 324355523485385682622200, 378358649363678452761737], 'label': '3072.bgb.96.FH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.ff1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.FH', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762508
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.FI', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.FG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.T', '48.BB', '48.CW', '48.CY', '48.HO'], 'contains': ['192.CN', '192.CZ', '192.DI', '192.LQ', '192.MC'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770648994141276807, 79804308125641822294440, 122002101738321960, 25903229683158464676480, 270189649267478943569286], 'label': '3072.bgb.96.FI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.fg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.FI', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184762509
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.BQ', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.D', '6.H', '6.N'], 'contains': ['24.DW', '24.EC', '24.ED', '24.HI'], 'core': '48.B', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [53952291033879672806278, 25903229681844523013167, 122002101738321960, 1313941673647, 79804429413572684637382, 134021529040297499210286, 25852017102974698844878, 54003125882410914585582], 'label': '3072.bgb.12.BQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BQ', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184762510
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.FJ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.CP', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.S', '48.T', '48.BG', '48.BH', '48.CT', '48.CU', '48.HR'], 'contains': ['192.CN', '192.DB', '192.DD'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [51347406816160329727, 256460345499052777, 122004885304085057, 122002101738321960, 1313941673647], 'label': '3072.bgb.96.FJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.fh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.FJ', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762511
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.FK', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BC', '48.CR', '48.DC', '48.DD', '48.HO'], 'contains': ['192.CR', '192.CS', '192.DJ', '192.LP', '192.LQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 378358770650295628183080, 270189649266165081739561, 54003503618341535825287, 25903229683158464676480], 'label': '3072.bgb.96.FK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.fi1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.FK', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762512
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '96.FL', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '192.BJ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.O', '48.BI', '48.CM', '48.CX', '48.DD', '48.HN'], 'contains': ['192.CM', '192.CR', '192.CW', '192.CX'], 'core': '3072.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [378358770650295628183080, 324355523484084195000247, 79804308125641822294440, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.96.FL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.fj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.FL', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 184762513
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.FM', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '384.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.P', '48.BJ', '48.CN', '48.CY', '48.DC', '48.HN'], 'contains': ['192.CQ', '192.CR', '192.CY', '192.CZ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [378358770648994141276807, 324355523484084195000247, 79804308125641822294440, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.96.FM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.fk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.FM', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184762514
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.FN', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.CU', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.U', '48.BI', '48.BJ', '48.CR', '48.CU', '48.CZ', '48.HS'], 'contains': ['192.CR', '192.DD', '192.DE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903363795619943623743, 256460345499052777, 122004885304085057, 122002101738321960, 1313941673647], 'label': '3072.bgb.96.FN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.fl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.FN', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762515
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.FO', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.CT', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.U', '48.BD', '48.CX', '48.CY', '48.HT'], 'contains': ['192.CR', '192.DH', '192.DI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 270189649266165081739561, 54003503618341535825287, 25903229683158464676480, 378358649362364591657542], 'label': '3072.bgb.96.FO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.fm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.FO', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184762516
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '96.FP', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.DN', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BU', '48.BW', '48.DD', '48.DE', '48.HV'], 'contains': ['192.CS', '192.CX', '192.DG'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 324355644776280741499582, 378358770648994141276807, 54003503618341535825287, 25903229683158464676480], 'label': '3072.bgb.96.FP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.fn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.FP', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184762517
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.FQ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BV', '48.BX', '48.DC', '48.DF', '48.HV'], 'contains': ['192.CS', '192.CY', '192.DG'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 324355644776280741499582, 378358770650295628183080, 54003503618341535825287, 25903229683158464676480], 'label': '3072.bgb.96.FQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.fo1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.FQ', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762518
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.FR', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BE', '48.CS', '48.DE', '48.DF', '48.HO'], 'contains': ['192.CS', '192.DA', '192.DJ', '192.LX', '192.MC'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 378358770648994141276807, 54003503618341535825287, 25903229683158464676480, 270189649267478943569286], 'label': '3072.bgb.96.FR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.fp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.FR', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762519
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.FS', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.FN', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BU', '48.BV', '48.CB', '48.CC', '48.CR', '48.CS', '48.HX'], 'contains': ['192.CS', '192.DC', '192.DD', '192.LU', '192.LV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903107682370587468807, 378358770650295628183080, 54003503618341535825287, 25903229683158464676480, 133970560084911187416382], 'label': '3072.bgb.96.FS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.fq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.FS', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762520
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '12.BR', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 12, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B', '6.K', '6.O'], 'contains': ['24.DX', '24.DY', '24.DZ', '24.EO', '24.EP', '24.EW', '24.EX', '24.FC', '24.FD'], 'core': '48.C', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [324355644776280741499582, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 79804429413572684637382, 378358649363678452761737], 'label': '3072.bgb.12.BR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.br1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BR', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 184762521
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.FT', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.FL', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.CA', '48.DA', '48.FK'], 'contains': ['192.CU', '192.DL', '192.DO', '192.LY', '192.ME'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 378358770648994141276807, 187973308220359388001840, 79804308125641822294440, 25903229683158464676480], 'label': '3072.bgb.96.FT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '96.fr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.FT', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762522
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.FU', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.EW', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.CK', '48.DA', '48.HX'], 'contains': ['192.CT', '192.DN', '192.DO', '192.LU', '192.LV'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [378358770650295628183080, 108169512287410083283217, 54003503618341535825287, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.96.FU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CW', 'old_label': '96.fs1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.FU', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762523
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.FV', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '384.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.Q', '48.BK', '48.CO', '48.CV', '48.DF', '48.HN'], 'contains': ['192.CV', '192.CW', '192.CY', '192.DA'], 'core': '3072.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [378358770650295628183080, 79804308125641822294440, 122002101738321960, 25903229683158464676480, 324355523485385682622200], 'label': '3072.bgb.96.FV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.ft1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.FV', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 184762524
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.FW', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BS', '48.BY', '48.DD', '48.DF', '48.HY'], 'contains': ['192.CW', '192.DG', '192.DJ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770650295628183080, 79804308125641822294440, 122002101738321960, 25903229683158464676480, 296092756945739609872576], 'label': '3072.bgb.96.FW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.fu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.FW', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762525
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '96.FX', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '192.DL', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.R', '48.BL', '48.CP', '48.CW', '48.DE', '48.HN'], 'contains': ['192.CX', '192.CZ', '192.DA', '192.DS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [378358770648994141276807, 79804308125641822294440, 122002101738321960, 25903229683158464676480, 324355523485385682622200], 'label': '3072.bgb.96.FX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.fv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.FX', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 184762526
    {'ambient': '3072.bgb', 'aut_centralizer_order': 32, 'aut_label': '96.FY', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.FY', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BU', '48.CD', '48.CM', '48.CP', '48.IC'], 'contains': ['192.CX', '192.DC', '192.DF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [404211043484134973872583, 79804308125641822294440, 122002101738321960, 324406991811924875755576, 25903229683158464676480], 'label': '3072.bgb.96.FY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.fw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.FY', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184762527
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.FZ', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '192.CX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BV', '48.CE', '48.CN', '48.CO', '48.IC'], 'contains': ['192.CY', '192.DC', '192.DF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [404211043482821032924936, 79804308125641822294440, 122002101738321960, 324406991811924875755576, 25903229683158464676480], 'label': '3072.bgb.96.FZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.fx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.FZ', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762528
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.GA', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BT', '48.BZ', '48.DC', '48.DE', '48.HY'], 'contains': ['192.CZ', '192.DG', '192.DJ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [378358770648994141276807, 79804308125641822294440, 122002101738321960, 25903229683158464676480, 296092756945739609872576], 'label': '3072.bgb.96.GA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.fy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.GA', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762529
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.GB', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.FI', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.V', '48.BK', '48.BL', '48.CS', '48.CT', '48.DB', '48.HS'], 'contains': ['192.DA', '192.DD', '192.DE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903363795619943623743, 122004885304085057, 122002101738321960, 25903485430815165863622, 1313941673647], 'label': '3072.bgb.96.GB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.fz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.GB', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762530
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.GC', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '384.FG', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.V', '48.BF', '48.CV', '48.CW', '48.HT'], 'contains': ['192.DA', '192.DH', '192.DI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25903107682370587468807, 54003503618341535825287, 25903229683158464676480, 270189649267478943569286, 378358649363678452761737], 'label': '3072.bgb.96.GC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.D', 'old_label': '96.ga1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.GC', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 184762531
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '12.BS', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 12, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.C', '6.K', '6.N'], 'contains': ['24.DX', '24.ED', '24.EE', '24.HW'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [53952291033879672806278, 108118421696801471190456, 25903229681844523013167, 122002101738321960, 1313941673647, 79804429413572684637382, 134021529040297499210286, 25852017102974698844878], 'label': '3072.bgb.12.BS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bs1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BS', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 184762532
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.GD', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.FE', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BS', '48.BT', '48.CD', '48.CE', '48.CR', '48.CS', '48.II'], 'contains': ['192.DC', '192.DE', '192.DJ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [270240484111912758504367, 404211043484134973872583, 79804308125641822294440, 122002101738321960, 25903229683158464676480], 'label': '3072.bgb.96.GD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.gb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.GD', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762533
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.GE', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.FN', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BU', '48.BV', '48.BY', '48.BZ', '48.CZ', '48.DB', '48.IJ'], 'contains': ['192.DD', '192.DF', '192.DG'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [256460345499052777, 79855264629178445030417, 122004885304085057, 122002101738321960, 1313941673647], 'label': '3072.bgb.96.GE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '96.gc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.GE', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762534
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.GF', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '192.CX', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.X', '48.CQ', '48.FL'], 'contains': ['192.DK', '192.DL', '192.DM', '192.DR', '192.DT'], 'core': '3072.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [54003503618341535825287, 122002101738321960, 324406870525295326154166, 25903229683158464676480, 404210922196204071249966], 'label': '3072.bgb.96.GF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.R', 'old_label': '96.gd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.GF', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 184762535
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.GG', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.CF', '48.CQ', '48.ID'], 'contains': ['192.DK', '192.DP', '192.DQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [324355644776280741499582, 54003503618341535825287, 122002101738321960, 25903229683158464676480, 378358649363678452761737], 'label': '3072.bgb.96.GG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CT', 'old_label': '96.ge1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.GG', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762536
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.GH', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.BZ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.E', '48.F', '48.IR'], 'contains': ['192.DV', '192.ED', '192.EH', '192.ES', '192.EU', '192.FF', '192.FG', '192.FK', '192.FN', '192.FW', '192.GG', '192.HK', '192.HN', '192.IU', '192.JX'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25852138757799544092222, 51212588579793007921, 25852138389591620222016, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.GH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.gf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.GH', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762537
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.GI', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.BL', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.E', '48.G', '48.IR'], 'contains': ['192.DU', '192.ED', '192.EG', '192.EQ', '192.ET', '192.FF', '192.FG', '192.FJ', '192.FO', '192.FV', '192.GF', '192.HJ', '192.HN', '192.IU', '192.JY'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25852017095880079467006, 25852138389591620222016, 1313941673647, 25852017102974698844878, 51090958997032170942], 'label': '3072.bgb.96.GI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.gg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.GI', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762538
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.GJ', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.FR', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.E', '48.F', '48.IS'], 'contains': ['192.DX', '192.EE', '192.EK', '192.ES', '192.EW', '192.FF', '192.FI', '192.FM', '192.FO', '192.GA', '192.GG', '192.HM', '192.HY', '192.IW', '192.LO'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25852017095880079467006, 25903107685154153232142, 1313941673647, 25852017101492540879976, 51090958997032170942], 'label': '3072.bgb.96.GJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.gh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.GJ', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762539
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.GK', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.CR', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.E', '48.G', '48.IS'], 'contains': ['192.DW', '192.EE', '192.EK', '192.EQ', '192.EV', '192.FF', '192.FH', '192.FL', '192.FN', '192.GA', '192.GF', '192.HL', '192.HY', '192.IV', '192.LS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25852138757799544092222, 51212588579793007921, 25903107685154153232142, 1313941673647, 25852017101492540879976], 'label': '3072.bgb.96.GK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.gi1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.GK', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762540
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.GL', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '768.I', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DG', '48.DI', '48.IO'], 'contains': ['192.DY', '192.EF', '192.EI', '192.ID', '192.IH', '192.JE', '192.JK'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25852017095880079467006, 162121669227129588479873, 1313941673647, 162070456274433112077942, 25852017102974698844878], 'label': '3072.bgb.96.GL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.gj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.GL', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184762541
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.GM', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '768.I', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DH', '48.DI', '48.IO'], 'contains': ['192.DZ', '192.EF', '192.EJ', '192.ID', '192.IH', '192.JG', '192.JT'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922473021741077083393, 51212588579793007921, 1313941673647, 162070456274433112077942, 25852017102974698844878], 'label': '3072.bgb.96.GM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.gk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.GM', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184762542
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.BT', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.C', '6.J', '6.O'], 'contains': ['24.DX', '24.EF', '24.EG', '24.HX'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [324355644776280741499582, 108118165248982343710201, 25903229681844523013167, 404210787739267985320182, 187922473375925652905521, 122002101738321960, 1313941673647, 79804429413572684637382], 'label': '3072.bgb.12.BT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BT', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184762543
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.GN', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.BV', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.F', '48.H', '48.IR'], 'contains': ['192.DU', '192.DZ', '192.ED', '192.ES', '192.EU', '192.EY', '192.EZ', '192.FJ', '192.FO', '192.FQ', '192.FT', '192.HK', '192.HZ', '192.IR', '192.JX'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25852138757799544092222, 25852017095880079467006, 25852138389591620222016, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.GN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.gl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.GN', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762544
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.GO', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.BK', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.G', '48.H', '48.IR'], 'contains': ['192.DV', '192.DY', '192.ED', '192.EQ', '192.ET', '192.EY', '192.EZ', '192.FK', '192.FN', '192.FP', '192.FS', '192.HJ', '192.HZ', '192.IR', '192.JY'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [51212588579793007921, 25852138389591620222016, 1313941673647, 25852017102974698844878, 51090958997032170942], 'label': '3072.bgb.96.GO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.gm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.GO', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762545
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.GP', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.EQ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.F', '48.H', '48.IS'], 'contains': ['192.DX', '192.EA', '192.EE', '192.ES', '192.EV', '192.EY', '192.FB', '192.FM', '192.FN', '192.FR', '192.FT', '192.HL', '192.IB', '192.IS', '192.LO'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [51212588579793007921, 25903107685154153232142, 1313941673647, 25852017101492540879976, 51090958997032170942], 'label': '3072.bgb.96.GP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.gn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.GP', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762546
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.GQ', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.CN', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.G', '48.H', '48.IS'], 'contains': ['192.DW', '192.EA', '192.EE', '192.EQ', '192.EW', '192.EY', '192.FA', '192.FL', '192.FO', '192.FR', '192.FS', '192.HM', '192.IA', '192.IS', '192.LS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25852138757799544092222, 25852017095880079467006, 25903107685154153232142, 1313941673647, 25852017101492540879976], 'label': '3072.bgb.96.GQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.go1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.GQ', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762547
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.GR', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '768.I', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DG', '48.DJ', '48.IO'], 'contains': ['192.EF', '192.EG', '192.EJ', '192.JE', '192.JF', '192.JK', '192.JS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [162121669227129588479873, 51212588579793007921, 1313941673647, 162070456274433112077942, 25852017102974698844878], 'label': '3072.bgb.96.GR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.gp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.GR', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184762548
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.GS', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '768.I', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DH', '48.DJ', '48.IO'], 'contains': ['192.EF', '192.EH', '192.EI', '192.JF', '192.JG', '192.JS', '192.JT'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922473021741077083393, 25852017095880079467006, 1313941673647, 162070456274433112077942, 25852017102974698844878], 'label': '3072.bgb.96.GS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.gq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.GS', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184762549
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.GT', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.CK', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.F', '48.G', '48.JJ'], 'contains': ['192.DU', '192.DV', '192.EA', '192.EK', '192.EL', '192.EP', '192.ER', '192.FJ', '192.FK', '192.FR', '192.GA', '192.GJ', '192.GK', '192.IE', '192.JH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229337376182892926, 51212594192254410823, 51212588579793007921, 1313941673647, 51212595674412385793], 'label': '3072.bgb.96.GT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.gr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.GT', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762550
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.GU', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.DN', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.E', '48.H', '48.JJ'], 'contains': ['192.DU', '192.DV', '192.DW', '192.DX', '192.EM', '192.EX', '192.FE', '192.FJ', '192.FK', '192.FL', '192.FM', '192.GM', '192.HC', '192.IG', '192.JI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229337376182892926, 51212588579793007921, 1313941673647, 51212595674412385793, 25852017101492540879976], 'label': '3072.bgb.96.GU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.gs1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.GU', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762551
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.GV', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.CS', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.G', '48.DG', '48.JJ'], 'contains': ['192.DW', '192.DY', '192.EG', '192.EL', '192.EP', '192.FL', '192.FP', '192.FV', '192.GJ', '192.IF', '192.JL'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229337376182892926, 51212588579793007921, 1313941673647, 25852017101492540879976, 25852017102974698844878], 'label': '3072.bgb.96.GV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.gt1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.GV', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762552
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.GW', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.DR', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.F', '48.DH', '48.JJ'], 'contains': ['192.DX', '192.DZ', '192.EH', '192.EL', '192.ER', '192.FM', '192.FQ', '192.FW', '192.GK', '192.IF', '192.JM'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [368207923870206, 51212588579793007921, 1313941673647, 25852017101492540879976, 25852017102974698844878], 'label': '3072.bgb.96.GW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.gu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.GW', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762553
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '12.BU', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 12, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.E', '6.K', '6.L'], 'contains': ['24.DY', '24.EB', '24.EE', '24.HR'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118421696801471190456, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 79804429413572684637382, 378358649363678452761737], 'label': '3072.bgb.12.BU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BU', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 184762554
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.GX', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.DO', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.H', '48.DI', '48.JJ'], 'contains': ['192.DY', '192.DZ', '192.EA', '192.EM', '192.EX', '192.FP', '192.FQ', '192.FR', '192.GM', '192.IT', '192.JJ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229337376182892926, 51212594192254410823, 51212588579793007921, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.GX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.gv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.GX', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762555
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.GY', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.DS', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.E', '48.DJ', '48.JJ'], 'contains': ['192.EG', '192.EH', '192.EK', '192.EM', '192.FE', '192.FV', '192.FW', '192.GA', '192.HC', '192.JJ', '192.JP'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229337376182892926, 51212594192254410823, 25852017095880079467006, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.GY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '96.gw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.GY', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762556
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.GZ', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.DV', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DG', '48.DH', '48.JQ'], 'contains': ['192.EI', '192.EJ', '192.EL', '192.FX', '192.FY', '192.JN', '192.JO'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [162121669227129588479873, 51212588579793007921, 1313941673647, 25852017101492540879976, 25852017102974698844878], 'label': '3072.bgb.96.GZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.gx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.GZ', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762557
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.HA', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.DU', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DI', '48.DJ', '48.JQ'], 'contains': ['192.EI', '192.EJ', '192.EM', '192.FX', '192.FY', '192.JQ', '192.JR'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922473021741077083393, 51212594192254410823, 51212588579793007921, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.HA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.gy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.HA', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762558
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.HB', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.X', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DG', '48.DI', '48.JS'], 'contains': ['192.DY', '192.EJ', '192.EO', '192.GL', '192.GS', '192.II', '192.KF', '192.QW', '192.QX'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922473375925652905521, 162121669227129588479873, 187973685961890096441600, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.96.HB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.gz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.HB', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762559
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.HC', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.X', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DH', '48.DI', '48.JS'], 'contains': ['192.DZ', '192.EI', '192.EO', '192.GL', '192.GW', '192.II', '192.KH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922473021741077083393, 187922473375925652905521, 1313941673647, 162070456272950954131199, 162070456280045573438767], 'label': '3072.bgb.96.HC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.ha1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.HC', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762560
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.HD', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.X', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DG', '48.DJ', '48.JS'], 'contains': ['192.EG', '192.EI', '192.EO', '192.GS', '192.GV', '192.KF', '192.KG'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922473375925652905521, 162121669227129588479873, 1313941673647, 162070456272950954131199, 162070456280045573438767], 'label': '3072.bgb.96.HD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.hb1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.HD', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762561
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.HE', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.X', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DH', '48.DJ', '48.JS'], 'contains': ['192.EH', '192.EJ', '192.EO', '192.GV', '192.GW', '192.KG', '192.KH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922473021741077083393, 187922473375925652905521, 187973685961890096441600, 1313941673647, 162070456272950954131199], 'label': '3072.bgb.96.HE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.hc1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.HE', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762562
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.HF', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.NQ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DG', '48.DH', '48.JW'], 'contains': ['192.EB', '192.EF', '192.EL', '192.EN', '192.EO', '192.FZ', '192.GN', '192.GT', '192.HF', '192.HH', '192.KD'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922473375925652905521, 187973685961890096441600, 25903229683158464676480, 108118287251071627990321, 162070456272950954131199], 'label': '3072.bgb.96.HF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.hd1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.HF', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184762563
    {'ambient': '3072.bgb', 'aut_centralizer_order': 16, 'aut_label': '96.HG', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '192.NQ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DI', '48.DJ', '48.JW'], 'contains': ['192.EC', '192.EF', '192.EM', '192.EN', '192.EO', '192.FZ', '192.GN', '192.GU', '192.HF', '192.HI', '192.KE'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [187922473375925652905521, 187973685961890096441600, 134021272931340477137406, 25903229683158464676480, 162070456272950954131199], 'label': '3072.bgb.96.HG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.he1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.HG', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 184762564
    {'ambient': '3072.bgb', 'aut_centralizer_order': 2, 'aut_label': '12.BV', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '1536.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.E', '6.H', '6.O'], 'contains': ['24.DY', '24.EC', '24.EF', '24.HM'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [324406614064956014978497, 108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 122002101738321960, 1313941673647, 79804429413572684637382, 378358649363678452761737], 'label': '3072.bgb.12.BV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BV', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 184762565
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.HH', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.CQ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.F', '48.G', '48.KE'], 'contains': ['192.EP', '192.ER', '192.EV', '192.EW', '192.EZ', '192.FC', '192.FG', '192.HL', '192.HM', '192.HS', '192.HT', '192.HZ', '192.IF', '192.IU', '192.JH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229337376182892926, 122007701746409022, 51212594192254410823, 1313941673647, 51212595674412385793], 'label': '3072.bgb.96.HH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.hf1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.HH', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762566
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.HI', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.ER', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.E', '48.H', '48.KE'], 'contains': ['192.ET', '192.EU', '192.EV', '192.EW', '192.EX', '192.FD', '192.FE', '192.HJ', '192.HK', '192.HL', '192.HM', '192.IG', '192.IN', '192.JJ', '192.LN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229337376182892926, 122007701746409022, 51212594192254410823, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.HI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.hg1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.HI', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762567
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.HJ', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.CV', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.G', '48.KE'], 'contains': ['192.EP', '192.ET', '192.FA', '192.FC', '192.FH', '192.HJ', '192.HS', '192.IA', '192.IE', '192.IV', '192.JL'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229337376182892926, 122007701746409022, 1313941673647, 25852017101492540879976, 25852017102974698844878], 'label': '3072.bgb.96.HJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.hh1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.HJ', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762568
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.HK', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.FS', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.F', '48.KE'], 'contains': ['192.ER', '192.EU', '192.FB', '192.FC', '192.FI', '192.HK', '192.HT', '192.IB', '192.IE', '192.IW', '192.JM'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [122007701746409022, 368207923870206, 1313941673647, 25852017101492540879976, 25852017102974698844878], 'label': '3072.bgb.96.HK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.hi1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.HK', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762569
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.HL', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.EU', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.H', '48.KE'], 'contains': ['192.EX', '192.EZ', '192.FA', '192.FB', '192.FD', '192.HZ', '192.IA', '192.IB', '192.IN', '192.IT', '192.JI'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229337376182892926, 25903107687970595565937, 1313941673647, 51212595674412385793, 25852017101492540879976], 'label': '3072.bgb.96.HL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.hj1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.HL', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762570
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.HM', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.FV', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.E', '48.KE'], 'contains': ['192.FD', '192.FE', '192.FG', '192.FH', '192.FI', '192.IU', '192.IV', '192.IW', '192.JI', '192.JP', '192.LN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229337376182892926, 122007701746409022, 1313941673647, 51212595674412385793, 25852017101492540879976], 'label': '3072.bgb.96.HM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.L', 'old_label': '96.hk1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.HM', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762571
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.HN', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '768.I', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DG', '48.DI', '48.KM'], 'contains': ['192.FP', '192.FX', '192.FZ', '192.IH', '192.II', '192.JK', '192.KF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229691554491852799, 108118165248982343710201, 134021273295424323553798, 133970303627361494479417, 1313941673647], 'label': '3072.bgb.96.HN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.hl1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.HN', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184762572
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.HO', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '768.I', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DH', '48.DI', '48.KM'], 'contains': ['192.FQ', '192.FY', '192.FZ', '192.IH', '192.II', '192.JT', '192.KH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [9709968839632, 108118165248982343710201, 133970303627361494479417, 1313941673647, 108118286902479131308678], 'label': '3072.bgb.96.HO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.hm1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.HO', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184762573
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.HP', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.Y', '48.BM', '48.KN'], 'contains': ['192.FS', '192.GD', '192.GH', '192.IC', '192.IJ', '192.IZ', '192.KW'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [122007701746409022, 25852138757799544092222, 25903107685154153232142, 1313941673647, 53952291036675691857216], 'label': '3072.bgb.96.HP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BN', 'old_label': '96.hn1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.HP', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762574
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.HQ', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.Z', '48.BM', '48.KN'], 'contains': ['192.FT', '192.GD', '192.GI', '192.IC', '192.IJ', '192.JD', '192.LB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903107687970595565937, 25903107685154153232142, 1313941673647, 53952291036675691857216, 51090958997032170942], 'label': '3072.bgb.96.HQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BN', 'old_label': '96.ho1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.HQ', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762575
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '12.BW', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 12, 'centralizer': '768.Q', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.D', '6.K', '6.M'], 'contains': ['24.DZ', '24.EB', '24.ED'], 'core': '48.C', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [108118165248982343710201, 25903229681844523013167, 187922473375925652905521, 296092500500710274860657, 122002101738321960, 1313941673647, 79804429413572684637382, 378358905093235639407953], 'label': '3072.bgb.12.BW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BW', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 184762576
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.HR', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.V', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.Y', '48.BM', '48.KO'], 'contains': ['192.FS', '192.GE', '192.GI', '192.IC', '192.IP', '192.IZ', '192.LR'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [53952291032377091563446, 79855398717732338388456, 53952412691500576681559, 1313941673647, 79855520715724195809353], 'label': '3072.bgb.96.HR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BN', 'old_label': '96.hp1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.HR', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762577
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.HS', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.V', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.Z', '48.BM', '48.KO'], 'contains': ['192.FT', '192.GE', '192.GH', '192.IC', '192.IP', '192.JD', '192.MF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79855520714221614566521, 79855398717732338388456, 79855399081842795124439, 1313941673647, 79855520715724195809353], 'label': '3072.bgb.96.HS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BN', 'old_label': '96.hq1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.HS', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762578
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.HT', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '768.I', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DG', '48.DJ', '48.KM'], 'contains': ['192.FV', '192.FY', '192.FZ', '192.JK', '192.JS', '192.KF', '192.KG'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [9709968839632, 108118165248982343710201, 134021273295424323553798, 133970303627361494479417, 1313941673647], 'label': '3072.bgb.96.HT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.hr1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.HT', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184762579
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.HU', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '768.I', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DH', '48.DJ', '48.KM'], 'contains': ['192.FW', '192.FX', '192.FZ', '192.JS', '192.JT', '192.KG', '192.KH'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229691554491852799, 108118165248982343710201, 133970303627361494479417, 1313941673647, 108118286902479131308678], 'label': '3072.bgb.96.HU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.hs1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.HU', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 184762580
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.HV', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.Y', '48.BP', '48.KN'], 'contains': ['192.GD', '192.GF', '192.GI', '192.IZ', '192.JC', '192.KW', '192.LA'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903107687970595565937, 25852138757799544092222, 25903107685154153232142, 1313941673647, 53952291036675691857216], 'label': '3072.bgb.96.HV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BN', 'old_label': '96.ht1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.HV', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762581
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.HW', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.Z', '48.BP', '48.KN'], 'contains': ['192.GD', '192.GG', '192.GH', '192.JC', '192.JD', '192.LA', '192.LB'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [122007701746409022, 25903107685154153232142, 1313941673647, 53952291036675691857216, 51090958997032170942], 'label': '3072.bgb.96.HW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BN', 'old_label': '96.hu1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.HW', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762582
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.HX', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.V', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.Y', '48.BP', '48.KO'], 'contains': ['192.GE', '192.GF', '192.GH', '192.IZ', '192.JC', '192.LR', '192.MD'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79855520714221614566521, 79855398717732338388456, 53952412691500576681559, 1313941673647, 79855520715724195809353], 'label': '3072.bgb.96.HX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BN', 'old_label': '96.hv1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.HX', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762583
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.HY', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.V', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.Z', '48.BP', '48.KO'], 'contains': ['192.GE', '192.GG', '192.GI', '192.JC', '192.JD', '192.MD', '192.MF'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [53952291032377091563446, 79855398717732338388456, 79855399081842795124439, 1313941673647, 79855520715724195809353], 'label': '3072.bgb.96.HY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BN', 'old_label': '96.hw1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.HY', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762584
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.HZ', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.F', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BA', '48.BC', '48.KZ'], 'contains': ['192.GJ', '192.HB', '192.HD', '192.HO', '192.HU', '192.LD', '192.LP'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79804429416356250372480, 378358770650295628183080, 25852272837936812846761, 25903229683158464676480, 242140721658215271465607], 'label': '3072.bgb.96.HZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BO', 'old_label': '96.hx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.HZ', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762585
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.IA', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.S', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BB', '48.BC', '48.KZ'], 'contains': ['192.GJ', '192.HB', '192.HE', '192.HQ', '192.HV', '192.LD', '192.LQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79804429416356250372480, 378358770648994141276807, 25852272837936812846761, 25903229683158464676480, 242140721658215271465607], 'label': '3072.bgb.96.IA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BO', 'old_label': '96.hy1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.IA', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762586
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '12.BX', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 12, 'centralizer': '768.P', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.D', '6.I', '6.O'], 'contains': ['24.DZ', '24.EC', '24.EG'], 'core': '48.C', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25903229681844523013167, 1313941673647, 122002101738321960, 404210787739267985320182, 79804429413572684637382, 187922473375925652905521, 108118165248982343710201, 324406614064956014978497], 'label': '3072.bgb.12.BX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bx1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BX', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 184762587
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.IB', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.F', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BA', '48.BE', '48.KZ'], 'contains': ['192.GK', '192.HB', '192.HD', '192.HO', '192.HV', '192.LI', '192.LX'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [51469042011382569606, 79804429416356250372480, 378358770650295628183080, 25903229683158464676480, 242140721658215271465607], 'label': '3072.bgb.96.IB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BO', 'old_label': '96.hz1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.IB', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762588
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.IC', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.S', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BB', '48.BE', '48.KZ'], 'contains': ['192.GK', '192.HB', '192.HE', '192.HQ', '192.HU', '192.LI', '192.MC'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [51469042011382569606, 79804429416356250372480, 378358770648994141276807, 25903229683158464676480, 242140721658215271465607], 'label': '3072.bgb.96.IC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BO', 'old_label': '96.ia1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.IC', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762589
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.ID', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.DP', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DG', '48.DH', '48.LA'], 'contains': ['192.GL', '192.GT', '192.GV', '192.IF', '192.IH', '192.JO', '192.JS'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [162121669227129588479873, 187973685961890096441600, 1313941673647, 25852017101492540879976, 25852017102974698844878], 'label': '3072.bgb.96.ID', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.ib1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ID', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762590
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.IE', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.DP', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DI', '48.LA'], 'contains': ['192.GL', '192.GU', '192.IH', '192.IT', '192.JR'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [187922473021741077083393, 51212594192254410823, 1313941673647, 25852017102974698844878, 162070456280045573438767], 'label': '3072.bgb.96.IE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.ic1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.IE', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762591
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.IF', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.K', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BQ', '48.BR', '48.LG'], 'contains': ['192.GQ', '192.HD', '192.HE', '192.JA', '192.JB', '192.KI', '192.KP'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79804429416356250372480, 378307558065813088567696, 25903229683158464676480, 134021272934136496216343, 216288705272228144236816], 'label': '3072.bgb.96.IF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BX', 'old_label': '96.id1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.IF', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762592
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.IG', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.K', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BR', '48.DK', '48.LG'], 'contains': ['192.GQ', '192.HD', '192.JA', '192.KM', '192.KQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804429416356250372480, 108118287253867647069496, 378307558064511680779583, 25903229683158464676480, 216288705272228144236816], 'label': '3072.bgb.96.IG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BA', 'old_label': '96.ie1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.IG', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762593
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.IH', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '768.K', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BQ', '48.DL', '48.LG'], 'contains': ['192.GQ', '192.HE', '192.JB', '192.KN', '192.KQ'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [79804429416356250372480, 108118287253867647069496, 378307558064511680779583, 216288705273529552035263, 25903229683158464676480], 'label': '3072.bgb.96.IH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BA', 'old_label': '96.if1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.IH', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 184762594
    {'ambient': '3072.bgb', 'aut_centralizer_order': 4, 'aut_label': '96.II', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '768.K', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DK', '48.DL', '48.LH'], 'contains': ['192.GQ', '192.KO', '192.KR'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [79804429416356250372480, 108118287253867647069496, 242140721662339602266753, 404159575154785525538638, 25903229683158464676480], 'label': '3072.bgb.96.II', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GO', 'old_label': '96.ig1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.II', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 184762595
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.IJ', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '384.DQ', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.DI', '48.DJ', '48.LL'], 'contains': ['192.GS', '192.GU', '192.GW', '192.JJ', '192.JK', '192.JQ', '192.JT'], 'core': '3072.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [368207923870206, 51212594192254410823, 187973685961890096441600, 1313941673647, 25852017102974698844878], 'label': '3072.bgb.96.IJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.ih1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.IJ', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 184762596
    {'ambient': '3072.bgb', 'aut_centralizer_order': 8, 'aut_label': '96.IK', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '384.DQ', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.DG', '48.LL'], 'contains': ['192.GS', '192.GT', '192.JK', '192.JL', '192.JN'], 'core': '3072.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229337376182892926, 187973685961890096441600, 1313941673647, 25852017101492540879976, 25852017102974698844878], 'label': '3072.bgb.96.IK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GA', 'old_label': '96.ii1', 'projective_image': '3072.bgb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.IK', 'subgroup_fusion': None, 'weyl_group': '16.14'}