Abstract group data - 384.17956

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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': 3, 'aut_exponent': 12, 'aut_gen_orders': [6, 2, 2, 2, 6, 2, 4, 2], 'aut_gens': [[132667, 5042476, 293524, 6164698, 4605946], [5814484, 531509, 697135, 4605946, 2981098], [2296241, 531509, 3042404, 6164698, 4549642], [3559400, 6236344, 6643792, 2990890, 6174490], [2122417, 5042476, 316168, 2981098, 4549642], [5720389, 6236344, 6606980, 2981098, 2990890], [5720389, 531509, 4273084, 4605946, 6164698], [5728804, 531509, 4374370, 4605946, 2990890], [6632585, 1725377, 2636141, 6164698, 4605946]], 'aut_group': '1536.408641059', 'aut_hash': 1418641417957792246, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1536, 'aut_permdeg': 32, 'aut_perms': [103071517019489506059338745333332770, 207617191100129693064065287926675448, 259575283414634561869365509135851361, 222319126012780672796347464770620937, 13519617270249274355879087240875112, 71032795751090259932839295571284748, 212545512234755561918632447964533413, 188280573621665042303723697751914314], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 2, 1], [2, 12, 1, 1], [2, 12, 2, 1], [2, 24, 1, 1], [3, 8, 1, 1], [4, 2, 2, 2], [4, 6, 1, 2], [4, 12, 1, 2], [4, 24, 1, 2], [6, 8, 1, 3], [6, 16, 2, 1], [8, 6, 4, 1], [8, 12, 2, 3], [12, 16, 2, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_2^6\\times S_4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '64.267', 'autcent_hash': 267, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '24.12', 'autcentquo_hash': 12, 'autcentquo_nilpotent': False, 'autcentquo_order': 24, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [2, 12, 3], [2, 24, 1], [3, 8, 1], [4, 2, 4], [4, 6, 2], [4, 12, 2], [4, 24, 2], [6, 8, 3], [6, 16, 2], [8, 6, 4], [8, 12, 6], [12, 16, 4]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '96.226', 'commutator_count': 1, 'commutator_label': '48.32', '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', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 17956, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [2, 12, 1, 3], [2, 24, 1, 1], [3, 8, 1, 1], [4, 2, 2, 2], [4, 6, 1, 2], [4, 12, 1, 2], [4, 24, 1, 2], [6, 8, 1, 3], [6, 16, 1, 2], [8, 6, 2, 2], [8, 12, 2, 3], [12, 16, 2, 2]], 'element_repr_type': 'GLZN', 'elementary': 1, 'eulerian_function': 10080, 'exponent': 24, 'exponents_of_order': [7, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '96.226', 'hash': 17956, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 2, 6, 2, 2], 'inner_gens': [[132667, 5042476, 284803, 6174490, 4549642], [132667, 5042476, 2636141, 6164698, 4605946], [3435199, 531509, 293524, 2981098, 2990890], [4604263, 5042476, 697135, 6164698, 4549642], [2122417, 5042476, 394810, 2990890, 4605946]], 'inner_hash': 226, 'inner_nilpotent': False, 'inner_order': 96, 'inner_split': True, 'inner_tex': 'C_2^2\\times S_4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 14], [3, 8], [4, 7], [6, 2], [8, 1]], 'label': '384.17956', 'linC_count': 16, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 12, 'linQ_dim': 10, 'linQ_dim_count': 12, 'linR_count': 8, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'GL(2,3):D4', 'ngens': 8, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 27, 'number_characteristic_subgroups': 32, 'number_conjugacy_classes': 40, 'number_divisions': 31, 'number_normal_subgroups': 36, 'number_subgroup_autclasses': 249, 'number_subgroup_classes': 305, 'number_subgroups': 1617, 'old_label': None, 'order': 384, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 67], [3, 8], [4, 92], [6, 56], [8, 96], [12, 64]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [132652, 132652, 132652, 132652], 'outer_gens': [[132667, 5042476, 394810, 2990890, 4605946], [4642835, 5042476, 293524, 6164698, 4605946], [132667, 6236344, 293524, 6164698, 4605946], [132667, 5042476, 4264363, 6164698, 4605946]], 'outer_group': '16.14', 'outer_hash': 14, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 16, 'outer_perms': [1327912203241, 2966658509284, 4396538203938, 5800737348096], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 6], [3, 8], [4, 1], [6, 2], [8, 6]], 'representations': {'PC': {'code': 768726718584351456422895533306329201463632754539650575880, 'gens': [1, 2, 3, 6, 7], 'pres': [8, -2, -2, -2, -2, -3, -2, 2, -2, 1545, 482, 2650, 66, 1283, 91, 1284, 16133, 1749, 1757, 469, 237, 16134, 3382, 2382, 878, 382, 166]}, 'GLZN': {'d': 2, 'p': 51, 'gens': [6721000, 2122432, 6324778, 132667, 1772389, 6632600, 3919406, 3909614]}, 'Perm': {'d': 20, 'gens': [2283861441336487, 1, 141986429951392096, 7, 524608910715000, 270143702759846880, 399507013713750600, 527966508282077520]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\GL(2,3):D_4', 'transitive_degree': 32, 'wreath_data': None, 'wreath_product': False}
• gps_conj_classes •

  Column	Type
  aut_label	text
  centralizer	text
  counter	integer
  group_counter	integer
  group_order	numeric
  label	text
  order	integer
  powers	integer[]
  representative	numeric
  size	numeric

  
  
  • id: 174777307
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 17956, 'group_order': 384, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 132652, 'size': 1}
  • id: 174777318
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 17956, 'group_order': 384, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 4642820, 'size': 1}
  • id: 174777329
    {'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 17956, 'group_order': 384, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 2122432, 'size': 1}
  • id: 174777340
    {'aut_label': '2C', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 17956, 'group_order': 384, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 6632600, 'size': 1}
  • id: 174777342
    {'aut_label': '2D', 'centralizer': '2.a1.a1', 'counter': 5, 'group_counter': 17956, 'group_order': 384, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 176903, 'size': 2}
  • id: 174777343
    {'aut_label': '2D', 'centralizer': '2.a1.a1', 'counter': 6, 'group_counter': 17956, 'group_order': 384, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 2166683, 'size': 2}
  • id: 174777344
    {'aut_label': '2F', 'centralizer': '12.e1.a1', 'counter': 7, 'group_counter': 17956, 'group_order': 384, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 132667, 'size': 12}
  • id: 174777345
    {'aut_label': '2G', 'centralizer': '12.v1.a1', 'counter': 8, 'group_counter': 17956, 'group_order': 384, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 2366842, 'size': 12}
  • id: 174777346
    {'aut_label': '2F', 'centralizer': '12.e1.a1', 'counter': 9, 'group_counter': 17956, 'group_order': 384, 'label': '2H', 'order': 2, 'powers': [1, 9], 'representative': 3465305, 'size': 12}
  • id: 174777308
    {'aut_label': '2I', 'centralizer': '24.c1.a1', 'counter': 10, 'group_counter': 17956, 'group_order': 384, 'label': '2I', 'order': 2, 'powers': [1, 10], 'representative': 3553756, 'size': 24}
  • id: 174777309
    {'aut_label': '3A', 'centralizer': '8.d1.a1', 'counter': 11, 'group_counter': 17956, 'group_order': 384, 'label': '3A', 'order': 3, 'powers': [11, 1], 'representative': 3333742, 'size': 8}
  • id: 174777310
    {'aut_label': '4A1', 'centralizer': '2.e1.a1', 'counter': 12, 'group_counter': 17956, 'group_order': 384, 'label': '4A1', 'order': 4, 'powers': [4, 13], 'representative': 575726, 'size': 2}
  • id: 174777311
    {'aut_label': '4A1', 'centralizer': '2.e1.a1', 'counter': 13, 'group_counter': 17956, 'group_order': 384, 'label': '4A-1', 'order': 4, 'powers': [4, 12], 'representative': 6324778, 'size': 2}
  • id: 174777312
    {'aut_label': '4B1', 'centralizer': '2.d1.a1', 'counter': 14, 'group_counter': 17956, 'group_order': 384, 'label': '4B1', 'order': 4, 'powers': [3, 15], 'representative': 6236344, 'size': 2}
  • id: 174777313
    {'aut_label': '4B1', 'centralizer': '2.d1.a1', 'counter': 15, 'group_counter': 17956, 'group_order': 384, 'label': '4B-1', 'order': 4, 'powers': [3, 14], 'representative': 5042476, 'size': 2}
  • id: 174777314
    {'aut_label': '4C', 'centralizer': '6.e1.a1', 'counter': 16, 'group_counter': 17956, 'group_order': 384, 'label': '4C', 'order': 4, 'powers': [3, 16], 'representative': 4549642, 'size': 6}
  • id: 174777315
    {'aut_label': '4D', 'centralizer': '6.e1.a1', 'counter': 17, 'group_counter': 17956, 'group_order': 384, 'label': '4D', 'order': 4, 'powers': [3, 17], 'representative': 3919406, 'size': 6}
  • id: 174777316
    {'aut_label': '4E', 'centralizer': '12.bf1.a1', 'counter': 18, 'group_counter': 17956, 'group_order': 384, 'label': '4E', 'order': 4, 'powers': [2, 18], 'representative': 4532591, 'size': 12}
  • id: 174777317
    {'aut_label': '4F', 'centralizer': '12.j1.a1', 'counter': 19, 'group_counter': 17956, 'group_order': 384, 'label': '4F', 'order': 4, 'powers': [3, 19], 'representative': 2383009, 'size': 12}
  • id: 174777319
    {'aut_label': '4G', 'centralizer': '24.i1.a1', 'counter': 20, 'group_counter': 17956, 'group_order': 384, 'label': '4G', 'order': 4, 'powers': [4, 20], 'representative': 575735, 'size': 24}
  • id: 174777320
    {'aut_label': '4H', 'centralizer': '24.j1.a1', 'counter': 21, 'group_counter': 17956, 'group_order': 384, 'label': '4H', 'order': 4, 'powers': [3, 21], 'representative': 4316353, 'size': 24}
  • id: 174777321
    {'aut_label': '6A', 'centralizer': '8.d1.a1', 'counter': 22, 'group_counter': 17956, 'group_order': 384, 'label': '6A', 'order': 6, 'powers': [11, 2], 'representative': 1179026, 'size': 8}
  • id: 174777322
    {'aut_label': '6B', 'centralizer': '8.d1.a1', 'counter': 23, 'group_counter': 17956, 'group_order': 384, 'label': '6B', 'order': 6, 'powers': [11, 4], 'representative': 3466394, 'size': 8}
  • id: 174777323
    {'aut_label': '6C', 'centralizer': '8.d1.a1', 'counter': 24, 'group_counter': 17956, 'group_order': 384, 'label': '6C', 'order': 6, 'powers': [11, 3], 'representative': 5721478, 'size': 8}
  • id: 174777324
    {'aut_label': '6D', 'centralizer': '16.b1.a1', 'counter': 25, 'group_counter': 17956, 'group_order': 384, 'label': '6D', 'order': 6, 'powers': [11, 5], 'representative': 3377942, 'size': 16}
  • id: 174777325
    {'aut_label': '6D', 'centralizer': '16.b1.a1', 'counter': 26, 'group_counter': 17956, 'group_order': 384, 'label': '6E', 'order': 6, 'powers': [11, 6], 'representative': 5733395, 'size': 16}
  • id: 174777326
    {'aut_label': '8A1', 'centralizer': '6.e1.a1', 'counter': 27, 'group_counter': 17956, 'group_order': 384, 'label': '8A1', 'order': 8, 'powers': [16, 27], 'representative': 6166711, 'size': 6}
  • id: 174777327
    {'aut_label': '8A1', 'centralizer': '6.e1.a1', 'counter': 28, 'group_counter': 17956, 'group_order': 384, 'label': '8A-1', 'order': 8, 'powers': [16, 28], 'representative': 2988877, 'size': 6}
  • id: 174777328
    {'aut_label': '8A1', 'centralizer': '6.e1.a1', 'counter': 29, 'group_counter': 17956, 'group_order': 384, 'label': '8B1', 'order': 8, 'powers': [16, 29], 'representative': 1905509, 'size': 6}
  • id: 174777330
    {'aut_label': '8A1', 'centralizer': '6.e1.a1', 'counter': 30, 'group_counter': 17956, 'group_order': 384, 'label': '8B-1', 'order': 8, 'powers': [16, 30], 'representative': 2739962, 'size': 6}
  • id: 174777331
    {'aut_label': '8C1', 'centralizer': '12.bf1.a1', 'counter': 31, 'group_counter': 17956, 'group_order': 384, 'label': '8C1', 'order': 8, 'powers': [17, 32], 'representative': 3857350, 'size': 12}
  • id: 174777332
    {'aut_label': '8C1', 'centralizer': '12.bf1.a1', 'counter': 32, 'group_counter': 17956, 'group_order': 384, 'label': '8C3', 'order': 8, 'powers': [17, 31], 'representative': 697885, 'size': 12}
  • id: 174777333
    {'aut_label': '8D1', 'centralizer': '12.v1.a1', 'counter': 33, 'group_counter': 17956, 'group_order': 384, 'label': '8D1', 'order': 8, 'powers': [16, 34], 'representative': 1974700, 'size': 12}
  • id: 174777334
    {'aut_label': '8D1', 'centralizer': '12.v1.a1', 'counter': 34, 'group_counter': 17956, 'group_order': 384, 'label': '8D3', 'order': 8, 'powers': [16, 33], 'representative': 2669020, 'size': 12}
  • id: 174777335
    {'aut_label': '8E1', 'centralizer': '12.j1.a1', 'counter': 35, 'group_counter': 17956, 'group_order': 384, 'label': '8E1', 'order': 8, 'powers': [16, 35], 'representative': 4243349, 'size': 12}
  • id: 174777336
    {'aut_label': '8E1', 'centralizer': '12.j1.a1', 'counter': 36, 'group_counter': 17956, 'group_order': 384, 'label': '8E-1', 'order': 8, 'powers': [16, 36], 'representative': 5000690, 'size': 12}
  • id: 174777337
    {'aut_label': '12A1', 'centralizer': '16.e1.a1', 'counter': 37, 'group_counter': 17956, 'group_order': 384, 'label': '12A1', 'order': 12, 'powers': [23, 12], 'representative': 293524, 'size': 16}
  • id: 174777338
    {'aut_label': '12A1', 'centralizer': '16.e1.a1', 'counter': 38, 'group_counter': 17956, 'group_order': 384, 'label': '12A-1', 'order': 12, 'powers': [23, 13], 'representative': 4264363, 'size': 16}
  • id: 174777339
    {'aut_label': '12B1', 'centralizer': '16.f1.a1', 'counter': 39, 'group_counter': 17956, 'group_order': 384, 'label': '12B1', 'order': 12, 'powers': [24, 14], 'representative': 4308580, 'size': 16}
  • id: 174777341
    {'aut_label': '12B1', 'centralizer': '16.f1.a1', 'counter': 40, 'group_counter': 17956, 'group_order': 384, 'label': '12B-1', 'order': 12, 'powers': [24, 15], 'representative': 2583203, 'size': 16}
• 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: 18116742
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '384.17956', 'group_order': 384, 'image': None, 'label': '384.17956.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 18116753
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '384.17956', 'group_order': 384, 'image': None, 'label': '384.17956.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 18116764
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '384.17956', 'group_order': 384, 'image': None, 'label': '384.17956.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 18116767
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '384.17956', 'group_order': 384, 'image': None, 'label': '384.17956.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 18116768
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '384.17956', 'group_order': 384, 'image': None, 'label': '384.17956.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 18116769
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '384.17956', 'group_order': 384, 'image': None, 'label': '384.17956.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 18116770
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '384.17956', 'group_order': 384, 'image': None, 'label': '384.17956.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 18116771
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '384.17956', 'group_order': 384, 'image': None, 'label': '384.17956.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 18116772
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '384.17956', 'group_order': 384, 'image': None, 'label': '384.17956.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 0, 2, 0, 0, -1, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1], 'schur_index': 1}
  • id: 18116743
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '384.17956', 'group_order': 384, 'image': None, 'label': '384.17956.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 0, 0, -2, 0, 2, 0, 2, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, -2, -2, 2, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18116744
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '384.17956', 'group_order': 384, 'image': None, 'label': '384.17956.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 0, 0, 2, 0, -2, 0, 2, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, -2, -2, 2, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18116745
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '384.17956', 'group_order': 384, 'image': None, 'label': '384.17956.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 0, -2, 0, 0, -1, 2, 2, -2, -2, 2, 2, 2, -2, 0, 0, -1, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, -1], 'schur_index': 1}
  • id: 18116746
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '384.17956', 'group_order': 384, 'image': None, 'label': '384.17956.2e', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 0, 2, 0, 0, -1, -2, -2, 2, 2, 2, 2, -2, -2, 0, 0, -1, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1], 'schur_index': 1}
  • id: 18116747
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '384.17956', 'group_order': 384, 'image': None, 'label': '384.17956.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 0, -2, 0, 0, -1, -2, -2, -2, -2, 2, 2, -2, 2, 0, 0, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1], 'schur_index': 1}
  • id: 18116750
    {'cdim': 3, 'counter': 17, 'faithful': False, 'group': '384.17956', 'group_order': 384, 'image': None, 'label': '384.17956.3a', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, 3, 3, 3, 3, 1, -1, 1, 1, 0, 3, 3, 3, 3, -1, -1, -1, -1, 1, 1, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18116751
    {'cdim': 3, 'counter': 18, 'faithful': False, 'group': '384.17956', 'group_order': 384, 'image': None, 'label': '384.17956.3b', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, 3, 3, 3, 3, -1, -1, -1, -1, 0, 3, 3, 3, 3, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18116752
    {'cdim': 3, 'counter': 19, 'faithful': False, 'group': '384.17956', 'group_order': 384, 'image': None, 'label': '384.17956.3c', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -3, -3, -1, -1, -1, 1, 0, -3, -3, 3, 3, -1, -1, 1, 1, 1, -1, 0, 0, 0, 0, 0, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18116754
    {'cdim': 3, 'counter': 20, 'faithful': False, 'group': '384.17956', 'group_order': 384, 'image': None, 'label': '384.17956.3d', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -3, -3, -1, 1, -1, 1, 0, 3, 3, -3, -3, -1, -1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18116755
    {'cdim': 3, 'counter': 21, 'faithful': False, 'group': '384.17956', 'group_order': 384, 'image': None, 'label': '384.17956.3e', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -3, -3, 1, -1, 1, -1, 0, -3, -3, 3, 3, -1, -1, 1, 1, -1, 1, 0, 0, 0, 0, 0, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18116756
    {'cdim': 3, 'counter': 22, 'faithful': False, 'group': '384.17956', 'group_order': 384, 'image': None, 'label': '384.17956.3f', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -3, -3, 1, 1, 1, -1, 0, 3, 3, -3, -3, -1, -1, -1, 1, 1, -1, 0, 0, 0, 0, 0, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18116757
    {'cdim': 3, 'counter': 23, 'faithful': False, 'group': '384.17956', 'group_order': 384, 'image': None, 'label': '384.17956.3g', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, 3, 3, 3, -1, 1, -1, -1, 0, -3, -3, -3, -3, -1, -1, 1, -1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18116758
    {'cdim': 3, 'counter': 24, 'faithful': False, 'group': '384.17956', 'group_order': 384, 'image': None, 'label': '384.17956.3h', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 0, -3, -3, -3, -3, -1, -1, 1, -1, -1, -1, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18116759
    {'cdim': 4, 'counter': 25, 'faithful': False, 'group': '384.17956', 'group_order': 384, 'image': None, 'label': '384.17956.4a', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18116763
    {'cdim': 6, 'counter': 29, 'faithful': False, 'group': '384.17956', 'group_order': 384, 'image': None, 'label': '384.17956.6a', 'multiplicity': 1, 'nt': [12, 86], 'qdim': 6, 'qvalues': [6, -6, -6, 6, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18116765
    {'cdim': 6, 'counter': 30, 'faithful': False, 'group': '384.17956', 'group_order': 384, 'image': None, 'label': '384.17956.6b', 'multiplicity': 1, 'nt': [12, 86], 'qdim': 6, 'qvalues': [6, -6, -6, 6, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18116748
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '384.17956', 'group_order': 384, 'image': None, 'label': '384.17956.2g', 'multiplicity': 4, 'nt': [48, 0], 'qdim': 8, 'qvalues': [8, -8, 8, -8, -8, 8, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18116749
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '384.17956', 'group_order': 384, 'image': None, 'label': '384.17956.2h', 'multiplicity': 4, 'nt': [48, 0], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 8, -8, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18116760
    {'cdim': 4, 'counter': 26, 'faithful': False, 'group': '384.17956', 'group_order': 384, 'image': None, 'label': '384.17956.4b', 'multiplicity': 2, 'nt': [16, 189], 'qdim': 8, 'qvalues': [8, -8, 8, -8, -8, 8, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18116761
    {'cdim': 4, 'counter': 27, 'faithful': False, 'group': '384.17956', 'group_order': 384, 'image': None, 'label': '384.17956.4c', 'multiplicity': 2, 'nt': [16, 189], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 8, -8, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18116762
    {'cdim': 4, 'counter': 28, 'faithful': False, 'group': '384.17956', 'group_order': 384, 'image': None, 'label': '384.17956.4d', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18116766
    {'cdim': 8, 'counter': 31, 'faithful': False, 'group': '384.17956', 'group_order': 384, 'image': None, 'label': '384.17956.8a', 'multiplicity': 1, 'nt': [16, 422], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 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: 39209409
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 384, 'label': '384.17956.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 39209420
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1.a1', 'kernel_order': 192, 'label': '384.17956.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 39209431
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1.a1', 'kernel_order': 192, 'label': '384.17956.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 39209442
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 192, 'label': '384.17956.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 39209444
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 192, 'label': '384.17956.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 39209445
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 192, 'label': '384.17956.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 39209446
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 192, 'label': '384.17956.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 39209447
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 192, 'label': '384.17956.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 39209448
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 64, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 64, 'label': '384.17956.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 39209410
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 96, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.b1', 'kernel_order': 48, 'label': '384.17956.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39209411
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 96, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.a1', 'kernel_order': 48, 'label': '384.17956.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39209412
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 64, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1.a1', 'kernel_order': 32, 'label': '384.17956.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 39209413
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 64, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1.a1', 'kernel_order': 32, 'label': '384.17956.2e', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 39209414
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 64, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 32, 'label': '384.17956.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 39209415
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 16, 'counter': 15, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '96.192', 'image_order': 96, 'indicator': 0, 'kernel': '96.b1.b1', 'kernel_order': 4, 'label': '384.17956.2g1', 'nt': [48, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]]]}
  • id: 39209416
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 16, 'counter': 16, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '96.192', 'image_order': 96, 'indicator': 0, 'kernel': '96.b1.b1', 'kernel_order': 4, 'label': '384.17956.2g2', 'nt': [48, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 2]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]]]}
  • id: 39209417
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 16, 'counter': 17, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '96.192', 'image_order': 96, 'indicator': 0, 'kernel': '96.b1.b1', 'kernel_order': 4, 'label': '384.17956.2g3', 'nt': [48, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]]]}
  • id: 39209418
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 16, 'counter': 18, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '96.192', 'image_order': 96, 'indicator': 0, 'kernel': '96.b1.b1', 'kernel_order': 4, 'label': '384.17956.2g4', 'nt': [48, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 2]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]]]}
  • id: 39209419
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 16, 'counter': 19, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '96.192', 'image_order': 96, 'indicator': 0, 'kernel': '96.b1.a1', 'kernel_order': 4, 'label': '384.17956.2h1', 'nt': [48, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 2]], [[2, 2]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]]]}
  • id: 39209421
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 16, 'counter': 20, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '96.192', 'image_order': 96, 'indicator': 0, 'kernel': '96.b1.a1', 'kernel_order': 4, 'label': '384.17956.2h2', 'nt': [48, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 2]], [[-2, 2]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]]]}
  • id: 39209422
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 16, 'counter': 21, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '96.192', 'image_order': 96, 'indicator': 0, 'kernel': '96.b1.a1', 'kernel_order': 4, 'label': '384.17956.2h3', 'nt': [48, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 2]], [[2, 2]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]]]}
  • id: 39209423
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 16, 'counter': 22, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '96.192', 'image_order': 96, 'indicator': 0, 'kernel': '96.b1.a1', 'kernel_order': 4, 'label': '384.17956.2h4', 'nt': [48, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 2]], [[-2, 2]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]]]}
  • id: 39209424
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 16, 'counter': 23, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 16, 'label': '384.17956.3a', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39209425
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 16, 'counter': 24, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 16, 'label': '384.17956.3b', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39209426
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 16, 'counter': 25, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.c1.a1', 'kernel_order': 8, 'label': '384.17956.3c', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39209427
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 16, 'counter': 26, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.b1.a1', 'kernel_order': 8, 'label': '384.17956.3d', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39209428
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 16, 'counter': 27, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.c1.a1', 'kernel_order': 8, 'label': '384.17956.3e', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39209429
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 16, 'counter': 28, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.b1.a1', 'kernel_order': 8, 'label': '384.17956.3f', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39209430
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 16, 'counter': 29, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1.a1', 'kernel_order': 8, 'label': '384.17956.3g', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39209432
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 16, 'counter': 30, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1.a1', 'kernel_order': 8, 'label': '384.17956.3h', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39209433
    {'center': '24.b1.a1', 'center_index': 24, 'center_order': 16, 'counter': 31, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '48.38', 'image_order': 48, 'indicator': 1, 'kernel': '48.d1.a1', 'kernel_order': 8, 'label': '384.17956.4a', 'nt': [12, 28], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39209434
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 16, 'counter': 32, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '96.192', 'image_order': 96, 'indicator': 0, 'kernel': '96.b1.b1', 'kernel_order': 4, 'label': '384.17956.4b1', 'nt': [16, 189], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-4, 1]], [[4, 1]], [[-4, 1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 39209435
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 16, 'counter': 33, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '96.192', 'image_order': 96, 'indicator': 0, 'kernel': '96.b1.b1', 'kernel_order': 4, 'label': '384.17956.4b2', 'nt': [16, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[4, 1]], [[-4, 1]], [[4, 1]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 39209436
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 16, 'counter': 34, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '96.192', 'image_order': 96, 'indicator': 0, 'kernel': '96.b1.a1', 'kernel_order': 4, 'label': '384.17956.4c1', 'nt': [16, 189], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-4, 1]], [[4, 1]], [[4, 1]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]]]}
  • id: 39209437
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 16, 'counter': 35, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '96.192', 'image_order': 96, 'indicator': 0, 'kernel': '96.b1.a1', 'kernel_order': 4, 'label': '384.17956.4c2', 'nt': [16, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[4, 1]], [[-4, 1]], [[-4, 1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]]]}
  • id: 39209438
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 4, 'counter': 36, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '192.1485', 'image_order': 192, 'indicator': 0, 'kernel': '192.c1.a1', 'kernel_order': 2, 'label': '384.17956.4d1', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 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]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39209439
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 4, 'counter': 37, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '192.1485', 'image_order': 192, 'indicator': 0, 'kernel': '192.c1.a1', 'kernel_order': 2, 'label': '384.17956.4d2', 'nt': [48, 2], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 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]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39209440
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 4, 'counter': 38, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '192.1472', 'image_order': 192, 'indicator': 1, 'kernel': '192.b1.a1', 'kernel_order': 2, 'label': '384.17956.6a', 'nt': [12, 86], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 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]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39209441
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 4, 'counter': 39, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '192.1472', 'image_order': 192, 'indicator': 1, 'kernel': '192.b1.a1', 'kernel_order': 2, 'label': '384.17956.6b', 'nt': [12, 86], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[2, 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]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39209443
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 4, 'counter': 40, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '384.17956', 'group_counter': 17956, 'group_order': 384, 'image': None, 'image_isoclass': '192.1485', 'image_order': 192, 'indicator': 1, 'kernel': '192.c1.a1', 'kernel_order': 2, 'label': '384.17956.8a', 'nt': [16, 422], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[-8, 0]], [[-8, 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]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• 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: 269514894
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 384, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '384.17956.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '384.17956', 'subgroup_hash': 17956, 'subgroup_order': 384, 'subgroup_tex': '\\GL(2,3):D_4', 'supersolvable': False, 'sylow': 0}
  • id: 269515005
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 192, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.17956.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.1475', 'subgroup_hash': 1475, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 269515116
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 192, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.17956.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.1003', 'subgroup_hash': 1003, 'subgroup_order': 192, 'subgroup_tex': '\\SL(2,3):D_4', 'supersolvable': False, 'sylow': 0}
  • id: 269515133
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 192, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.17956.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.978', 'subgroup_hash': 978, 'subgroup_order': 192, 'subgroup_tex': 'C_2.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 269515144
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 192, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.17956.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.1480', 'subgroup_hash': 1480, 'subgroup_order': 192, 'subgroup_tex': '\\GL(2,3):C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 269515155
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 192, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.17956.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.951', 'subgroup_hash': 951, 'subgroup_order': 192, 'subgroup_tex': 'C_4\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 269515166
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 192, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.17956.2.f1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.986', 'subgroup_hash': 986, 'subgroup_order': 192, 'subgroup_tex': '\\SL(2,3):D_4', 'supersolvable': False, 'sylow': 0}
  • id: 269515177
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 192, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.17956.2.g1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.954', 'subgroup_hash': 954, 'subgroup_order': 192, 'subgroup_tex': 'Q_8.D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 269515188
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '384.17956.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2014', 'subgroup_hash': 2014, 'subgroup_order': 128, 'subgroup_tex': '\\SD_{16}:D_4', 'supersolvable': True, 'sylow': 2}
  • id: 269514895
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 96, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.17956.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.198', 'subgroup_hash': 198, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 269514906
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': True, 'centralizer_order': 16, 'characteristic': True, 'core_order': 96, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.17956.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 269514917
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 96, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.17956.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.200', 'subgroup_hash': 200, 'subgroup_order': 96, 'subgroup_tex': '\\SL(2,3):C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 269514928
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 96, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.17956.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 269514939
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 96, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.17956.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.69', 'subgroup_hash': 69, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 269514950
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 96, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.17956.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.66', 'subgroup_hash': 66, 'subgroup_order': 96, 'subgroup_tex': '\\SL(2,3):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 269514961
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 96, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.17956.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.188', 'subgroup_hash': 188, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 269514972
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.4.h1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 269514983
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.4.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 269514994
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.4.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 269515006
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.4.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.192', 'subgroup_hash': 192, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 269515017
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.4.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.192', 'subgroup_hash': 192, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 269515028
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.17956.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.229', 'subgroup_hash': 229, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515039
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.227', 'subgroup_hash': 227, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515050
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.128', 'subgroup_hash': 128, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515061
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 269515072
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.115', 'subgroup_hash': 115, 'subgroup_order': 64, 'subgroup_tex': 'C_8\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515083
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.6.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.146', 'subgroup_hash': 146, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515094
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.6.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.132', 'subgroup_hash': 132, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 269515105
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.6.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.133', 'subgroup_hash': 133, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515117
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.6.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.144', 'subgroup_hash': 144, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515124
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.6.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.253', 'subgroup_hash': 253, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 269515125
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.6.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.119', 'subgroup_hash': 119, 'subgroup_order': 64, 'subgroup_tex': 'C_4\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 269515126
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.6.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.146', 'subgroup_hash': 146, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515127
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.6.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.176', 'subgroup_hash': 176, 'subgroup_order': 64, 'subgroup_tex': 'C_8.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515128
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.6.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.130', 'subgroup_hash': 130, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515129
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.6.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.145', 'subgroup_hash': 145, 'subgroup_order': 64, 'subgroup_tex': 'Q_8.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515130
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 48, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.17956.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', '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': '48.32', 'subgroup_hash': 32, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 269515131
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': True, 'centralizer_order': 16, 'characteristic': False, 'core_order': 48, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.17956.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 269515132
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': True, 'centralizer_order': 16, 'characteristic': False, 'core_order': 48, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.17956.8.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 269515134
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 269515135
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 16, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 269515136
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515137
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 269515138
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 269515139
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515140
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515141
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.32', 'subgroup_hash': 32, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 269515142
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.8.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.33', 'subgroup_hash': 33, 'subgroup_order': 48, 'subgroup_tex': '\\SL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 269515143
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.8.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 269515145
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.8.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.28', 'subgroup_hash': 28, 'subgroup_order': 48, 'subgroup_tex': 'C_2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 269515146
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.17956.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 269515147
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.17956.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 269515148
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 53, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.17956.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 269515149
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 269515150
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515151
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515152
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515153
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515154
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 269515156
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 269515157
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 269515158
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515159
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515160
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 269515161
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 269515162
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515163
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515164
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 269515165
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 269515167
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515168
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 269515169
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 269515170
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 269515171
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 269515172
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 269515173
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515174
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 269515175
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 269515176
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515178
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 269515179
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 269515180
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 269515181
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 269515182
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.13', 'subgroup_hash': 13, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515183
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515184
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bj1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515185
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bk1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.41', 'subgroup_hash': 41, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 269515186
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bl1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515187
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bm1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.41', 'subgroup_hash': 41, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 269515189
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bn1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 269515190
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.bn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bn1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 269515191
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bo1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 269515192
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.bo1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bo1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 269515193
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bp1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 269515194
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.bp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bp1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 269515195
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bq1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 269515196
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.12.bq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bq1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 269515197
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 24, 'counter': 98, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.17956.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 269515198
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 269514896
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 269514897
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 269514898
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 269514899
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 269514900
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269514901
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.16.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269514902
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.16.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 269514903
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.16.i1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.i1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 269514904
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.16.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 269514905
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.16.i1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.i1.b2', 'outer_equivalence': False, 'perfect': False, '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 269514907
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.16.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 269514908
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.16.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 269514909
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.16.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 269514910
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.16.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 269514911
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.16.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 269514912
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.16.l1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.l1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 269514913
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.16.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 269514914
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.16.m1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.m1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 269514915
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': True, 'centralizer_order': 96, 'characteristic': True, 'core_order': 16, 'counter': 118, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.17956.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, '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': ['U0'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269514916
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 119, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.17956.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 269514918
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 269514919
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 269514920
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269514921
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269514922
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 269514923
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 269514924
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269514925
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269514926
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269514927
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 269514929
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 269514930
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269514931
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269514932
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269514933
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 269514934
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269514935
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269514936
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269514937
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 269514938
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 269514940
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269514941
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269514942
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 269514943
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269514944
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 269514945
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 269514946
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 269514947
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 269514948
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 269514949
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269514951
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 269514952
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.bg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 269514953
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 269514954
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 269514955
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bj1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 269514956
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.bj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bj1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 269514957
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bk1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 269514958
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bl1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 269514959
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.bl1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bl1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 269514960
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bm1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 269514962
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bn1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 269514963
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.bn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bn1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 269514964
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bo1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 269514965
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.bo1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bo1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 269514966
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bp1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 269514967
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.bp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bp1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 269514968
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bq1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 269514969
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.bq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bq1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 269514970
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.br1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 269514971
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.br1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.br1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 269514973
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bs1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 269514974
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bt1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 269514975
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.bt1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bt1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 269514976
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bu1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 269514977
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bv1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 269514978
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bw1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 269514979
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bx1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 269514980
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.bx1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bx1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 269514981
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.by1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 269514982
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bz1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 269514984
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ca1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 269514985
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.24.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cb1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 269514986
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 269514987
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 269514988
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.32.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 269514989
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 269514990
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.32.c1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.c1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 269514991
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.32.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 269514992
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.32.d1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.d1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 269514993
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.32.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 269514995
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.32.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 269514996
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.32.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 269514997
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.32.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 269514998
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 193, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.17956.32.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 269514999
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.32.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515000
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.32.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 269515001
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.32.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 269515002
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.32.k1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.k1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 269515003
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.32.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 269515004
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 199, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.17956.32.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 269515007
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.32.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515008
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.32.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 269515009
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.32.o1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.o1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 269515010
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.32.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 269515011
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.32.o1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.o1.b2', 'outer_equivalence': False, 'perfect': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 269515012
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.32.o1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.o1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 269515013
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.32.o1.c2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.o1.c2', 'outer_equivalence': False, 'perfect': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 269515014
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.32.o1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.o1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 269515015
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.32.o1.d2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.o1.d2', 'outer_equivalence': False, 'perfect': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 269515016
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': True, 'core_order': 8, 'counter': 209, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.17956.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 269515018
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': True, 'core_order': 8, 'counter': 210, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.17956.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.48', '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515019
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': True, 'core_order': 8, 'counter': 211, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.17956.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.48', '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515020
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 8, 'counter': 212, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.17956.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.38', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 269515021
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 269515022
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 269515023
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 269515024
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515025
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515026
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515027
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515029
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515030
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 269515031
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515032
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515033
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515034
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 269515035
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515036
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515037
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515038
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515040
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515041
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515042
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515043
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515044
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515045
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515046
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515047
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515048
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515049
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515051
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515052
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515053
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515054
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515055
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515056
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515057
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515058
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 247, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.17956.48.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515059
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 248, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.17956.48.bf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bf1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515060
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 249, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.17956.48.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515062
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 250, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.17956.48.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515063
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515064
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515065
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 253, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.17956.48.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515066
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515067
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515068
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.48.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, '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: 269515069
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 257, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.17956.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 269515070
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 258, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.17956.64.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 269515071
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 259, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.17956.64.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 269515073
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 260, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.17956.64.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 269515074
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 261, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.17956.64.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 269515075
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.64.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 269515076
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.64.e1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.e1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 269515077
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.64.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 269515078
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.64.e1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.e1.b2', 'outer_equivalence': False, 'perfect': False, '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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 269515079
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.64.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 269515080
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.64.f1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.f1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 269515081
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': True, 'central_factor': False, 'centralizer_order': 384, 'characteristic': True, 'core_order': 4, 'counter': 268, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.17956.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.226', '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': ['Z', 'Phi', 'S', 'U1'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 269515082
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 4, 'counter': 269, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.17956.96.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.192', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 192, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\GL(2,3):C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 269515084
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 4, 'counter': 270, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.17956.96.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.192', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 192, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\GL(2,3):C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 269515085
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.96.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 269515086
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.96.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 269515087
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.96.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 269515088
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 274, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.17956.96.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 269515089
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.96.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 269515090
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.96.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 269515091
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.96.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 269515092
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.96.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 269515093
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.96.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 269515095
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 280, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.17956.96.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 269515096
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 281, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.17956.96.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 269515097
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 282, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.17956.96.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 269515098
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 283, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.17956.96.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 269515099
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 284, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.17956.96.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 269515100
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.96.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 269515101
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.96.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 269515102
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.96.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 269515103
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.96.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 269515104
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 289, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.17956.96.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 269515106
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 290, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.17956.96.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 269515107
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.96.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 269515108
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.96.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 269515109
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.96.v1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.v1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 269515110
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.17956.96.v1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.v1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 269515111
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 295, 'cyclic': True, 'direct': None, 'hall': 3, 'label': '384.17956.128.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, '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: 269515112
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': True, 'central_factor': False, 'centralizer_order': 384, 'characteristic': True, 'core_order': 2, 'counter': 296, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '384.17956.192.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '192.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '192.1480', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1480, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\GL(2,3):C_2^2', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 269515113
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': True, 'central_factor': False, 'centralizer_order': 384, 'characteristic': True, 'core_order': 2, 'counter': 297, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '384.17956.192.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '192.b1.a1', 'outer_equivalence': False, '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': True, 'solvable': True, 'special_labels': ['D3', 'C6'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 269515114
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': True, 'central_factor': False, 'centralizer_order': 384, 'characteristic': True, 'core_order': 2, 'counter': 298, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '384.17956.192.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '192.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '192.1485', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1485, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\GL(2,3):C_2^2', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 269515115
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 299, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.17956.192.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, '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: 269515118
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 300, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.17956.192.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, '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: 269515119
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 301, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.17956.192.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, '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: 269515120
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 302, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.17956.192.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, '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: 269515121
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 303, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.17956.192.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, '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: 269515122
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 304, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.17956.192.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, '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: 269515123
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.17956', 'ambient_counter': 17956, 'ambient_order': 384, 'ambient_tex': '\\GL(2,3):D_4', 'central': True, 'central_factor': False, 'centralizer_order': 384, 'characteristic': True, 'core_order': 1, 'counter': 305, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '384.17956.384.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '384.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '384.17956', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 17956, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 384, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\GL(2,3):D_4', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'D4', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 269514894
    {'ambient': '384.17956', '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': '96.a1.a1', 'complements': ['384.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1', '3.a1.a1', '4.h1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3010, 4650, 3725, 5662, 2384, 4399, 6572, 4200], 'generators': [132667, 3333742, 6174490, 5042476, 4642820, 2122432, 4605946, 575726], 'label': '384.17956.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 269514895
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '96.226', 'aut_weyl_index': 16, 'centralizer': '48.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.j1.a1', '12.a1.a1', '16.b1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3352, 9305, 4006, 9178, 2156, 8327, 6968, 8316], 'generators': [2166683, 2122432, 4605946, 4642820, 3333742, 6174490], 'label': '384.17956.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 269514896
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 64, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '8.c1.a1', '8.f1.a1', '8.g1.a1'], 'contains': ['32.a1.a1', '32.c1.a1', '32.c1.a2', '32.f1.a1', '32.f1.b1', '32.k1.a1', '32.k1.a2', '48.e1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [677, -1, 1242, -1, 974, -1, 8389, -1], 'generators': [132667, 4642820, 2122432, 3333742], 'label': '384.17956.16.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.c1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269514897
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 64, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '8.c1.a1', '8.h1.a1', '8.i1.a1'], 'contains': ['32.a1.a1', '32.d1.a1', '32.d1.a2', '32.g1.a1', '32.l1.a1', '48.g1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [370, -1, 2184, -1, 436, -1, 8720, -1], 'generators': [5734448, 4642820, 2122432, 3333742], 'label': '384.17956.16.d1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.d1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 269514898
    {'ambient': '384.17956', 'aut_centralizer_order': 48, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 192, 'centralizer': '16.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '8.d1.a1', '8.f1.a1', '8.h1.a1'], 'contains': ['32.a1.a1', '32.m1.a1', '48.b1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [869, -1, 1824, -1, 1157, -1, 7875, -1], 'generators': [575726, 2122432, 3333742, 6632600], 'label': '384.17956.16.e1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.e1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269514899
    {'ambient': '384.17956', 'aut_centralizer_order': 48, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 192, 'centralizer': '16.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '8.d1.a1', '8.g1.a1', '8.i1.a1'], 'contains': ['32.a1.a1', '32.h1.a1', '48.c1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2213, -1, 2669, -1, 1865, -1, 7329, -1], 'generators': [5042476, 4642820, 3333742, 2122432], 'label': '384.17956.16.f1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.f1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269514900
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 64, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '8.e1.a1', '8.f1.a1', '8.i1.a1'], 'contains': ['32.a1.a1', '32.n1.a1', '48.k1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1387, -1, 1946, -1, 1676, -1, 7719, -1], 'generators': [4265251, 2122432, 6632600, 3333742], 'label': '384.17956.16.g1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.g1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 269514901
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 64, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '8.e1.a1', '8.g1.a1', '8.h1.a1'], 'contains': ['32.a1.a1', '32.i1.a1', '48.l1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4021, -1, 2905, -1, 2054, -1, 7484, -1], 'generators': [5042485, 4642820, 2122432, 3333742], 'label': '384.17956.16.h1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.h1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 269514902
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.14', 'aut_weyl_index': 64, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1'], 'contains': ['32.b1.a1', '32.c1.a1', '32.d1.a1', '32.o1.a1', '32.o1.b1', '48.m1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [67, -1, 1706, -1, 79, -1, 9162, -1], 'generators': [132667, 176903, 4642820, 3333742], 'label': '384.17956.16.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.i1.a1', 'projective_image': '192.1480', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 269514903
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.14', 'aut_weyl_index': 64, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1'], 'contains': ['32.b1.a1', '32.c1.a2', '32.d1.a2', '32.o1.a2', '32.o1.b2', '48.m1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [67, -1, 1358, -1, 79, -1, 8868, -1], 'generators': [2122417, 176903, 4642820, 3333742], 'label': '384.17956.16.i1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.i1.a2', 'projective_image': '192.1480', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.a2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 269514904
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.14', 'aut_weyl_index': 64, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1'], 'contains': ['32.b1.b1', '32.c1.a1', '32.d1.a2', '32.o1.c1', '32.o1.d1', '48.m1.b1'], 'core': '96.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [67, -1, 1011, -1, 79, -1, 9457, -1], 'generators': [132667, 2166683, 4642820, 3333742], 'label': '384.17956.16.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.i1.b1', 'projective_image': '192.1480', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 269514905
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.14', 'aut_weyl_index': 64, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1'], 'contains': ['32.b1.b1', '32.c1.a2', '32.d1.a1', '32.o1.c2', '32.o1.d2', '48.m1.b1'], 'core': '96.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [67, -1, 1126, -1, 79, -1, 9016, -1], 'generators': [2122417, 2166683, 4642820, 3333742], 'label': '384.17956.16.i1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.i1.b2', 'projective_image': '192.1480', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.b2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 269514906
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '96.226', 'aut_weyl_index': 16, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '12.s1.a1', '16.c1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3566, 1009, 4393, 823, 2408, 886, 6760, 818], 'generators': [132667, 2122432, 4605946, 4642820, 3333742, 6174490], 'label': '384.17956.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.b1', '8.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 269514907
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.14', 'aut_weyl_index': 64, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '8.c1.a1'], 'contains': ['32.e1.a1', '32.f1.a1', '32.g1.a1', '32.o1.a1', '32.o1.a2', '32.o1.c1', '32.o1.c2', '48.o1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1061, -1, 1473, -1, 615, -1, 9935, -1], 'generators': [132667, 2166683, 2122432, 3333742], 'label': '384.17956.16.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '16.j1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269514908
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.14', 'aut_weyl_index': 64, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.b1', '8.c1.a1'], 'contains': ['32.e1.a1', '32.f1.b1', '32.g1.a1', '32.o1.b1', '32.o1.b2', '32.o1.d1', '32.o1.d2', '48.o1.b1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1061, -1, 1590, -1, 615, -1, 9310, -1], 'generators': [4642835, 2166683, 2122432, 3333742], 'label': '384.17956.16.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '16.j1.b1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269514909
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.14', 'aut_weyl_index': 64, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '8.g1.a1'], 'contains': ['32.f1.a1', '32.h1.a1', '32.i1.a1', '48.t1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2988, -1, 3101, -1, 2227, -1, 7061, -1], 'generators': [132667, 5042476, 2122432, 3333742], 'label': '384.17956.16.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.g1.a1', 'old_label': '16.k1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269514910
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.14', 'aut_weyl_index': 64, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.b1', '8.g1.a1'], 'contains': ['32.f1.b1', '32.h1.a1', '32.i1.a1', '48.t1.b1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2988, -1, 3202, -1, 2227, -1, 7188, -1], 'generators': [4642835, 5042476, 2122432, 3333742], 'label': '384.17956.16.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.g1.a1', 'old_label': '16.k1.b1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269514911
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.14', 'aut_weyl_index': 64, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1'], 'contains': ['32.j1.a1', '32.k1.a1', '32.l1.a1', '32.o1.a1', '32.o1.b2', '32.o1.c1', '32.o1.d2', '48.bl1.a1'], 'core': '192.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [219, -1, 506, -1, 258, -1, 9604, -1], 'generators': [132667, 2166683, 6632600, 3333742], 'label': '384.17956.16.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '16.l1.a1', 'projective_image': '192.1485', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269514912
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.14', 'aut_weyl_index': 64, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1'], 'contains': ['32.j1.a1', '32.k1.a2', '32.l1.a1', '32.o1.a2', '32.o1.b1', '32.o1.c2', '32.o1.d1', '48.bl1.a1'], 'core': '192.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [219, -1, 648, -1, 258, -1, 9788, -1], 'generators': [2122417, 2166683, 6632600, 3333742], 'label': '384.17956.16.l1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '16.l1.a2', 'projective_image': '192.1485', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269514913
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.14', 'aut_weyl_index': 64, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1'], 'contains': ['32.k1.a1', '32.m1.a1', '32.n1.a1', '48.bm1.a1'], 'core': '192.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1240, -1, 103, -1, 1503, -1, 8015, -1], 'generators': [132667, 575726, 6632600, 3333742], 'label': '384.17956.16.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1.a1', 'old_label': '16.m1.a1', 'projective_image': '192.1485', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269514914
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.14', 'aut_weyl_index': 64, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1'], 'contains': ['32.k1.a2', '32.m1.a1', '32.n1.a1', '48.bm1.a1'], 'core': '192.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1240, -1, 204, -1, 1503, -1, 8143, -1], 'generators': [2122417, 575726, 6632600, 3333742], 'label': '384.17956.16.m1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1.a1', 'old_label': '16.m1.a2', 'projective_image': '192.1485', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269514915
    {'ambient': '384.17956', 'aut_centralizer_order': 96, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '16.14', 'aut_weyl_index': 96, 'centralizer': '4.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.e1.a1', '12.g1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.c1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2174, 8743, 2998, 8264, 2649, 7751, 6535, 7781], 'generators': [5042476, 575726], 'label': '384.17956.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['6.a1.a1'], 'normal_contains': ['48.a1.a1', '48.c1.a1', '48.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269514916
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '24.b1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 64, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1', '12.s1.a1', '12.be1.a1', '12.bl1.a1', '12.bm1.a1'], 'contains': ['48.d1.a1', '48.h1.a1', '48.bc1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7519, 6497, 7507, 6051, 6781, 6196, 2758, 6171], 'generators': [4642820, 6164698, 4605946], 'label': '384.17956.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1'], 'normal_contains': ['48.d1.a1', '96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 269514917
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '96.226', 'aut_weyl_index': 16, 'centralizer': '48.c1.a1', 'complements': ['96.v1.a1', '96.v1.c1', '96.v1.b1', '96.v1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'contains': ['8.a1.a1', '8.k1.a1', '12.b1.a1', '16.f1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3124, 4637, 3552, 7488, 3084, 6823, 5958, 4097], 'generators': [5042476, 2122432, 4605946, 4642820, 3333742, 6174490], 'label': '384.17956.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'normal_contains': ['8.a1.a1', '12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '96.226', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 269514918
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 96, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.d1.a1', '12.e1.a1', '12.f1.a1'], 'contains': ['48.a1.a1', '48.e1.a1', '48.g1.a1', '48.m1.a1', '48.m1.b1', '48.o1.a1', '48.o1.b1', '48.bl1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1838, -1, 2896, -1, 2537, -1, 7602, -1], 'generators': [132667, 2166683, 4642820, 2122432], 'label': '384.17956.24.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.c1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269514919
    {'ambient': '384.17956', 'aut_centralizer_order': 32, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.14', 'aut_weyl_index': 96, 'centralizer': '24.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.g1.a1', '12.h1.a1'], 'contains': ['48.a1.a1', '48.f1.a1', '48.i1.a1', '48.n1.a1', '48.n1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2796, -1, 3985, -1, 4219, -1, 6096, -1], 'generators': [1974553, 4142903, 2122432], 'label': '384.17956.24.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.d1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 269514920
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 192, 'centralizer': '12.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.f1.a1', '12.g1.a1', '12.h1.a1', '12.i1.a1', '12.j1.a1', '12.k1.a1'], 'contains': ['48.a1.a1', '48.h1.a1', '48.j1.a1', '48.p1.a1', '48.q1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5387, -1, 5849, -1, 5363, -1, 4414, -1], 'generators': [2166683, 4642820, 6164698], 'label': '384.17956.24.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.e1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269514921
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 96, 'centralizer': '48.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.d1.a1', '12.e1.a1', '12.i1.a1'], 'contains': ['48.a1.a1', '48.k1.a1', '48.l1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2917, -1, 3081, -1, 3217, -1, 6428, -1], 'generators': [4265251, 2166683], 'label': '384.17956.24.f1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.f1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 269514922
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 96, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.l1.a1', '12.n1.a1'], 'contains': ['48.e1.a1', '48.f1.a1', '48.l1.a1', '48.r1.a1', '48.r1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4204, -1, 4456, -1, 4611, -1, 5236, -1], 'generators': [132667, 2366842, 4642820], 'label': '384.17956.24.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.g1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 269514923
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 96, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.l1.a1', '12.m1.a1'], 'contains': ['48.e1.a1', '48.g1.a1', '48.j1.a1', '48.s1.a1', '48.s1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2663, -1, 4087, -1, 3955, -1, 5583, -1], 'generators': [132667, 4593842, 4642820], 'label': '384.17956.24.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.h1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 269514924
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 96, 'centralizer': '24.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.e1.a1', '12.l1.a1', '12.p1.a1'], 'contains': ['48.b1.a1', '48.e1.a1', '48.k1.a1', '48.bm1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2042, -1, 2751, -1, 2804, -1, 6769, -1], 'generators': [132667, 575726, 2122432], 'label': '384.17956.24.i1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.i1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269514925
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 96, 'centralizer': '24.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '12.e1.a1', '12.m1.a1', '12.n1.a1'], 'contains': ['48.c1.a1', '48.e1.a1', '48.l1.a1', '48.t1.a1', '48.t1.b1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4481, -1, 4793, -1, 3658, -1, 5722, -1], 'generators': [132667, 5042476, 4642820], 'label': '384.17956.24.j1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.j1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269514926
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 96, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.m1.a1', '12.p1.a1'], 'contains': ['48.e1.a1', '48.i1.a1', '48.k1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2393, -1, 3391, -1, 3503, -1, 5978, -1], 'generators': [132667, 4532591], 'label': '384.17956.24.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.k1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 269514927
    {'ambient': '384.17956', 'aut_centralizer_order': 32, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.n1.a1', '12.o1.a1', '12.p1.a1', '12.q1.a1', '12.r1.a1', '12.s1.a1'], 'contains': ['48.e1.a1', '48.h1.a1', '48.u1.a1', '48.u1.b1', '48.v1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5530, -1, 5740, -1, 7201, -1, 4058, -1], 'generators': [132667, 4642820, 4605946], 'label': '384.17956.24.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.l1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269514928
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '96.226', 'aut_weyl_index': 16, 'centralizer': '48.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.l1.a1', '12.be1.a1', '16.d1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2831, 6240, 3842, 2334, 1860, 5384, 7176, 5546], 'generators': [5734448, 2122432, 4605946, 4642820, 3333742, 2981098], 'label': '384.17956.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 269514929
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.l1.a1', '12.t1.a1'], 'contains': ['48.f1.a1', '48.g1.a1', '48.k1.a1', '48.bn1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3298, -1, 3484, -1, 3360, -1, 5860, -1], 'generators': [4265251, 1873267, 2122432], 'label': '384.17956.24.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.m1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 269514930
    {'ambient': '384.17956', 'aut_centralizer_order': 32, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.14', 'aut_weyl_index': 96, 'centralizer': '24.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.l1.a1', '12.y1.a1'], 'contains': ['48.b1.a1', '48.f1.a1', '48.j1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3488, -1, 4364, -1, 4468, -1, 5030, -1], 'generators': [1974553, 575726], 'label': '384.17956.24.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.n1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 269514931
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 192, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.g1.a1', '12.n1.a1', '12.t1.a1', '12.u1.a1', '12.v1.a1', '12.w1.a1'], 'contains': ['48.c1.a1', '48.f1.a1', '48.h1.a1', '48.w1.a1', '48.x1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5672, -1, 5631, -1, 7526, -1, 3790, -1], 'generators': [5042476, 4642820, 6164698], 'label': '384.17956.24.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.o1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269514932
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '12.u1.a1', '12.y1.a1'], 'contains': ['48.f1.a1', '48.i1.a1', '48.j1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4083, -1, 4964, -1, 5613, -1, 4541, -1], 'generators': [2366842, 4142903], 'label': '384.17956.24.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.p1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 269514933
    {'ambient': '384.17956', 'aut_centralizer_order': 32, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.h1.a1', '12.o1.a1', '12.x1.a1', '12.y1.a1', '12.z1.a1', '12.ba1.a1'], 'contains': ['48.f1.a1', '48.h1.a1', '48.y1.a1', '48.z1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7157, -1, 6065, -1, 8798, -1, 2629, -1], 'generators': [2366842, 4642820, 6164698], 'label': '384.17956.24.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.q1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.q1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 269514934
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 96, 'centralizer': '48.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.e1.a1', '12.l1.a1', '12.bb1.a1'], 'contains': ['48.b1.a1', '48.g1.a1', '48.l1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2284, -1, 3308, -1, 2958, -1, 6641, -1], 'generators': [5042485, 575726], 'label': '384.17956.24.r1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.r1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 269514935
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 96, 'centralizer': '48.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '12.e1.a1', '12.m1.a1', '12.t1.a1'], 'contains': ['48.c1.a1', '48.g1.a1', '48.k1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3065, -1, 3577, -1, 3088, -1, 6321, -1], 'generators': [4265251, 5042476], 'label': '384.17956.24.s1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.s1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.s1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 269514936
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.m1.a1', '12.bb1.a1'], 'contains': ['48.g1.a1', '48.i1.a1', '48.l1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2541, -1, 3872, -1, 3812, -1, 6215, -1], 'generators': [5042485, 4532591], 'label': '384.17956.24.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.t1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.t1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 269514937
    {'ambient': '384.17956', 'aut_centralizer_order': 32, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.t1.a1', '12.x1.a1', '12.bb1.a1', '12.bc1.a1', '12.bd1.a1', '12.be1.a1'], 'contains': ['48.g1.a1', '48.h1.a1', '48.ba1.a1', '48.bb1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4846, -1, 5135, -1, 5756, -1, 4747, -1], 'generators': [5734448, 4642820, 6174490], 'label': '384.17956.24.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.u1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.u1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 269514938
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '24.v1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 192, 'centralizer': '12.bf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.g1.a1', '12.p1.a1', '12.y1.a1', '12.bb1.a1', '12.bf1.a1', '12.bg1.a1'], 'contains': ['48.b1.a1', '48.h1.a1', '48.i1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3987, -1, 4882, -1, 5501, -1, 4938, -1], 'generators': [575726, 6164698], 'label': '384.17956.24.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.v1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.v1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269514939
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '96.226', 'aut_weyl_index': 16, 'centralizer': '48.b1.a1', 'complements': ['96.v1.a1', '96.v1.c1', '96.v1.b1', '96.v1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '12.c1.a1', '16.e1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2475, 7737, 3073, 5036, 1533, 4040, 6562, 6899], 'generators': [575726, 2122432, 4605946, 3333742, 6632600, 6174490], 'label': '384.17956.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1', '12.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '96.226', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 269514940
    {'ambient': '384.17956', 'aut_centralizer_order': 32, 'aut_label': '24.w1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.14', 'aut_weyl_index': 96, 'centralizer': '24.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.m1.a1', '12.u1.a1'], 'contains': ['48.c1.a1', '48.i1.a1', '48.j1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3680, -1, 4541, -1, 4350, -1, 5128, -1], 'generators': [5042476, 4142903], 'label': '384.17956.24.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.w1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.w1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 269514941
    {'ambient': '384.17956', 'aut_centralizer_order': 32, 'aut_label': '24.x1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.h1.a1', '12.q1.a1', '12.u1.a1', '12.bc1.a1', '12.bh1.a1', '12.bi1.a1'], 'contains': ['48.h1.a1', '48.i1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5042, -1, 5221, -1, 6912, -1, 4856, -1], 'generators': [4532591, 6164698], 'label': '384.17956.24.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.x1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.x1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 269514942
    {'ambient': '384.17956', 'aut_centralizer_order': 32, 'aut_label': '24.y1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.r1.a1', '12.u1.a1', '12.y1.a1', '12.bd1.a1', '12.bj1.a1', '12.bk1.a1'], 'contains': ['48.h1.a1', '48.j1.a1', '48.bd1.a1', '48.bi1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6422, -1, 7195, -1, 7044, -1, 3111, -1], 'generators': [4593842, 4642820, 6164698], 'label': '384.17956.24.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.y1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.y1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 269514943
    {'ambient': '384.17956', 'aut_centralizer_order': 32, 'aut_label': '24.z1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.p1.a1', '12.t1.a1', '12.z1.a1', '12.bh1.a1', '12.bj1.a1', '12.bl1.a1'], 'contains': ['48.h1.a1', '48.k1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5132, -1, 5049, -1, 6492, -1, 4638, -1], 'generators': [4265251, 6174490], 'label': '384.17956.24.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.z1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.z1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 269514944
    {'ambient': '384.17956', 'aut_centralizer_order': 32, 'aut_label': '24.ba1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.n1.a1', '12.ba1.a1', '12.bb1.a1', '12.bi1.a1', '12.bk1.a1', '12.bm1.a1'], 'contains': ['48.h1.a1', '48.l1.a1', '48.be1.a1', '48.bj1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8795, -1, 6172, -1, 7963, -1, 3651, -1], 'generators': [5042485, 4642820, 4605946], 'label': '384.17956.24.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.ba1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 269514945
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '24.bb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 192, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.s1.a1', '12.v1.a1', '12.ba1.a1', '12.bd1.a1', '12.bf1.a1', '12.bh1.a1'], 'contains': ['48.h1.a1', '48.bf1.a1', '48.bf1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8530, -1, 8672, -1, 7806, -1, 1476, -1], 'generators': [6166711, 4642820], 'label': '384.17956.24.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bb1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269514946
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '24.bc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 192, 'centralizer': '12.bf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.q1.a1', '12.w1.a1', '12.x1.a1', '12.bf1.a1', '12.bk1.a1', '12.bl1.a1'], 'contains': ['48.h1.a1', '48.bk1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7386, -1, 6274, -1, 8955, -1, 3521, -1], 'generators': [697885, 6174490], 'label': '384.17956.24.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bc1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269514947
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '24.bd1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 192, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.o1.a1', '12.v1.a1', '12.bc1.a1', '12.bg1.a1', '12.bj1.a1', '12.bm1.a1'], 'contains': ['48.h1.a1', '48.bg1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8661, -1, 7400, -1, 8222, -1, 2500, -1], 'generators': [1974700, 4642820], 'label': '384.17956.24.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bd1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269514948
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '24.be1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 192, 'centralizer': '12.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.r1.a1', '12.w1.a1', '12.z1.a1', '12.be1.a1', '12.bg1.a1', '12.bi1.a1'], 'contains': ['48.h1.a1', '48.bh1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8264, -1, 7715, -1, 7358, -1, 3240, -1], 'generators': [5000690, 4642820], 'label': '384.17956.24.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.be1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.be1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269514949
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '24.bf1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.l1.a1', '12.m1.a1'], 'contains': ['48.j1.a1', '48.k1.a1', '48.l1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3587, -1, 4187, -1, 4087, -1, 5474, -1], 'generators': [4265251, 3025298], 'label': '384.17956.24.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.bf1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 269514950
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '96.226', 'aut_weyl_index': 16, 'centralizer': '48.b1.a1', 'complements': ['96.v1.a1', '96.v1.c1', '96.v1.b1', '96.v1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'contains': ['8.a1.a1', '12.bl1.a1', '16.g1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2671, 2178, 3363, 6209, 2595, 2997, 6408, 1874], 'generators': [4265251, 2122432, 4605946, 6632600, 3333742, 2981098], 'label': '384.17956.4.f1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '96.226', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 269514951
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '24.bg1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.bn1.a1', '12.bo1.a1'], 'contains': ['48.o1.a1', '48.p1.a1', '48.s1.a1', '48.u1.a1', '48.ba1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5244, -1, 6727, -1, 4768, -1, 3928, -1], 'generators': [132667, 2166683, 4605946], 'label': '384.17956.24.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.bg1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269514952
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '24.bg1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.bn1.b1', '12.bo1.b1'], 'contains': ['48.o1.b1', '48.p1.a1', '48.s1.b1', '48.u1.b1', '48.ba1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5244, -1, 7093, -1, 4768, -1, 4187, -1], 'generators': [4642835, 2166683, 4605946], 'label': '384.17956.24.bg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.bg1.b1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bg1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269514953
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '24.bh1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1'], 'contains': ['48.o1.a1', '48.o1.b1', '48.q1.a1', '48.s1.a1', '48.s1.b1', '48.v1.a1', '48.bb1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3800, -1, 4627, -1, 4925, -1, 5366, -1], 'generators': [132667, 2166683, 2350862], 'label': '384.17956.24.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1.a1', 'old_label': '24.bh1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269514954
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '24.bi1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.bn1.a1', '12.bn1.b1'], 'contains': ['48.p1.a1', '48.q1.a1', '48.bc1.a1', '48.bd1.a1', '48.bi1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6142, -1, 8846, -1, 6624, -1, 2370, -1], 'generators': [2166683, 2350862, 6164698], 'label': '384.17956.24.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.bi1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269514955
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '24.bj1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 192, 'centralizer': '12.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.bn1.b1', '12.bo1.a1'], 'contains': ['48.p1.a1', '48.bf1.a1', '48.bh1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8397, -1, 9803, -1, 6025, -1, 1882, -1], 'generators': [6166711, 2166683], 'label': '384.17956.24.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.bj1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269514956
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '24.bj1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 192, 'centralizer': '12.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.bn1.a1', '12.bo1.b1'], 'contains': ['48.p1.a1', '48.bf1.b1', '48.bh1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8397, -1, 9902, -1, 6025, -1, 1347, -1], 'generators': [3911627, 2166683], 'label': '384.17956.24.bj1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.bj1.b1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bj1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269514957
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '24.bk1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 32, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '12.a1.a1', '12.bo1.a1', '12.bo1.b1'], 'contains': ['48.d1.a1', '48.p1.a1', '48.bd1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6275, -1, 8947, -1, 5195, -1, 2888, -1], 'generators': [2166683, 6164698, 4605946], 'label': '384.17956.24.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.bk1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 269514958
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '24.bl1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '12.bp1.a1', '12.bq1.a1'], 'contains': ['48.r1.a1', '48.t1.a1', '48.u1.a1', '48.w1.a1', '48.be1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6886, -1, 6359, -1, 8352, -1, 1990, -1], 'generators': [132667, 5042476, 4605946], 'label': '384.17956.24.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '24.bl1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269514959
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '24.bl1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '12.bp1.b1', '12.bq1.b1'], 'contains': ['48.r1.b1', '48.t1.b1', '48.u1.b1', '48.w1.a1', '48.be1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6886, -1, 6615, -1, 8352, -1, 2077, -1], 'generators': [4642835, 5042476, 4605946], 'label': '384.17956.24.bl1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '24.bl1.b1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bl1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269514960
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '24.bm1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1'], 'contains': ['48.r1.a1', '48.r1.b1', '48.t1.a1', '48.t1.b1', '48.v1.a1', '48.x1.a1', '48.bj1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5794, -1, 5515, -1, 8458, -1, 4296, -1], 'generators': [132667, 5042476, 2350862], 'label': '384.17956.24.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1.a1', 'old_label': '24.bm1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269514961
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '4.g1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '96.226', 'aut_weyl_index': 16, 'centralizer': '48.c1.a1', 'complements': ['96.v1.a1', '96.v1.c1', '96.v1.b1', '96.v1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.m1.a1', '12.bm1.a1', '16.h1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4156, 3189, 3703, 3685, 3317, 2089, 6274, 2789], 'generators': [5042485, 2122432, 4605946, 4642820, 3333742, 6174490], 'label': '384.17956.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '96.226', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 269514962
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '24.bn1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '12.bp1.a1', '12.bq1.a1'], 'contains': ['48.u1.a1', '48.y1.a1', '48.bg1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9352, -1, 7585, -1, 9229, -1, 246, -1], 'generators': [132667, 1974553], 'label': '384.17956.24.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '24.bn1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269514963
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '24.bn1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '12.bp1.b1', '12.bq1.b1'], 'contains': ['48.u1.b1', '48.y1.a1', '48.bg1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9352, -1, 7638, -1, 9229, -1, 314, -1], 'generators': [4642835, 1974553], 'label': '384.17956.24.bn1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '24.bn1.b1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bn1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269514964
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '24.bo1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1.a1', '12.bn1.a1', '12.bp1.a1'], 'contains': ['48.u1.a1', '48.bc1.a1', '48.bf1.b1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8910, -1, 9108, -1, 7673, -1, 874, -1], 'generators': [132667, 3909614], 'label': '384.17956.24.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bo1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269514965
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '24.bo1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1.a1', '12.bn1.b1', '12.bp1.b1'], 'contains': ['48.u1.b1', '48.bc1.a1', '48.bf1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8910, -1, 9036, -1, 7673, -1, 967, -1], 'generators': [6166711, 3909614], 'label': '384.17956.24.bo1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bo1.b1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bo1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269514966
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '24.bp1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1.a1', '12.bn1.a1', '12.bo1.a1'], 'contains': ['48.u1.a1', '48.bd1.a1', '48.bh1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7272, -1, 9570, -1, 6271, -1, 2166, -1], 'generators': [132667, 3035090], 'label': '384.17956.24.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.bp1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269514967
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '24.bp1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1.a1', '12.bn1.b1', '12.bo1.b1'], 'contains': ['48.u1.b1', '48.bd1.a1', '48.bh1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7272, -1, 9642, -1, 6271, -1, 1772, -1], 'generators': [4642835, 3035090], 'label': '384.17956.24.bp1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.bp1.b1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bp1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269514968
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '24.bq1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.s1.a1', '12.bo1.a1', '12.bq1.a1'], 'contains': ['48.d1.a1', '48.u1.a1', '48.bf1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9005, -1, 8085, -1, 6383, -1, 1586, -1], 'generators': [132667, 6164698], 'label': '384.17956.24.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bq1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269514969
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '24.bq1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '12.s1.a1', '12.bo1.b1', '12.bq1.b1'], 'contains': ['48.d1.a1', '48.u1.b1', '48.bf1.b1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9005, -1, 8758, -1, 6383, -1, 1144, -1], 'generators': [4642835, 6164698], 'label': '384.17956.24.bq1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bq1.b1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bq1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269514970
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '24.br1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 192, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1.a1', '12.bp1.b1', '12.bq1.a1'], 'contains': ['48.w1.a1', '48.bf1.a1', '48.bg1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9495, -1, 8405, -1, 9111, -1, 505, -1], 'generators': [6166711, 5042476], 'label': '384.17956.24.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '24.br1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.br1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269514971
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '24.br1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 192, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1.a1', '12.bp1.a1', '12.bq1.b1'], 'contains': ['48.w1.a1', '48.bf1.b1', '48.bg1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9495, -1, 8570, -1, 9111, -1, 148, -1], 'generators': [3911627, 5042476], 'label': '384.17956.24.br1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '24.br1.b1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.br1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269514972
    {'ambient': '384.17956', 'aut_centralizer_order': 1, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '384.20168', 'aut_weyl_index': 4, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.c1.a1', '8.d1.a1', '8.e1.a1', '8.f1.a1', '8.g1.a1', '8.h1.a1', '8.i1.a1', '12.e1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1321, -1, 2168, -1, 1306, -1, 7867, -1], 'generators': [132667, 3333742, 2122432, 5042476, 575726, 4642820], 'label': '384.17956.4.h1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '4.h1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 269514973
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '24.bs1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.x1.a1'], 'contains': ['48.z1.a1', '48.bb1.a1', '48.bk1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5956, -1, 5935, -1, 9529, -1, 3423, -1], 'generators': [4653262, 1974553], 'label': '384.17956.24.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1.a1', 'old_label': '24.bs1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269514974
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '24.bt1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ba1.a1', '12.bp1.b1', '12.bq1.a1'], 'contains': ['48.y1.a1', '48.be1.a1', '48.bf1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9608, -1, 7802, -1, 9327, -1, 395, -1], 'generators': [6166711, 1974553], 'label': '384.17956.24.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '24.bt1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269514975
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '24.bt1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ba1.a1', '12.bp1.a1', '12.bq1.b1'], 'contains': ['48.y1.a1', '48.be1.a1', '48.bf1.b1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9608, -1, 8013, -1, 9327, -1, 38, -1], 'generators': [3911627, 1974553], 'label': '384.17956.24.bt1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '24.bt1.b1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bt1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269514976
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '24.bu1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.bp1.a1', '12.bp1.b1'], 'contains': ['48.w1.a1', '48.x1.a1', '48.y1.a1', '48.z1.a1', '48.bc1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7009, -1, 6966, -1, 9435, -1, 785, -1], 'generators': [5042476, 2350862, 6164698], 'label': '384.17956.24.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '24.bu1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269514977
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '24.bv1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 32, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '12.b1.a1', '12.bq1.a1', '12.bq1.b1'], 'contains': ['48.d1.a1', '48.w1.a1', '48.y1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7726, -1, 6855, -1, 8666, -1, 698, -1], 'generators': [5042476, 6164698, 4605946], 'label': '384.17956.24.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '24.bv1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 269514978
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '24.bw1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.be1.a1', '12.bn1.a1', '12.bn1.b1'], 'contains': ['48.ba1.a1', '48.bc1.a1', '48.bh1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7826, -1, 9715, -1, 5891, -1, 2259, -1], 'generators': [5734448, 2350862], 'label': '384.17956.24.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.bw1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269514979
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '24.bx1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bd1.a1', '12.bn1.b1', '12.bo1.a1'], 'contains': ['48.ba1.a1', '48.bd1.a1', '48.bf1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6682, -1, 9497, -1, 6159, -1, 1679, -1], 'generators': [6166711, 3035090], 'label': '384.17956.24.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.bx1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269514980
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '24.bx1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bd1.a1', '12.bn1.a1', '12.bo1.b1'], 'contains': ['48.ba1.a1', '48.bd1.a1', '48.bf1.b1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6682, -1, 9424, -1, 6159, -1, 1237, -1], 'generators': [3911627, 3035090], 'label': '384.17956.24.bx1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.bx1.b1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bx1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269514981
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '24.by1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '12.be1.a1', '12.bo1.a1', '12.bo1.b1'], 'contains': ['48.d1.a1', '48.ba1.a1', '48.bh1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8012, -1, 9351, -1, 5060, -1, 2999, -1], 'generators': [5734448, 4605946], 'label': '384.17956.24.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.by1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.by1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269514982
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '24.bz1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bm1.a1', '12.bp1.a1', '12.bp1.b1'], 'contains': ['48.bc1.a1', '48.be1.a1', '48.bg1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9787, -1, 8154, -1, 8562, -1, 612, -1], 'generators': [5042485, 3909614], 'label': '384.17956.24.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '24.bz1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269514983
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.226', 'aut_weyl_index': 16, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.a1', '8.j1.a1', '8.l1.a1', '12.bo1.a1', '16.j1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3807, -1, 4550, -1, 2827, -1, 7573, -1], 'generators': [132667, 2122432, 4605946, 2166683, 3333742, 6174490], 'label': '384.17956.4.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.i1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 269514984
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '24.ca1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '12.bm1.a1', '12.bq1.a1', '12.bq1.b1'], 'contains': ['48.d1.a1', '48.be1.a1', '48.bg1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9701, -1, 7942, -1, 8093, -1, 1056, -1], 'generators': [5042485, 6164698], 'label': '384.17956.24.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '24.ca1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269514985
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '24.cb1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bk1.a1'], 'contains': ['48.bi1.a1', '48.bj1.a1', '48.bk1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7629, -1, 7279, -1, 9622, -1, 3347, -1], 'generators': [4653262, 3035090], 'label': '384.17956.24.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1.a1', 'old_label': '24.cb1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269514986
    {'ambient': '384.17956', 'aut_centralizer_order': 192, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 768, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '16.b1.a1', '16.c1.a1', '16.d1.a1', '16.e1.a1', '16.f1.a1', '16.g1.a1', '16.h1.a1'], 'contains': ['64.a1.a1', '64.b1.a1', '64.c1.a1', '96.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1128, -1, 2516, -1, 1509, -1, 7718, -1], 'generators': [4642820, 2122432, 3333742], 'label': '384.17956.32.a1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.a1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269514987
    {'ambient': '384.17956', 'aut_centralizer_order': 48, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.i1.a1', '16.i1.a2'], 'contains': ['64.a1.a1', '64.d1.a1', '96.b1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [473, -1, 1924, -1, 795, -1, 8419, -1], 'generators': [176903, 4642820, 3333742], 'label': '384.17956.32.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.b1.a1', 'projective_image': '192.1480', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269514988
    {'ambient': '384.17956', 'aut_centralizer_order': 48, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.i1.b1', '16.i1.b2'], 'contains': ['64.a1.a1', '64.d1.b1', '96.b1.b1'], 'core': '96.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [473, -1, 1317, -1, 795, -1, 8676, -1], 'generators': [2166683, 4642820, 3333742], 'label': '384.17956.32.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.b1.b1', 'projective_image': '192.1480', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269514989
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 128, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.i1.a1', '16.i1.b1'], 'contains': ['64.a1.a1', '64.e1.a1', '64.e1.b1', '96.c1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [574, -1, 1096, -1, 1069, -1, 8841, -1], 'generators': [132667, 4642820, 3333742], 'label': '384.17956.32.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.c1.a1', 'projective_image': '192.1480', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269514990
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 128, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.i1.a2', '16.i1.b2'], 'contains': ['64.a1.a1', '64.e1.a2', '64.e1.b2', '96.c1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [574, -1, 1187, -1, 1069, -1, 8321, -1], 'generators': [2122417, 4642820, 3333742], 'label': '384.17956.32.c1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.c1.a2', 'projective_image': '192.1480', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269514991
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 128, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.i1.a1', '16.i1.b2'], 'contains': ['64.a1.a1', '64.f1.a1', '96.e1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [301, -1, 1711, -1, 511, -1, 8773, -1], 'generators': [3376889, 4642820, 3333742], 'label': '384.17956.32.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.d1.a1', 'projective_image': '192.1480', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 269514992
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 128, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.i1.a2', '16.i1.b1'], 'contains': ['64.a1.a1', '64.f1.a2', '96.e1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [301, -1, 1635, -1, 511, -1, 8909, -1], 'generators': [5734448, 4642820, 3333742], 'label': '384.17956.32.d1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.d1.a2', 'projective_image': '192.1480', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.a2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 269514993
    {'ambient': '384.17956', 'aut_centralizer_order': 48, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '16.b1.a1', '16.j1.a1', '16.j1.b1'], 'contains': ['64.b1.a1', '64.d1.a1', '64.d1.b1', '96.g1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1346, -1, 2078, -1, 1353, -1, 8547, -1], 'generators': [2166683, 2122432, 3333742], 'label': '384.17956.32.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '32.e1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269514994
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.226', 'aut_weyl_index': 16, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.b1', '8.j1.a1', '8.l1.a1', '12.bo1.b1', '16.j1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3807, -1, 4705, -1, 2827, -1, 7374, -1], 'generators': [4642835, 2122432, 4605946, 2166683, 3333742, 6174490], 'label': '384.17956.4.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.i1.b1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 269514995
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 128, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '16.c1.a1', '16.j1.a1', '16.k1.a1'], 'contains': ['64.b1.a1', '64.e1.a1', '64.e1.a2', '96.h1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1574, -1, 1764, -1, 1628, -1, 8253, -1], 'generators': [132667, 2122432, 3333742], 'label': '384.17956.32.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.f1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269514996
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 128, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '16.c1.a1', '16.j1.b1', '16.k1.b1'], 'contains': ['64.b1.a1', '64.e1.b1', '64.e1.b2', '96.h1.b1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1574, -1, 1847, -1, 1628, -1, 7894, -1], 'generators': [4642835, 2122432, 3333742], 'label': '384.17956.32.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.f1.b1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.f1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269514997
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '32.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 128, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '16.d1.a1', '16.j1.a1', '16.j1.b1'], 'contains': ['64.b1.a1', '64.f1.a1', '64.f1.a2', '96.j1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [990, -1, 2001, -1, 1234, -1, 9310, -1], 'generators': [5734448, 2122432, 3333742], 'label': '384.17956.32.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '32.g1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269514998
    {'ambient': '384.17956', 'aut_centralizer_order': 48, 'aut_label': '32.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '16.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '16.f1.a1', '16.k1.a1', '16.k1.b1'], 'contains': ['64.b1.a1', '96.k1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3057, -1, 3185, -1, 2629, -1, 7036, -1], 'generators': [5042476, 3333742, 2122432], 'label': '384.17956.32.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.g1.a1', 'old_label': '32.h1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269514999
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 128, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '16.h1.a1', '16.k1.a1', '16.k1.b1'], 'contains': ['64.b1.a1', '96.o1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4290, -1, 3647, -1, 2732, -1, 7121, -1], 'generators': [5042485, 2122432, 3333742], 'label': '384.17956.32.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.g1.a1', 'old_label': '32.i1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269515000
    {'ambient': '384.17956', 'aut_centralizer_order': 48, 'aut_label': '32.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.l1.a1', '16.l1.a2'], 'contains': ['64.c1.a1', '64.d1.a1', '64.d1.b1', '96.p1.a1'], 'core': '192.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [782, -1, 447, -1, 950, -1, 9008, -1], 'generators': [2166683, 6632600, 3333742], 'label': '384.17956.32.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '32.j1.a1', 'projective_image': '192.1485', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515001
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '32.k1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 128, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.l1.a1', '16.m1.a1'], 'contains': ['64.c1.a1', '64.e1.a1', '64.e1.b2', '96.q1.a1'], 'core': '192.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [920, -1, 254, -1, 1152, -1, 8117, -1], 'generators': [132667, 6632600, 3333742], 'label': '384.17956.32.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.k1.a1', 'projective_image': '192.1485', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269515002
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '32.k1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 128, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.l1.a2', '16.m1.a2'], 'contains': ['64.c1.a1', '64.e1.a2', '64.e1.b1', '96.q1.a1'], 'core': '192.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [920, -1, 307, -1, 1152, -1, 8185, -1], 'generators': [2122417, 6632600, 3333742], 'label': '384.17956.32.k1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.k1.a2', 'projective_image': '192.1485', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.k1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269515003
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '32.l1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 128, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.l1.a1', '16.l1.a2'], 'contains': ['64.c1.a1', '64.f1.a1', '64.f1.a2', '96.s1.a1'], 'core': '192.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [681, -1, 703, -1, 675, -1, 9378, -1], 'generators': [5734448, 6632600, 3333742], 'label': '384.17956.32.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '32.l1.a1', 'projective_image': '192.1485', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.l1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269515004
    {'ambient': '384.17956', 'aut_centralizer_order': 48, 'aut_label': '32.m1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '16.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '16.m1.a1', '16.m1.a2'], 'contains': ['64.c1.a1', '96.t1.a1'], 'core': '192.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1237, -1, 98, -1, 1720, -1, 7612, -1], 'generators': [575726, 3333742, 6632600], 'label': '384.17956.32.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1.a1', 'old_label': '32.m1.a1', 'projective_image': '192.1485', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515005
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '384.20162', 'aut_weyl_index': 4, 'centralizer': '48.a1.a1', 'complements': ['192.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.d1.a1', '4.i1.a1', '4.i1.b1', '6.d1.a1', '8.c1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3248, 6119, 4374, 765, 2384, 7099, 7174, 7144], 'generators': [132667, 4605946, 6174490, 2166683, 2122432, 4642820, 3333742], 'label': '384.17956.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '96.226', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 269515006
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.226', 'aut_weyl_index': 16, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.b1.a1', '8.k1.a1', '8.m1.a1', '12.bq1.a1', '16.k1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3974, -1, 4168, -1, 3487, -1, 5782, -1], 'generators': [132667, 2122432, 4605946, 5042476, 3333742, 6174490], 'label': '384.17956.4.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.j1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 269515007
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '32.n1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 128, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '16.m1.a1', '16.m1.a2'], 'contains': ['64.c1.a1', '96.u1.a1'], 'core': '192.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1494, -1, 165, -1, 1823, -1, 7527, -1], 'generators': [4265251, 6632600, 3333742], 'label': '384.17956.32.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1.a1', 'old_label': '32.n1.a1', 'projective_image': '192.1485', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.n1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269515008
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '32.o1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '6.1', 'aut_weyl_index': 256, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.j1.a1', '16.l1.a1'], 'contains': ['64.d1.a1', '64.e1.a1', '64.f1.a1', '96.v1.a1'], 'core': '384.a1.a1', 'coset_action_label': '32T9401', 'count': 8, 'diagramx': [371, -1, 1448, -1, 593, -1, 9514, -1], 'generators': [132667, 176903, 3333742], 'label': '384.17956.32.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '32.o1.a1', 'projective_image': '384.17956', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.o1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269515009
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '32.o1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '6.1', 'aut_weyl_index': 256, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a2', '16.j1.a1', '16.l1.a2'], 'contains': ['64.d1.a1', '64.e1.a2', '64.f1.a2', '96.v1.a1'], 'core': '384.a1.a1', 'coset_action_label': '32T9401', 'count': 8, 'diagramx': [371, -1, 1240, -1, 593, -1, 9446, -1], 'generators': [2122417, 176903, 3333742], 'label': '384.17956.32.o1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '32.o1.a2', 'projective_image': '384.17956', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.o1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269515010
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '32.o1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '6.1', 'aut_weyl_index': 256, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.j1.b1', '16.l1.a2'], 'contains': ['64.d1.a1', '64.e1.b1', '64.f1.a1', '96.v1.b1'], 'core': '384.a1.a1', 'coset_action_label': '32T9401', 'count': 8, 'diagramx': [371, -1, 1501, -1, 593, -1, 9242, -1], 'generators': [4642835, 176903, 3333742], 'label': '384.17956.32.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '32.o1.b1', 'projective_image': '384.17956', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.o1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269515011
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '32.o1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '6.1', 'aut_weyl_index': 256, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a2', '16.j1.b1', '16.l1.a1'], 'contains': ['64.d1.a1', '64.e1.b2', '64.f1.a2', '96.v1.b1'], 'core': '384.a1.a1', 'coset_action_label': '32T9401', 'count': 8, 'diagramx': [371, -1, 1394, -1, 593, -1, 9106, -1], 'generators': [6632585, 176903, 3333742], 'label': '384.17956.32.o1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '32.o1.b2', 'projective_image': '384.17956', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.o1.b2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269515012
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '32.o1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '6.1', 'aut_weyl_index': 256, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.b1', '16.j1.a1', '16.l1.a1'], 'contains': ['64.d1.b1', '64.e1.a1', '64.f1.a2', '96.v1.c1'], 'core': '384.a1.a1', 'coset_action_label': '32T9401', 'count': 8, 'diagramx': [371, -1, 588, -1, 593, -1, 9718, -1], 'generators': [132667, 2166683, 3333742], 'label': '384.17956.32.o1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '32.o1.c1', 'projective_image': '384.17956', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.o1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269515013
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '32.o1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '6.1', 'aut_weyl_index': 256, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.b2', '16.j1.a1', '16.l1.a2'], 'contains': ['64.d1.b1', '64.e1.a2', '64.f1.a1', '96.v1.c1'], 'core': '384.a1.a1', 'coset_action_label': '32T9401', 'count': 8, 'diagramx': [371, -1, 757, -1, 593, -1, 9650, -1], 'generators': [2122417, 2166683, 3333742], 'label': '384.17956.32.o1.c2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '32.o1.c2', 'projective_image': '384.17956', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.o1.c2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269515014
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '32.o1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '6.1', 'aut_weyl_index': 256, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.b1', '16.j1.b1', '16.l1.a2'], 'contains': ['64.d1.b1', '64.e1.b1', '64.f1.a2', '96.v1.d1'], 'core': '384.a1.a1', 'coset_action_label': '32T9401', 'count': 8, 'diagramx': [371, -1, 650, -1, 593, -1, 9582, -1], 'generators': [4642835, 2166683, 3333742], 'label': '384.17956.32.o1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '32.o1.d1', 'projective_image': '384.17956', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.o1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269515015
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '32.o1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '6.1', 'aut_weyl_index': 256, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.b2', '16.j1.b1', '16.l1.a1'], 'contains': ['64.d1.b1', '64.e1.b2', '64.f1.a1', '96.v1.d1'], 'core': '384.a1.a1', 'coset_action_label': '32T9401', 'count': 8, 'diagramx': [371, -1, 810, -1, 593, -1, 9174, -1], 'generators': [6632585, 2166683, 3333742], 'label': '384.17956.32.o1.d2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '32.o1.d2', 'projective_image': '384.17956', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.o1.d2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269515016
    {'ambient': '384.17956', 'aut_centralizer_order': 384, 'aut_label': '48.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.a1.a1', '24.c1.a1', '24.d1.a1', '24.e1.a1', '24.f1.a1'], 'contains': ['96.a1.a1', '96.b1.a1', '96.b1.b1', '96.g1.a1', '96.p1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2542, 8871, 3486, 8444, 2833, 8327, 6956, 8316], 'generators': [2166683, 4642820, 2122432], 'label': '384.17956.48.a1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['12.a1.a1', '24.a1.a1'], 'normal_contains': ['96.a1.a1', '96.b1.a1', '96.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '96.226', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.12', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515017
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.226', 'aut_weyl_index': 16, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.b1.b1', '8.k1.a1', '8.m1.a1', '12.bq1.b1', '16.k1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3974, -1, 4267, -1, 3487, -1, 6133, -1], 'generators': [4642835, 2122432, 4605946, 5042476, 3333742, 6174490], 'label': '384.17956.4.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.j1.b1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 269515018
    {'ambient': '384.17956', 'aut_centralizer_order': 384, 'aut_label': '48.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '2.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '24.a1.a1', '24.i1.a1', '24.n1.a1', '24.r1.a1', '24.v1.a1'], 'contains': ['96.a1.a1', '96.t1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2648, 8094, 3097, 6683, 2958, 6760, 6252, 7614], 'generators': [575726, 2122432], 'label': '384.17956.48.b1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.b1.a1', 'normal_contained_in': ['12.c1.a1', '24.a1.a1'], 'normal_contains': ['96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '96.226', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.12', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515019
    {'ambient': '384.17956', 'aut_centralizer_order': 384, 'aut_label': '48.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '2.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '24.a1.a1', '24.j1.a1', '24.o1.a1', '24.s1.a1', '24.w1.a1'], 'contains': ['96.a1.a1', '96.k1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3621, 7124, 4188, 7661, 3653, 7629, 5722, 6738], 'generators': [5042476, 4642820], 'label': '384.17956.48.c1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.c1.a1', 'normal_contained_in': ['12.b1.a1', '24.a1.a1'], 'normal_contains': ['96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.c1.a1', 'projective_image': '96.226', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.12', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515020
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '48.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 64, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.b1.a1', '24.bk1.a1', '24.bq1.a1', '24.bq1.b1', '24.bv1.a1', '24.by1.a1', '24.ca1.a1'], 'contains': ['96.l1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7763, 6113, 7986, 5662, 6506, 5851, 2125, 5823], 'generators': [6164698, 4605946], 'label': '384.17956.48.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.d1.a1', 'normal_contained_in': ['16.a1.a1', '24.b1.a1'], 'normal_contains': ['192.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.d1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 269515021
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.c1.a1', '24.g1.a1', '24.h1.a1', '24.i1.a1', '24.j1.a1', '24.k1.a1', '24.l1.a1'], 'contains': ['96.a1.a1', '96.c1.a1', '96.h1.a1', '96.h1.b1', '96.q1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2753, -1, 3335, -1, 3528, -1, 6021, -1], 'generators': [132667, 4642820, 2122432], 'label': '384.17956.48.e1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.e1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515022
    {'ambient': '384.17956', 'aut_centralizer_order': 128, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.g1.a1', '24.m1.a1', '24.n1.a1', '24.o1.a1', '24.p1.a1', '24.q1.a1'], 'contains': ['96.a1.a1', '96.d1.a1', '96.i1.a1', '96.r1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3727, -1, 4499, -1, 4593, -1, 5354, -1], 'generators': [1974553, 4642820, 2122432], 'label': '384.17956.48.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.f1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269515023
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.c1.a1', '24.h1.a1', '24.m1.a1', '24.r1.a1', '24.s1.a1', '24.t1.a1', '24.u1.a1'], 'contains': ['96.a1.a1', '96.e1.a1', '96.j1.a1', '96.s1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2055, -1, 3546, -1, 3088, -1, 6491, -1], 'generators': [5734448, 4642820, 2122432], 'label': '384.17956.48.g1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.g1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269515024
    {'ambient': '384.17956', 'aut_centralizer_order': 256, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 768, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.e1.a1', '24.l1.a1', '24.o1.a1', '24.q1.a1', '24.u1.a1', '24.v1.a1', '24.x1.a1', '24.y1.a1', '24.z1.a1', '24.ba1.a1', '24.bb1.a1', '24.bc1.a1', '24.bd1.a1', '24.be1.a1'], 'contains': ['96.a1.a1', '96.l1.a1', '96.m1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6021, -1, 6057, -1, 6978, -1, 3813, -1], 'generators': [4642820, 6164698], 'label': '384.17956.48.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.h1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515025
    {'ambient': '384.17956', 'aut_centralizer_order': 128, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '12.bf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.k1.a1', '24.p1.a1', '24.t1.a1', '24.v1.a1', '24.w1.a1', '24.x1.a1'], 'contains': ['96.a1.a1', '96.f1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3142, -1, 4418, -1, 4219, -1, 5593, -1], 'generators': [4142903, 2122432], 'label': '384.17956.48.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.i1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269515026
    {'ambient': '384.17956', 'aut_centralizer_order': 128, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '12.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.h1.a1', '24.n1.a1', '24.p1.a1', '24.w1.a1', '24.y1.a1', '24.bf1.a1'], 'contains': ['96.a1.a1', '96.n1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3834, -1, 4739, -1, 4468, -1, 4994, -1], 'generators': [3035090, 4642820], 'label': '384.17956.48.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.j1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269515027
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '24.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '24.f1.a1', '24.i1.a1', '24.k1.a1', '24.m1.a1', '24.s1.a1', '24.z1.a1', '24.bf1.a1'], 'contains': ['96.a1.a1', '96.u1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2940, -1, 3199, -1, 3301, -1, 6124, -1], 'generators': [4265251, 2122432], 'label': '384.17956.48.k1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.k1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269515028
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '384.20162', 'aut_weyl_index': 4, 'centralizer': '96.a1.a1', 'complements': ['64.e1.a1', '64.e1.a2', '64.e1.b2', '64.e1.b1', '64.f1.a1', '64.f1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.c1.a1', '12.g1.a1', '12.h1.a1', '12.u1.a1', '12.y1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5124, 9327, 5030, 8898, 5792, 9562, 4562, 9559], 'generators': [5042476, 575726, 6164698, 4605946], 'label': '384.17956.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['12.a1.a1', '12.b1.a1', '12.c1.a1', '24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '96.226', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 269515029
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '24.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '24.f1.a1', '24.g1.a1', '24.j1.a1', '24.r1.a1', '24.t1.a1', '24.ba1.a1', '24.bf1.a1'], 'contains': ['96.a1.a1', '96.o1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4071, -1, 4317, -1, 3810, -1, 5850, -1], 'generators': [5042485, 4642820], 'label': '384.17956.48.l1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.l1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269515030
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.i1.a2', '24.c1.a1'], 'contains': ['96.b1.a1', '96.c1.a1', '96.e1.a1', '96.v1.a1', '96.v1.b1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1357, -1, 2754, -1, 2282, -1, 7821, -1], 'generators': [132667, 176903, 4642820], 'label': '384.17956.48.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '48.m1.a1', 'projective_image': '192.1480', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515031
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.b1', '16.i1.b2', '24.c1.a1'], 'contains': ['96.b1.b1', '96.c1.a1', '96.e1.a1', '96.v1.c1', '96.v1.d1'], 'core': '96.b1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [1357, -1, 2440, -1, 2282, -1, 7966, -1], 'generators': [132667, 2166683, 4642820], 'label': '384.17956.48.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '48.m1.b1', 'projective_image': '192.1480', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515032
    {'ambient': '384.17956', 'aut_centralizer_order': 32, 'aut_label': '48.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '24.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1'], 'contains': ['96.b1.a1', '96.d1.a1', '96.f1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2371, -1, 3949, -1, 4087, -1, 6350, -1], 'generators': [1974553, 4142903], 'label': '384.17956.48.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '48.n1.a1', 'projective_image': '192.1480', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.n1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269515033
    {'ambient': '384.17956', 'aut_centralizer_order': 32, 'aut_label': '48.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '24.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1'], 'contains': ['96.b1.b1', '96.d1.a1', '96.f1.a1'], 'core': '96.b1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [2371, -1, 4005, -1, 4087, -1, 6418, -1], 'generators': [2669167, 4142903], 'label': '384.17956.48.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '48.n1.b1', 'projective_image': '192.1480', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.n1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269515034
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '24.c1.a1', '24.bg1.a1', '24.bh1.a1'], 'contains': ['96.g1.a1', '96.h1.a1', '96.j1.a1', '96.v1.a1', '96.v1.c1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2834, -1, 3396, -1, 3434, -1, 7280, -1], 'generators': [132667, 2166683, 2122432], 'label': '384.17956.48.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1.a1', 'old_label': '48.o1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515035
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.b1', '24.c1.a1', '24.bg1.b1', '24.bh1.a1'], 'contains': ['96.g1.a1', '96.h1.b1', '96.j1.a1', '96.v1.b1', '96.v1.d1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2834, -1, 3666, -1, 3434, -1, 7203, -1], 'generators': [4642835, 2166683, 2122432], 'label': '384.17956.48.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1.a1', 'old_label': '48.o1.b1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.o1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515036
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '48.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '12.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.bg1.a1', '24.bg1.b1', '24.bi1.a1', '24.bj1.a1', '24.bj1.b1', '24.bk1.a1'], 'contains': ['96.g1.a1', '96.l1.a1', '96.n1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5588, -1, 7455, -1, 5271, -1, 3617, -1], 'generators': [2166683, 6164698], 'label': '384.17956.48.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.p1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.p1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515037
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '48.q1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '12.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.bh1.a1', '24.bi1.a1'], 'contains': ['96.g1.a1', '96.m1.a1', '96.n1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5130, -1, 5780, -1, 5426, -1, 4514, -1], 'generators': [2166683, 3909614], 'label': '384.17956.48.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.q1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.q1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515038
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '48.r1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.bl1.a1', '24.bm1.a1'], 'contains': ['96.h1.a1', '96.i1.a1', '96.o1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5285, -1, 5009, -1, 7097, -1, 4303, -1], 'generators': [132667, 2366842], 'label': '384.17956.48.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1.a1', 'old_label': '48.r1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.r1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269515039
    {'ambient': '384.17956', 'aut_centralizer_order': 2, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '256.56083', 'aut_weyl_index': 6, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.d1.a1', '12.e1.a1', '12.f1.a1', '12.g1.a1', '12.i1.a1', '12.l1.a1', '12.m1.a1', '12.n1.a1', '12.p1.a1', '12.t1.a1', '12.bb1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2732, -1, 3782, -1, 4089, -1, 5568, -1], 'generators': [132667, 5042476, 575726, 4605946], 'label': '384.17956.6.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 269515040
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '48.r1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.bl1.b1', '24.bm1.a1'], 'contains': ['96.h1.b1', '96.i1.a1', '96.o1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5285, -1, 4931, -1, 7097, -1, 4400, -1], 'generators': [4642835, 2366842], 'label': '384.17956.48.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1.a1', 'old_label': '48.r1.b1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.r1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269515041
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.bg1.a1', '24.bh1.a1'], 'contains': ['96.h1.a1', '96.j1.a1', '96.n1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3483, -1, 4584, -1, 4349, -1, 5495, -1], 'generators': [132667, 4593842], 'label': '384.17956.48.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1.a1', 'old_label': '48.s1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.s1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269515042
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.bg1.b1', '24.bh1.a1'], 'contains': ['96.h1.b1', '96.j1.a1', '96.n1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3483, -1, 4646, -1, 4349, -1, 5427, -1], 'generators': [4642835, 4593842], 'label': '384.17956.48.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1.a1', 'old_label': '48.s1.b1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.s1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269515043
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '48.t1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '24.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '24.j1.a1', '24.bl1.a1', '24.bm1.a1'], 'contains': ['96.h1.a1', '96.k1.a1', '96.o1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5387, -1, 5140, -1, 5115, -1, 5123, -1], 'generators': [132667, 5042476], 'label': '384.17956.48.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1.a1', 'old_label': '48.t1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.t1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515044
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '48.t1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '24.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.b1', '24.j1.a1', '24.bl1.b1', '24.bm1.a1'], 'contains': ['96.h1.b1', '96.k1.a1', '96.o1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5387, -1, 5247, -1, 5115, -1, 5251, -1], 'generators': [4642835, 5042476], 'label': '384.17956.48.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1.a1', 'old_label': '48.t1.b1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.t1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515045
    {'ambient': '384.17956', 'aut_centralizer_order': 32, 'aut_label': '48.u1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 192, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '24.bg1.a1', '24.bl1.a1', '24.bn1.a1', '24.bo1.a1', '24.bp1.a1', '24.bq1.a1'], 'contains': ['96.h1.a1', '96.l1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6884, -1, 7153, -1, 6776, -1, 1989, -1], 'generators': [132667, 4605946], 'label': '384.17956.48.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.u1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.u1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269515046
    {'ambient': '384.17956', 'aut_centralizer_order': 32, 'aut_label': '48.u1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 192, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '24.bg1.b1', '24.bl1.b1', '24.bn1.b1', '24.bo1.b1', '24.bp1.b1', '24.bq1.b1'], 'contains': ['96.h1.b1', '96.l1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6884, -1, 7325, -1, 6776, -1, 2057, -1], 'generators': [4642835, 4605946], 'label': '384.17956.48.u1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.u1.b1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.u1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269515047
    {'ambient': '384.17956', 'aut_centralizer_order': 32, 'aut_label': '48.v1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 192, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '24.bh1.a1', '24.bm1.a1'], 'contains': ['96.h1.a1', '96.h1.b1', '96.m1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5009, -1, 4847, -1, 6859, -1, 4620, -1], 'generators': [132667, 2350862], 'label': '384.17956.48.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.v1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.v1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269515048
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '48.w1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '24.bl1.a1', '24.bl1.b1', '24.br1.a1', '24.br1.b1', '24.bu1.a1', '24.bv1.a1'], 'contains': ['96.i1.a1', '96.k1.a1', '96.l1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6984, -1, 6657, -1, 8346, -1, 1823, -1], 'generators': [5042476, 6164698], 'label': '384.17956.48.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '48.w1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.w1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515049
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '48.x1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '24.bm1.a1', '24.bu1.a1'], 'contains': ['96.i1.a1', '96.k1.a1', '96.m1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5721, -1, 5617, -1, 8190, -1, 3420, -1], 'generators': [5042476, 3909614], 'label': '384.17956.48.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '48.x1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.x1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515050
    {'ambient': '384.17956', 'aut_centralizer_order': 2, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '256.56083', 'aut_weyl_index': 6, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.f1.a1', '12.h1.a1', '12.k1.a1', '12.o1.a1', '12.q1.a1', '12.x1.a1', '12.bc1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5433, -1, 5312, -1, 7952, -1, 4835, -1], 'generators': [132667, 1974553, 4142903], 'label': '384.17956.6.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 269515051
    {'ambient': '384.17956', 'aut_centralizer_order': 32, 'aut_label': '48.y1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 192, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '24.bn1.a1', '24.bn1.b1', '24.bt1.a1', '24.bt1.b1', '24.bu1.a1', '24.bv1.a1'], 'contains': ['96.i1.a1', '96.l1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7421, -1, 7206, -1, 8775, -1, 544, -1], 'generators': [2366842, 6164698], 'label': '384.17956.48.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '48.y1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.y1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269515052
    {'ambient': '384.17956', 'aut_centralizer_order': 32, 'aut_label': '48.z1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 192, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '24.bs1.a1', '24.bu1.a1'], 'contains': ['96.i1.a1', '96.m1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5822, -1, 5923, -1, 8858, -1, 3254, -1], 'generators': [2366842, 3909614], 'label': '384.17956.48.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '48.z1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.z1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269515053
    {'ambient': '384.17956', 'aut_centralizer_order': 32, 'aut_label': '48.ba1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 192, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.u1.a1', '24.bg1.a1', '24.bg1.b1', '24.bw1.a1', '24.bx1.a1', '24.bx1.b1', '24.by1.a1'], 'contains': ['96.j1.a1', '96.l1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5487, -1, 7378, -1, 4996, -1, 3518, -1], 'generators': [5734448, 6174490], 'label': '384.17956.48.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.ba1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269515054
    {'ambient': '384.17956', 'aut_centralizer_order': 32, 'aut_label': '48.bb1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 192, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.u1.a1', '24.bh1.a1', '24.bs1.a1'], 'contains': ['96.j1.a1', '96.m1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4575, -1, 5063, -1, 5756, -1, 4747, -1], 'generators': [5734448, 3919406], 'label': '384.17956.48.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '48.bb1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269515055
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '48.bc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 192, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.bi1.a1', '24.bo1.a1', '24.bo1.b1', '24.bu1.a1', '24.bw1.a1', '24.bz1.a1'], 'contains': ['96.l1.a1', '96.m1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7314, -1, 8152, -1, 7262, -1, 1921, -1], 'generators': [2350862, 6164698], 'label': '384.17956.48.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.bc1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269515056
    {'ambient': '384.17956', 'aut_centralizer_order': 32, 'aut_label': '48.bd1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 192, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1.a1', '24.bi1.a1', '24.bk1.a1', '24.bp1.a1', '24.bp1.b1', '24.bx1.a1', '24.bx1.b1'], 'contains': ['96.l1.a1', '96.n1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6497, -1, 9140, -1, 6271, -1, 2193, -1], 'generators': [4593842, 6164698], 'label': '384.17956.48.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.bd1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269515057
    {'ambient': '384.17956', 'aut_centralizer_order': 32, 'aut_label': '48.be1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 192, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1.a1', '24.bl1.a1', '24.bl1.b1', '24.bt1.a1', '24.bt1.b1', '24.bz1.a1', '24.ca1.a1'], 'contains': ['96.l1.a1', '96.o1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9458, -1, 7271, -1, 7989, -1, 1724, -1], 'generators': [5042485, 4605946], 'label': '384.17956.48.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '48.be1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.be1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269515058
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '48.bf1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bb1.a1', '24.bj1.a1', '24.bo1.b1', '24.bq1.a1', '24.br1.a1', '24.bt1.a1', '24.bx1.a1'], 'contains': ['96.l1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8759, -1, 8633, -1, 7179, -1, 1531, -1], 'generators': [6166711], 'label': '384.17956.48.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.bf1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515059
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '48.bf1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bb1.a1', '24.bj1.b1', '24.bo1.a1', '24.bq1.b1', '24.br1.b1', '24.bt1.b1', '24.bx1.b1'], 'contains': ['96.l1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8759, -1, 8816, -1, 7179, -1, 1191, -1], 'generators': [3911627], 'label': '384.17956.48.bf1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.bf1.b1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bf1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515060
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '48.bg1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bd1.a1', '24.bn1.a1', '24.bn1.b1', '24.br1.a1', '24.br1.b1', '24.bz1.a1', '24.ca1.a1'], 'contains': ['96.l1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9349, -1, 8039, -1, 8071, -1, 612, -1], 'generators': [1974700], 'label': '384.17956.48.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '48.bg1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515061
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 12, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.f1.a1', '12.j1.a1', '12.r1.a1', '12.s1.a1', '12.bd1.a1', '12.be1.a1', '12.bn1.a1', '12.bn1.b1', '12.bo1.a1', '12.bo1.b1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6867, -1, 8851, -1, 5479, -1, 2494, -1], 'generators': [132667, 2166683, 4642820, 6164698], 'label': '384.17956.6.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 269515062
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '48.bh1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '12.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.be1.a1', '24.bj1.a1', '24.bj1.b1', '24.bp1.a1', '24.bp1.b1', '24.bw1.a1', '24.by1.a1'], 'contains': ['96.l1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7976, -1, 9589, -1, 6106, -1, 2261, -1], 'generators': [5000690], 'label': '384.17956.48.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.bh1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515063
    {'ambient': '384.17956', 'aut_centralizer_order': 32, 'aut_label': '48.bi1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 192, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1.a1', '24.bi1.a1', '24.cb1.a1'], 'contains': ['96.m1.a1', '96.n1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6128, -1, 7532, -1, 7344, -1, 3322, -1], 'generators': [4593842, 3909614], 'label': '384.17956.48.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '48.bi1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269515064
    {'ambient': '384.17956', 'aut_centralizer_order': 32, 'aut_label': '48.bj1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 192, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1.a1', '24.bm1.a1', '24.cb1.a1'], 'contains': ['96.m1.a1', '96.o1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7086, -1, 5977, -1, 8464, -1, 3911, -1], 'generators': [5042485, 2350862], 'label': '384.17956.48.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '48.bj1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269515065
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '48.bk1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '12.bf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bc1.a1', '24.bs1.a1', '24.cb1.a1'], 'contains': ['96.m1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6710, -1, 6140, -1, 8976, -1, 3715, -1], 'generators': [4653262], 'label': '384.17956.48.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.m1.a1', 'old_label': '48.bk1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515066
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '48.bl1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '16.l1.a2', '24.c1.a1'], 'contains': ['96.p1.a1', '96.q1.a1', '96.s1.a1', '96.v1.a1', '96.v1.b1', '96.v1.c1', '96.v1.d1'], 'core': '192.c1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1539, -1, 1620, -1, 2375, -1, 8044, -1], 'generators': [132667, 2166683, 6632600], 'label': '384.17956.48.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '48.bl1.a1', 'projective_image': '192.1485', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 269515067
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '48.bm1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '24.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.a1', '16.m1.a2', '24.i1.a1'], 'contains': ['96.q1.a1', '96.t1.a1', '96.u1.a1'], 'core': '192.c1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2198, -1, 44, -1, 2500, -1, 7384, -1], 'generators': [132667, 575726], 'label': '384.17956.48.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.i1.a1', 'old_label': '48.bm1.a1', 'projective_image': '192.1485', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 269515068
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '48.bn1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1'], 'contains': ['96.r1.a1', '96.s1.a1', '96.u1.a1'], 'core': '192.c1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3041, -1, 2382, -1, 3180, -1, 5948, -1], 'generators': [4265251, 1873267], 'label': '384.17956.48.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.m1.a1', 'old_label': '48.bn1.a1', 'projective_image': '192.1485', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269515069
    {'ambient': '384.17956', 'aut_centralizer_order': 192, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 768, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.b1.a1', '32.b1.b1', '32.c1.a1', '32.c1.a2', '32.d1.a1', '32.d1.a2'], 'contains': ['128.a1.a1', '192.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [708, -1, 1940, -1, 1069, -1, 8423, -1], 'generators': [4642820, 3333742], 'label': '384.17956.64.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '64.a1.a1', 'projective_image': '192.1480', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515070
    {'ambient': '384.17956', 'aut_centralizer_order': 192, 'aut_label': '64.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 768, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '32.a1.a1', '32.e1.a1', '32.f1.a1', '32.f1.b1', '32.g1.a1', '32.h1.a1', '32.i1.a1'], 'contains': ['128.a1.a1', '192.b1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1778, -1, 2582, -1, 1628, -1, 7744, -1], 'generators': [2122432, 3333742], 'label': '384.17956.64.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '64.b1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515071
    {'ambient': '384.17956', 'aut_centralizer_order': 192, 'aut_label': '64.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 768, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.j1.a1', '32.k1.a1', '32.k1.a2', '32.l1.a1', '32.m1.a1', '32.n1.a1'], 'contains': ['128.a1.a1', '192.c1.a1'], 'core': '192.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1193, -1, 215, -1, 1371, -1, 8045, -1], 'generators': [6632600, 3333742], 'label': '384.17956.64.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '64.c1.a1', 'projective_image': '192.1485', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515072
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 12, 'centralizer': '24.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.g1.a1', '12.j1.a1', '12.k1.a1', '12.v1.a1', '12.w1.a1', '12.bf1.a1', '12.bg1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8027, -1, 7075, -1, 7771, -1, 3636, -1], 'generators': [6166711, 5042476, 575726], 'label': '384.17956.6.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.e1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 269515073
    {'ambient': '384.17956', 'aut_centralizer_order': 48, 'aut_label': '64.d1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 768, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '32.e1.a1', '32.j1.a1', '32.o1.a1', '32.o1.a2', '32.o1.b1', '32.o1.b2'], 'contains': ['128.a1.a1', '192.d1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [780, -1, 2087, -1, 969, -1, 8974, -1], 'generators': [176903, 3333742], 'label': '384.17956.64.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '64.d1.a1', 'projective_image': '384.17956', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515074
    {'ambient': '384.17956', 'aut_centralizer_order': 48, 'aut_label': '64.d1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 768, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.b1', '32.e1.a1', '32.j1.a1', '32.o1.c1', '32.o1.c2', '32.o1.d1', '32.o1.d2'], 'contains': ['128.a1.a1', '192.d1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [780, -1, 676, -1, 969, -1, 9042, -1], 'generators': [2166683, 3333742], 'label': '384.17956.64.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '64.d1.b1', 'projective_image': '384.17956', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515075
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '64.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 256, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '32.f1.a1', '32.k1.a1', '32.o1.a1', '32.o1.c1'], 'contains': ['128.a1.a1', '192.e1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [850, -1, 729, -1, 1152, -1, 8695, -1], 'generators': [132667, 3333742], 'label': '384.17956.64.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '64.e1.a1', 'projective_image': '384.17956', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269515076
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '64.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 256, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a2', '32.f1.a1', '32.k1.a2', '32.o1.a2', '32.o1.c2'], 'contains': ['128.a1.a1', '192.e1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [850, -1, 880, -1, 1152, -1, 8627, -1], 'generators': [2122417, 3333742], 'label': '384.17956.64.e1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '64.e1.a2', 'projective_image': '384.17956', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.e1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269515077
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '64.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 256, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '32.f1.b1', '32.k1.a2', '32.o1.b1', '32.o1.d1'], 'contains': ['128.a1.a1', '192.e1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [850, -1, 934, -1, 1152, -1, 8559, -1], 'generators': [4642835, 3333742], 'label': '384.17956.64.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '64.e1.b1', 'projective_image': '384.17956', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.e1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269515078
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '64.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 256, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a2', '32.f1.b1', '32.k1.a1', '32.o1.b2', '32.o1.d2'], 'contains': ['128.a1.a1', '192.e1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [850, -1, 1288, -1, 1152, -1, 8491, -1], 'generators': [6632585, 3333742], 'label': '384.17956.64.e1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '64.e1.b2', 'projective_image': '384.17956', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.e1.b2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269515079
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '64.f1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 256, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '32.g1.a1', '32.l1.a1', '32.o1.a1', '32.o1.b1', '32.o1.c2', '32.o1.d2'], 'contains': ['128.a1.a1', '192.g1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [432, -1, 1567, -1, 781, -1, 9242, -1], 'generators': [3376889, 3333742], 'label': '384.17956.64.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '64.f1.a1', 'projective_image': '384.17956', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269515080
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '64.f1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 256, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a2', '32.g1.a1', '32.l1.a1', '32.o1.a2', '32.o1.b2', '32.o1.c1', '32.o1.d1'], 'contains': ['128.a1.a1', '192.g1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [432, -1, 1016, -1, 781, -1, 9310, -1], 'generators': [5734448, 3333742], 'label': '384.17956.64.f1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '64.f1.a2', 'projective_image': '384.17956', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.f1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269515081
    {'ambient': '384.17956', 'aut_centralizer_order': 1536, 'aut_label': '96.a1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1536, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.a1.a1', '48.b1.a1', '48.c1.a1', '48.e1.a1', '48.f1.a1', '48.g1.a1', '48.h1.a1', '48.i1.a1', '48.j1.a1', '48.k1.a1', '48.l1.a1'], 'contains': ['192.a1.a1', '192.b1.a1', '192.c1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2958, 7730, 3651, 7265, 3528, 7022, 6021, 7260], 'generators': [4642820, 2122432], 'label': '384.17956.96.a1.a1', 'mobius_quo': 2, 'mobius_sub': -96, 'normal_closure': '96.a1.a1', 'normal_contained_in': ['24.b1.a1', '48.a1.a1', '48.c1.a1', '48.b1.a1'], 'normal_contains': ['192.c1.a1', '192.a1.a1', '192.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '96.226', 'quotient_action_image': '1.1', 'quotient_action_kernel': '96.226', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 269515082
    {'ambient': '384.17956', 'aut_centralizer_order': 384, 'aut_label': '96.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 768, 'centralizer': '2.a1.a1', 'complements': ['4.j1.a1', '4.j1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '48.a1.a1', '48.m1.a1', '48.n1.a1'], 'contains': ['192.a1.a1', '192.d1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1495, 8778, 2956, 7855, 2833, 8065, 7439, 7788], 'generators': [176903, 4642820], 'label': '384.17956.96.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '96.b1.a1', 'normal_contained_in': ['48.a1.a1'], 'normal_contains': ['192.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.b1.a1', 'projective_image': '192.1480', 'quotient_action_image': '2.1', 'quotient_action_kernel': '48.29', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '96.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515083
    {'ambient': '384.17956', 'aut_centralizer_order': 2, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '256.56083', 'aut_weyl_index': 6, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.h1.a1', '12.i1.a1', '12.j1.a1', '12.z1.a1', '12.ba1.a1', '12.bh1.a1', '12.bi1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7257, -1, 6468, -1, 6954, -1, 4016, -1], 'generators': [6166711, 1974553, 4142903], 'label': '384.17956.6.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.f1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 269515084
    {'ambient': '384.17956', 'aut_centralizer_order': 384, 'aut_label': '96.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 768, 'centralizer': '2.a1.a1', 'complements': ['4.j1.a1', '4.j1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['32.b1.b1', '48.a1.a1', '48.m1.b1', '48.n1.b1'], 'contains': ['192.a1.a1', '192.d1.b1'], 'core': '96.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1495, 8778, 2400, 8444, 2833, 8065, 7671, 8316], 'generators': [2166683, 4642820], 'label': '384.17956.96.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '96.b1.b1', 'normal_contained_in': ['48.a1.a1'], 'normal_contains': ['192.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.b1.b1', 'projective_image': '192.1480', 'quotient_action_image': '2.1', 'quotient_action_kernel': '48.29', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '96.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515085
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '96.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 768, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '32.c1.a2', '48.e1.a1', '48.m1.a1', '48.m1.b1'], 'contains': ['192.a1.a1', '192.e1.a1', '192.e1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1575, -1, 2024, -1, 2563, -1, 7817, -1], 'generators': [132667, 4642820], 'label': '384.17956.96.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '96.c1.a1', 'projective_image': '192.1480', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 269515086
    {'ambient': '384.17956', 'aut_centralizer_order': 128, 'aut_label': '96.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 768, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '48.n1.a1', '48.n1.b1'], 'contains': ['192.a1.a1', '192.f1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2690, -1, 4118, -1, 4443, -1, 6346, -1], 'generators': [1974553, 4642820], 'label': '384.17956.96.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '96.d1.a1', 'projective_image': '192.1480', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515087
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '96.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 768, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '32.d1.a2', '48.g1.a1', '48.m1.a1', '48.m1.b1'], 'contains': ['192.a1.a1', '192.g1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1336, -1, 2521, -1, 2188, -1, 7894, -1], 'generators': [5734448, 4642820], 'label': '384.17956.96.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '96.e1.a1', 'projective_image': '192.1480', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515088
    {'ambient': '384.17956', 'aut_centralizer_order': 128, 'aut_label': '96.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 768, 'centralizer': '12.bf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '48.n1.a1', '48.n1.b1'], 'contains': ['192.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2395, -1, 3963, -1, 4073, -1, 6418, -1], 'generators': [4142903], 'label': '384.17956.96.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '96.f1.a1', 'projective_image': '192.1480', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515089
    {'ambient': '384.17956', 'aut_centralizer_order': 384, 'aut_label': '96.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 768, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '48.a1.a1', '48.o1.a1', '48.o1.b1', '48.p1.a1', '48.q1.a1'], 'contains': ['192.b1.a1', '192.d1.a1', '192.d1.b1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2879, -1, 3590, -1, 3434, -1, 7203, -1], 'generators': [2166683, 2122432], 'label': '384.17956.96.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '96.g1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 269515090
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '96.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 768, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '48.e1.a1', '48.o1.a1', '48.r1.a1', '48.s1.a1', '48.t1.a1', '48.u1.a1', '48.v1.a1'], 'contains': ['192.b1.a1', '192.e1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3573, -1, 3530, -1, 4349, -1, 5509, -1], 'generators': [132667, 2122432], 'label': '384.17956.96.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '96.h1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515091
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '96.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 768, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.b1', '48.e1.a1', '48.o1.b1', '48.r1.b1', '48.s1.b1', '48.t1.b1', '48.u1.b1', '48.v1.a1'], 'contains': ['192.b1.a1', '192.e1.b1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3573, -1, 4315, -1, 4349, -1, 5432, -1], 'generators': [4642835, 2122432], 'label': '384.17956.96.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '96.h1.b1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.h1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515092
    {'ambient': '384.17956', 'aut_centralizer_order': 128, 'aut_label': '96.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 768, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '48.r1.a1', '48.r1.b1', '48.w1.a1', '48.x1.a1', '48.y1.a1', '48.z1.a1'], 'contains': ['192.b1.a1', '192.f1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5460, -1, 5159, -1, 7798, -1, 3790, -1], 'generators': [1974553, 2122432], 'label': '384.17956.96.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '96.i1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515093
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '96.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 768, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1.a1', '48.g1.a1', '48.o1.a1', '48.o1.b1', '48.s1.a1', '48.s1.b1', '48.ba1.a1', '48.bb1.a1'], 'contains': ['192.b1.a1', '192.g1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2610, -1, 3781, -1, 4161, -1, 6491, -1], 'generators': [5734448, 2122432], 'label': '384.17956.96.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1.a1', 'old_label': '96.j1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515094
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 12, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.i1.a1', '12.k1.a1', '12.bj1.a1', '12.bk1.a1', '12.bl1.a1', '12.bm1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7421, -1, 6816, -1, 7612, -1, 3504, -1], 'generators': [4265251, 2166683, 4605946], 'label': '384.17956.6.g1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.g1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 269515095
    {'ambient': '384.17956', 'aut_centralizer_order': 384, 'aut_label': '96.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 768, 'centralizer': '2.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.h1.a1', '48.c1.a1', '48.t1.a1', '48.t1.b1', '48.w1.a1', '48.x1.a1'], 'contains': ['192.b1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5222, -1, 4513, -1, 4892, -1, 5251, -1], 'generators': [5042476], 'label': '384.17956.96.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '96.k1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.k1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 269515096
    {'ambient': '384.17956', 'aut_centralizer_order': 256, 'aut_label': '96.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 768, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '48.h1.a1', '48.p1.a1', '48.u1.a1', '48.u1.b1', '48.w1.a1', '48.y1.a1', '48.ba1.a1', '48.bc1.a1', '48.bd1.a1', '48.be1.a1', '48.bf1.a1', '48.bf1.b1', '48.bg1.a1', '48.bh1.a1'], 'contains': ['192.b1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7264, -1, 7410, -1, 6877, -1, 2023, -1], 'generators': [6164698], 'label': '384.17956.96.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '96.l1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515097
    {'ambient': '384.17956', 'aut_centralizer_order': 256, 'aut_label': '96.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 768, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '48.q1.a1', '48.v1.a1', '48.x1.a1', '48.z1.a1', '48.bb1.a1', '48.bc1.a1', '48.bi1.a1', '48.bj1.a1', '48.bk1.a1'], 'contains': ['192.b1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5651, -1, 5923, -1, 7262, -1, 3862, -1], 'generators': [3909614], 'label': '384.17956.96.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '96.m1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515098
    {'ambient': '384.17956', 'aut_centralizer_order': 128, 'aut_label': '96.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 768, 'centralizer': '12.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '48.p1.a1', '48.q1.a1', '48.s1.a1', '48.s1.b1', '48.bd1.a1', '48.bi1.a1'], 'contains': ['192.b1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5046, -1, 5417, -1, 5152, -1, 4728, -1], 'generators': [3035090], 'label': '384.17956.96.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '96.n1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.n1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515099
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '96.o1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 768, 'centralizer': '24.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.i1.a1', '48.l1.a1', '48.r1.a1', '48.r1.b1', '48.t1.a1', '48.t1.b1', '48.be1.a1', '48.bj1.a1'], 'contains': ['192.b1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5721, -1, 5019, -1, 5234, -1, 5123, -1], 'generators': [5042485], 'label': '384.17956.96.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1.a1', 'old_label': '96.o1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515100
    {'ambient': '384.17956', 'aut_centralizer_order': 384, 'aut_label': '96.p1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 768, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.j1.a1', '48.a1.a1', '48.bl1.a1'], 'contains': ['192.c1.a1', '192.d1.a1', '192.d1.b1'], 'core': '192.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1853, -1, 1753, -1, 2375, -1, 7972, -1], 'generators': [2166683, 6632600], 'label': '384.17956.96.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '96.p1.a1', 'projective_image': '192.1485', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.p1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 269515101
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '96.q1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 768, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.k1.a1', '32.k1.a2', '48.e1.a1', '48.bl1.a1', '48.bm1.a1'], 'contains': ['192.c1.a1', '192.e1.a1', '192.e1.b1'], 'core': '192.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2015, -1, 1398, -1, 2657, -1, 7594, -1], 'generators': [132667, 6632600], 'label': '384.17956.96.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '96.q1.a1', 'projective_image': '192.1485', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.q1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 269515102
    {'ambient': '384.17956', 'aut_centralizer_order': 128, 'aut_label': '96.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 768, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '48.bn1.a1'], 'contains': ['192.c1.a1', '192.f1.a1'], 'core': '192.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3086, -1, 2460, -1, 4255, -1, 5354, -1], 'generators': [1974553, 6632600], 'label': '384.17956.96.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '96.r1.a1', 'projective_image': '192.1485', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.r1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515103
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '96.s1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 768, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.l1.a1', '48.g1.a1', '48.bl1.a1', '48.bn1.a1'], 'contains': ['192.c1.a1', '192.g1.a1'], 'core': '192.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1935, -1, 1874, -1, 2469, -1, 7517, -1], 'generators': [5734448, 6632600], 'label': '384.17956.96.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '96.s1.a1', 'projective_image': '192.1485', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.s1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515104
    {'ambient': '384.17956', 'aut_centralizer_order': 384, 'aut_label': '96.t1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 768, 'centralizer': '2.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.m1.a1', '48.b1.a1', '48.bm1.a1'], 'contains': ['192.c1.a1'], 'core': '192.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2092, -1, 63, -1, 2745, -1, 7367, -1], 'generators': [575726], 'label': '384.17956.96.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '96.t1.a1', 'projective_image': '192.1485', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.t1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 269515105
    {'ambient': '384.17956', 'aut_centralizer_order': 2, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '256.56083', 'aut_weyl_index': 6, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.n1.a1', '12.q1.a1', '12.r1.a1', '12.u1.a1', '12.w1.a1', '12.bi1.a1', '12.bk1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6613, -1, 6687, -1, 8277, -1, 4392, -1], 'generators': [132667, 5042476, 4142903], 'label': '384.17956.6.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.h1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 269515106
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '96.u1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 768, 'centralizer': '24.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.n1.a1', '48.k1.a1', '48.bm1.a1', '48.bn1.a1'], 'contains': ['192.c1.a1'], 'core': '192.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2325, -1, 993, -1, 2922, -1, 7299, -1], 'generators': [4265251], 'label': '384.17956.96.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1.a1', 'old_label': '96.u1.a1', 'projective_image': '192.1485', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.u1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515107
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '96.v1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1536, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.o1.a1', '32.o1.a2', '48.m1.a1', '48.o1.a1', '48.bl1.a1'], 'contains': ['192.d1.a1', '192.e1.a1', '192.g1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1416, -1, 2085, -1, 2282, -1, 8195, -1], 'generators': [132667, 176903], 'label': '384.17956.96.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '96.v1.a1', 'projective_image': '384.17956', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.v1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 269515108
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '96.v1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1536, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.o1.b1', '32.o1.b2', '48.m1.a1', '48.o1.b1', '48.bl1.a1'], 'contains': ['192.d1.a1', '192.e1.b1', '192.g1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1416, -1, 2265, -1, 2282, -1, 8117, -1], 'generators': [4642835, 176903], 'label': '384.17956.96.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '96.v1.b1', 'projective_image': '384.17956', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.v1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 269515109
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '96.v1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1536, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.o1.c1', '32.o1.c2', '48.m1.b1', '48.o1.a1', '48.bl1.a1'], 'contains': ['192.d1.b1', '192.e1.a1', '192.g1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1416, -1, 1814, -1, 2282, -1, 8350, -1], 'generators': [132667, 2166683], 'label': '384.17956.96.v1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '96.v1.c1', 'projective_image': '384.17956', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.v1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 269515110
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '96.v1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1536, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.o1.d1', '32.o1.d2', '48.m1.b1', '48.o1.b1', '48.bl1.a1'], 'contains': ['192.d1.b1', '192.e1.b1', '192.g1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1416, -1, 1964, -1, 2282, -1, 8272, -1], 'generators': [4642835, 2166683], 'label': '384.17956.96.v1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '96.v1.d1', 'projective_image': '384.17956', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.v1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 269515111
    {'ambient': '384.17956', 'aut_centralizer_order': 192, 'aut_label': '128.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 768, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '64.b1.a1', '64.c1.a1', '64.d1.a1', '64.d1.b1', '64.e1.a1', '64.e1.a2', '64.e1.b1', '64.e1.b2', '64.f1.a1', '64.f1.a2'], 'contains': ['384.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1112, -1, 1274, -1, 1152, -1, 8593, -1], 'generators': [3333742], 'label': '384.17956.128.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '128.a1.a1', 'projective_image': '384.17956', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269515112
    {'ambient': '384.17956', 'aut_centralizer_order': 1536, 'aut_label': '192.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1536, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.a1.a1', '96.b1.a1', '96.b1.b1', '96.c1.a1', '96.d1.a1', '96.e1.a1', '96.f1.a1'], 'contains': ['384.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1740, 8244, 2521, 7840, 2787, 7482, 7671, 7775], 'generators': [4642820], 'label': '384.17956.192.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '192.a1.a1', 'normal_contained_in': ['96.a1.a1', '96.b1.a1', '96.b1.b1'], 'normal_contains': ['384.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.a1.a1', 'projective_image': '192.1480', 'quotient_action_image': '1.1', 'quotient_action_kernel': '192.1480', 'quotient_action_kernel_order': 192, 'quotient_fusion': None, 'short_label': '192.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 269515113
    {'ambient': '384.17956', 'aut_centralizer_order': 1536, 'aut_label': '192.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1536, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.b1.a1', '96.a1.a1', '96.g1.a1', '96.h1.a1', '96.h1.b1', '96.i1.a1', '96.j1.a1', '96.k1.a1', '96.l1.a1', '96.m1.a1', '96.n1.a1', '96.o1.a1'], 'contains': ['384.a1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4059, 7217, 4315, 6769, 4351, 6561, 5432, 6815], 'generators': [2122432], 'label': '384.17956.192.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '192.b1.a1', 'normal_contained_in': ['48.d1.a1', '96.a1.a1'], 'normal_contains': ['384.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.b1.a1', 'projective_image': '192.1472', 'quotient_action_image': '1.1', 'quotient_action_kernel': '192.1472', 'quotient_action_kernel_order': 192, 'quotient_fusion': None, 'short_label': '192.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 269515114
    {'ambient': '384.17956', 'aut_centralizer_order': 1536, 'aut_label': '192.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1536, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.c1.a1', '96.a1.a1', '96.p1.a1', '96.q1.a1', '96.r1.a1', '96.s1.a1', '96.t1.a1', '96.u1.a1'], 'contains': ['384.a1.a1'], 'core': '192.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2016, 7730, 1398, 7287, 2657, 7022, 7517, 7279], 'generators': [6632600], 'label': '384.17956.192.c1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '192.c1.a1', 'normal_contained_in': ['96.a1.a1'], 'normal_contains': ['384.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.c1.a1', 'projective_image': '192.1485', 'quotient_action_image': '1.1', 'quotient_action_kernel': '192.1485', 'quotient_action_kernel_order': 192, 'quotient_fusion': None, 'short_label': '192.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 269515115
    {'ambient': '384.17956', 'aut_centralizer_order': 384, 'aut_label': '192.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1536, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.d1.a1', '96.b1.a1', '96.g1.a1', '96.p1.a1', '96.v1.a1', '96.v1.b1'], 'contains': ['384.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1403, -1, 2132, -1, 2458, -1, 7947, -1], 'generators': [176903], 'label': '384.17956.192.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '192.d1.a1', 'projective_image': '384.17956', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 269515116
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '384.20162', 'aut_weyl_index': 4, 'centralizer': '96.a1.a1', 'complements': ['192.e1.a1', '192.e1.b1', '192.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '4.e1.a1', '6.a1.a1', '8.d1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3010, 9155, 3455, 9235, 1655, 8218, 6572, 8271], 'generators': [5042476, 4605946, 6174490, 575726, 2122432, 3333742, 4642820], 'label': '384.17956.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.c1.a1', '4.e1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '96.226', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 269515117
    {'ambient': '384.17956', 'aut_centralizer_order': 2, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '256.56083', 'aut_weyl_index': 6, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.o1.a1', '12.p1.a1', '12.r1.a1', '12.y1.a1', '12.z1.a1', '12.bg1.a1', '12.bj1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6258, -1, 6207, -1, 7217, -1, 3201, -1], 'generators': [132667, 1974553, 575726], 'label': '384.17956.6.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.i1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 269515118
    {'ambient': '384.17956', 'aut_centralizer_order': 384, 'aut_label': '192.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1536, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.d1.b1', '96.b1.b1', '96.g1.a1', '96.p1.a1', '96.v1.c1', '96.v1.d1'], 'contains': ['384.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1403, -1, 1851, -1, 2458, -1, 8151, -1], 'generators': [2166683], 'label': '384.17956.192.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '192.d1.b1', 'projective_image': '384.17956', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 269515119
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '192.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1536, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.e1.a1', '64.e1.a2', '96.c1.a1', '96.h1.a1', '96.q1.a1', '96.v1.a1', '96.v1.c1'], 'contains': ['384.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1526, -1, 1609, -1, 2569, -1, 8083, -1], 'generators': [132667], 'label': '384.17956.192.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '192.e1.a1', 'projective_image': '384.17956', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 269515120
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '192.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1536, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.e1.b1', '64.e1.b2', '96.c1.a1', '96.h1.b1', '96.q1.a1', '96.v1.b1', '96.v1.d1'], 'contains': ['384.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1526, -1, 1796, -1, 2569, -1, 8015, -1], 'generators': [4642835], 'label': '384.17956.192.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '192.e1.b1', 'projective_image': '384.17956', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 269515121
    {'ambient': '384.17956', 'aut_centralizer_order': 128, 'aut_label': '192.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1536, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.d1.a1', '96.i1.a1', '96.r1.a1'], 'contains': ['384.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2618, -1, 3345, -1, 4440, -1, 5359, -1], 'generators': [1974553], 'label': '384.17956.192.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1.a1', 'old_label': '192.f1.a1', 'projective_image': '384.17956', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 269515122
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '192.g1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1536, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.f1.a1', '64.f1.a2', '96.e1.a1', '96.j1.a1', '96.s1.a1', '96.v1.a1', '96.v1.b1', '96.v1.c1', '96.v1.d1'], 'contains': ['384.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1279, -1, 1949, -1, 2317, -1, 8219, -1], 'generators': [5734448], 'label': '384.17956.192.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '192.g1.a1', 'projective_image': '384.17956', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 269515123
    {'ambient': '384.17956', 'aut_centralizer_order': None, 'aut_label': '384.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['128.a1.a1', '192.a1.a1', '192.b1.a1', '192.c1.a1', '192.d1.a1', '192.d1.b1', '192.e1.a1', '192.e1.b1', '192.f1.a1', '192.g1.a1'], 'contains': [], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1610, 7730, 1893, 7287, 2616, 7022, 7981, 7279], 'generators': [], 'label': '384.17956.384.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '384.a1.a1', 'normal_contained_in': ['192.c1.a1', '192.a1.a1', '192.b1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '384.a1.a1', 'projective_image': '384.17956', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 269515124
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '6.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 12, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.n1.a1', '12.o1.a1', '12.s1.a1', '12.v1.a1', '12.ba1.a1', '12.bm1.a1', '12.bp1.a1', '12.bp1.b1', '12.bq1.a1', '12.bq1.b1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8973, -1, 7638, -1, 8490, -1, 1028, -1], 'generators': [132667, 5042476, 4642820, 6164698], 'label': '384.17956.6.j1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.j1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.j1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 269515125
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '6.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 12, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.p1.a1', '12.q1.a1', '12.s1.a1', '12.bf1.a1', '12.bh1.a1', '12.bl1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5743, -1, 5553, -1, 6714, -1, 5024, -1], 'generators': [132667, 575726, 6164698], 'label': '384.17956.6.k1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.k1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.k1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 269515126
    {'ambient': '384.17956', 'aut_centralizer_order': 2, 'aut_label': '6.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '256.56083', 'aut_weyl_index': 6, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.t1.a1', '12.u1.a1', '12.v1.a1', '12.bc1.a1', '12.bd1.a1', '12.bh1.a1', '12.bj1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5947, -1, 5837, -1, 6475, -1, 4202, -1], 'generators': [6166711, 5042476, 4142903], 'label': '384.17956.6.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.l1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.l1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 269515127
    {'ambient': '384.17956', 'aut_centralizer_order': 2, 'aut_label': '6.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '256.56083', 'aut_weyl_index': 6, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.x1.a1', '12.y1.a1', '12.ba1.a1', '12.bb1.a1', '12.bd1.a1', '12.bf1.a1', '12.bk1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6468, -1, 6576, -1, 8106, -1, 3879, -1], 'generators': [6166711, 1974553, 575726], 'label': '384.17956.6.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.m1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.m1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 269515128
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '6.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 12, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.t1.a1', '12.w1.a1', '12.x1.a1', '12.z1.a1', '12.be1.a1', '12.bl1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7091, -1, 6057, -1, 7449, -1, 3768, -1], 'generators': [4265251, 5042476, 4605946], 'label': '384.17956.6.n1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.n1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.n1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 269515129
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '6.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 12, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.bb1.a1', '12.bc1.a1', '12.be1.a1', '12.bg1.a1', '12.bi1.a1', '12.bm1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7836, -1, 6350, -1, 6292, -1, 4693, -1], 'generators': [5042485, 575726, 6164698], 'label': '384.17956.6.o1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.o1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.o1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 269515130
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '8.a1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 64, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['16.a1.a1', '24.b1.a1', '32.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3212, 4694, 4042, 5036, 2408, 4578, 6756, 4097], 'generators': [4642820, 2122432, 3333742, 6174490, 4605946], 'label': '384.17956.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'normal_contains': ['16.a1.a1', '24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 269515131
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 32, 'centralizer': '24.a1.a1', 'complements': ['48.n1.a1', '48.n1.b1', '48.bn1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.i1.a1', '4.j1.a1'], 'contains': ['16.a1.a1', '24.bq1.a1', '32.f1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4020, 3625, 4307, 2211, 2665, 2524, 6896, 1256], 'generators': [132667, 2122432, 3333742, 6174490, 4605946], 'label': '384.17956.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '192.1472', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 269515132
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 32, 'centralizer': '24.a1.a1', 'complements': ['48.n1.a1', '48.n1.b1', '48.bn1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.i1.b1', '4.j1.b1'], 'contains': ['16.a1.a1', '24.bq1.b1', '32.f1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4020, 3625, 4374, 1499, 2665, 2524, 7051, 2699], 'generators': [4642835, 2122432, 3333742, 6174490, 4605946], 'label': '384.17956.8.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.b1', 'projective_image': '192.1472', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.b1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 269515133
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '384.20162', 'aut_weyl_index': 4, 'centralizer': '96.a1.a1', 'complements': ['192.f1.a1', '192.e1.a1', '192.e1.b1', '192.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.f1.a1', '4.g1.a1', '6.g1.a1', '8.e1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3435, 3460, 3875, 8257, 2811, 3106, 6274, 3124], 'generators': [4265251, 4605946, 2981098, 2166683, 2122432, 6632600, 3333742], 'label': '384.17956.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.f1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '96.226', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 269515134
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.230', 'aut_weyl_index': 16, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.h1.a1'], 'contains': ['16.b1.a1', '16.c1.a1', '16.d1.a1', '16.i1.a1', '16.i1.a2', '16.i1.b1', '16.i1.b2', '16.j1.a1', '16.j1.b1', '16.l1.a1', '16.l1.a2', '24.c1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [744, -1, 1820, -1, 629, -1, 8941, -1], 'generators': [132667, 3333742, 2166683, 4642820, 2122432], 'label': '384.17956.8.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.c1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 269515135
    {'ambient': '384.17956', 'aut_centralizer_order': 12, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.51', 'aut_weyl_index': 48, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '4.h1.a1'], 'contains': ['16.b1.a1', '16.e1.a1', '16.f1.a1', '24.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1348, -1, 2170, -1, 956, -1, 7943, -1], 'generators': [5042476, 2122432, 575726, 3333742, 4642820], 'label': '384.17956.8.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.d1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 269515136
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.230', 'aut_weyl_index': 16, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '4.h1.a1'], 'contains': ['16.b1.a1', '16.g1.a1', '16.h1.a1', '24.f1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1913, -1, 2283, -1, 1611, -1, 7775, -1], 'generators': [4265251, 3333742, 2166683, 6632600, 2122432], 'label': '384.17956.8.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.e1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 269515137
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.230', 'aut_weyl_index': 16, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '4.h1.a1'], 'contains': ['16.c1.a1', '16.e1.a1', '16.g1.a1', '16.m1.a1', '16.m1.a2', '24.i1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1028, -1, 1631, -1, 1184, -1, 8217, -1], 'generators': [132667, 3333742, 575726, 2122432, 6632600], 'label': '384.17956.8.f1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.f1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 269515138
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.230', 'aut_weyl_index': 16, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '4.h1.a1'], 'contains': ['16.c1.a1', '16.f1.a1', '16.h1.a1', '16.k1.a1', '16.k1.b1', '24.j1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2933, -1, 3025, -1, 1827, -1, 7473, -1], 'generators': [132667, 3333742, 5042476, 4642820, 2122432], 'label': '384.17956.8.g1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.g1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 269515139
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.230', 'aut_weyl_index': 16, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '4.h1.a1'], 'contains': ['16.d1.a1', '16.e1.a1', '16.h1.a1', '24.r1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1175, -1, 2579, -1, 1400, -1, 8075, -1], 'generators': [5042485, 3333742, 575726, 4642820, 2122432], 'label': '384.17956.8.h1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.h1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 269515140
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.230', 'aut_weyl_index': 16, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '4.h1.a1'], 'contains': ['16.d1.a1', '16.f1.a1', '16.g1.a1', '24.s1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1522, -1, 2386, -1, 1505, -1, 7688, -1], 'generators': [4265251, 3333742, 5042476, 6632600, 2122432], 'label': '384.17956.8.i1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.i1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 269515141
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 32, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.i1.a1', '4.i1.b1'], 'contains': ['16.a1.a1', '24.bk1.a1', '32.e1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3502, -1, 4556, -1, 2168, -1, 7192, -1], 'generators': [2166683, 2122432, 3333742, 6174490, 4605946], 'label': '384.17956.8.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.j1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 269515142
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 32, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.j1.a1', '4.j1.b1'], 'contains': ['16.a1.a1', '24.bv1.a1', '32.h1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3920, -1, 4163, -1, 2827, -1, 6479, -1], 'generators': [5042476, 2122432, 3333742, 6174490, 4605946], 'label': '384.17956.8.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.k1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 269515143
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 32, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.i1.a1', '4.i1.b1'], 'contains': ['16.a1.a1', '24.by1.a1', '32.g1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3357, -1, 4444, -1, 1998, -1, 7333, -1], 'generators': [5734448, 2122432, 3333742, 2981098, 4605946], 'label': '384.17956.8.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.l1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 269515144
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '384.20162', 'aut_weyl_index': 4, 'centralizer': '48.c1.a1', 'complements': ['192.d1.a1', '192.d1.b1', '192.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.a1', '4.g1.a1', '4.j1.a1', '4.j1.b1', '6.j1.a1', '8.g1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3610, 673, 4196, 5662, 3084, 605, 6104, 1965], 'generators': [132667, 4605946, 6174490, 5042476, 2122432, 4642820, 3333742], 'label': '384.17956.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.c1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '96.226', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 269515145
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 32, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.j1.a1', '4.j1.b1'], 'contains': ['16.a1.a1', '24.ca1.a1', '32.i1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4293, -1, 4240, -1, 2946, -1, 6577, -1], 'generators': [5042485, 2122432, 3333742, 6174490, 4605946], 'label': '384.17956.8.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.m1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 269515146
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '96.226', 'aut_weyl_index': 16, 'centralizer': '48.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.d1.a1', '6.g1.a1'], 'contains': ['24.b1.a1', '24.e1.a1', '24.y1.a1', '24.bi1.a1', '24.bk1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5947, 8635, 7561, 8314, 5479, 8327, 2882, 8316], 'generators': [2166683, 4642820, 6164698, 4605946], 'label': '384.17956.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['24.b1.a1', '48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 269515147
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '96.226', 'aut_weyl_index': 16, 'centralizer': '48.c1.a1', 'complements': ['32.o1.a1', '32.o1.a2', '32.o1.c1', '32.o1.c2', '32.o1.b2', '32.o1.b1', '32.o1.d2', '32.o1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.a1.a1', '6.j1.a1', '6.n1.a1'], 'contains': ['24.b1.a1', '24.o1.a1', '24.q1.a1', '24.bu1.a1', '24.bv1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6833, 6497, 6070, 7144, 8246, 7239, 1172, 6261], 'generators': [5042476, 4642820, 6164698, 4605946], 'label': '384.17956.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.c1.a1', '6.a1.a1'], 'normal_contains': ['24.b1.a1', '48.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '96.226', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 269515148
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '12.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '96.226', 'aut_weyl_index': 16, 'centralizer': '48.b1.a1', 'complements': ['32.o1.a1', '32.o1.a2', '32.o1.c1', '32.o1.c2', '32.o1.b2', '32.o1.b1', '32.o1.d2', '32.o1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.a1.a1', '6.k1.a1', '6.o1.a1'], 'contains': ['24.b1.a1', '24.v1.a1', '24.x1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5041, 7580, 4974, 6051, 5649, 6222, 5226, 7266], 'generators': [575726, 6164698, 4605946], 'label': '384.17956.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.e1.a1', '6.a1.a1'], 'normal_contains': ['24.b1.a1', '48.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '96.226', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 269515149
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1'], 'contains': ['24.c1.a1', '24.d1.a1', '24.f1.a1', '24.g1.a1', '24.k1.a1', '24.m1.a1', '24.t1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2007, -1, 3345, -1, 3313, -1, 6164, -1], 'generators': [132667, 2366842, 4532591], 'label': '384.17956.12.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.d1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 269515150
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 24, 'centralizer': '48.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.b1.a1'], 'contains': ['24.a1.a1', '24.c1.a1', '24.f1.a1', '24.i1.a1', '24.j1.a1', '24.r1.a1', '24.s1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1831, -1, 2793, -1, 3106, -1, 6334, -1], 'generators': [132667, 5042476, 575726], 'label': '384.17956.12.e1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.e1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 269515151
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 24, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.c1.a1', '6.d1.a1'], 'contains': ['24.c1.a1', '24.e1.a1', '24.h1.a1', '24.l1.a1', '24.u1.a1', '24.bg1.a1', '24.bg1.b1', '24.bh1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3610, -1, 4141, -1, 4017, -1, 5366, -1], 'generators': [132667, 2166683, 4642820, 4605946], 'label': '384.17956.12.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.f1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 269515152
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.51', 'aut_weyl_index': 48, 'centralizer': '24.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.b1.a1', '6.e1.a1'], 'contains': ['24.a1.a1', '24.d1.a1', '24.e1.a1', '24.n1.a1', '24.o1.a1', '24.v1.a1', '24.w1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3774, -1, 4457, -1, 3848, -1, 5505, -1], 'generators': [5042476, 575726, 6164698], 'label': '384.17956.12.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.g1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 269515153
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.c1.a1', '6.f1.a1'], 'contains': ['24.d1.a1', '24.e1.a1', '24.p1.a1', '24.q1.a1', '24.x1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5162, -1, 5069, -1, 5792, -1, 4720, -1], 'generators': [2366842, 4532591, 6164698], 'label': '384.17956.12.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.h1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 269515154
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.f1.a1', '6.g1.a1'], 'contains': ['24.e1.a1', '24.f1.a1', '24.z1.a1', '24.ba1.a1', '24.bf1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5382, -1, 4882, -1, 4817, -1, 4826, -1], 'generators': [4265251, 2166683, 6174490], 'label': '384.17956.12.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.i1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 269515155
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '384.20162', 'aut_weyl_index': 4, 'centralizer': '48.b1.a1', 'complements': ['192.f1.a1', '192.d1.a1', '192.d1.b1', '192.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.e1.a1', '4.f1.a1', '6.k1.a1', '8.f1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2409, 2164, 3332, 4159, 1843, 1942, 6727, 618], 'generators': [132667, 4605946, 6174490, 575726, 2122432, 6632600, 3333742], 'label': '384.17956.2.e1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.e1.a1', '4.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '96.226', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 269515156
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.51', 'aut_weyl_index': 48, 'centralizer': '12.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.e1.a1', '6.f1.a1'], 'contains': ['24.e1.a1', '24.bb1.a1', '24.be1.a1', '24.bj1.a1', '24.bj1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8679, -1, 9155, -1, 6182, -1, 2315, -1], 'generators': [6166711, 2166683, 4642820], 'label': '384.17956.12.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.j1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269515157
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.51', 'aut_weyl_index': 48, 'centralizer': '24.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.e1.a1', '6.g1.a1'], 'contains': ['24.e1.a1', '24.bc1.a1', '24.bd1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7749, -1, 6602, -1, 8563, -1, 3636, -1], 'generators': [697885, 2166683], 'label': '384.17956.12.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.k1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 269515158
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1'], 'contains': ['24.g1.a1', '24.h1.a1', '24.i1.a1', '24.m1.a1', '24.n1.a1', '24.r1.a1', '24.bf1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2628, -1, 3575, -1, 3705, -1, 5841, -1], 'generators': [132667, 2366842, 575726], 'label': '384.17956.12.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.l1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 269515159
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1'], 'contains': ['24.h1.a1', '24.j1.a1', '24.k1.a1', '24.s1.a1', '24.t1.a1', '24.w1.a1', '24.bf1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2780, -1, 3731, -1, 3526, -1, 5988, -1], 'generators': [132667, 5042476, 4532591], 'label': '384.17956.12.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.m1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 269515160
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 24, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.h1.a1', '6.j1.a1'], 'contains': ['24.g1.a1', '24.j1.a1', '24.l1.a1', '24.o1.a1', '24.ba1.a1', '24.bl1.a1', '24.bl1.b1', '24.bm1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5788, -1, 5728, -1, 7866, -1, 4481, -1], 'generators': [132667, 5042476, 4642820, 4605946], 'label': '384.17956.12.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.n1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 269515161
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 24, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.i1.a1', '6.j1.a1'], 'contains': ['24.l1.a1', '24.q1.a1', '24.bd1.a1', '24.bn1.a1', '24.bn1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7871, -1, 6440, -1, 9122, -1, 1028, -1], 'generators': [132667, 1974553, 4642820], 'label': '384.17956.12.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.o1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.o1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 269515162
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '12.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 24, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.i1.a1', '6.k1.a1'], 'contains': ['24.i1.a1', '24.k1.a1', '24.l1.a1', '24.v1.a1', '24.z1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3316, -1, 4032, -1, 4545, -1, 5635, -1], 'generators': [132667, 575726, 4605946], 'label': '384.17956.12.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.p1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.p1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 269515163
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '12.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 24, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.h1.a1', '6.k1.a1'], 'contains': ['24.l1.a1', '24.x1.a1', '24.bc1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5572, -1, 5436, -1, 8681, -1, 5010, -1], 'generators': [132667, 4142903], 'label': '384.17956.12.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.q1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.q1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 269515164
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '12.r1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 24, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.h1.a1', '6.i1.a1'], 'contains': ['24.l1.a1', '24.y1.a1', '24.be1.a1', '24.bp1.a1', '24.bp1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6644, -1, 9014, -1, 7221, -1, 2703, -1], 'generators': [132667, 3035090, 4642820], 'label': '384.17956.12.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.r1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.r1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 269515165
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '12.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 48, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.d1.a1', '6.j1.a1', '6.k1.a1'], 'contains': ['24.b1.a1', '24.l1.a1', '24.bb1.a1', '24.bo1.a1', '24.bo1.b1', '24.bq1.a1', '24.bq1.b1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8973, -1, 8686, -1, 6651, -1, 1355, -1], 'generators': [132667, 4642820, 6164698], 'label': '384.17956.12.s1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.s1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.s1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269515166
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '384.20162', 'aut_weyl_index': 4, 'centralizer': '96.a1.a1', 'complements': ['192.d1.a1', '192.d1.b1', '192.e1.a1', '192.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.d1.a1', '4.f1.a1', '6.n1.a1', '8.i1.a1'], 'core': '2.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2606, 4650, 3565, 7057, 2619, 5781, 6432, 4200], 'generators': [4265251, 4605946, 2981098, 5042476, 2122432, 6632600, 3333742], 'label': '384.17956.2.f1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.d1.a1', '4.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.f1.a1', 'projective_image': '96.226', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.f1.a1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 269515167
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '12.t1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.l1.a1', '6.n1.a1'], 'contains': ['24.m1.a1', '24.o1.a1', '24.s1.a1', '24.u1.a1', '24.z1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4463, -1, 4585, -1, 4688, -1, 5108, -1], 'generators': [4265251, 5042476, 6174490], 'label': '384.17956.12.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.t1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.t1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 269515168
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '12.u1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.h1.a1', '6.l1.a1'], 'contains': ['24.o1.a1', '24.p1.a1', '24.w1.a1', '24.x1.a1', '24.y1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5272, -1, 5226, -1, 6027, -1, 4613, -1], 'generators': [5042476, 4532591, 6164698], 'label': '384.17956.12.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.u1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.u1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 269515169
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '12.v1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.51', 'aut_weyl_index': 48, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.j1.a1', '6.l1.a1'], 'contains': ['24.o1.a1', '24.bb1.a1', '24.bd1.a1', '24.br1.a1', '24.br1.b1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9157, -1, 8296, -1, 8953, -1, 681, -1], 'generators': [6166711, 5042476, 4642820], 'label': '384.17956.12.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.v1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.v1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269515170
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '12.w1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.51', 'aut_weyl_index': 48, 'centralizer': '24.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.h1.a1', '6.n1.a1'], 'contains': ['24.o1.a1', '24.bc1.a1', '24.be1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7992, -1, 6878, -1, 8799, -1, 3742, -1], 'generators': [697885, 5042476], 'label': '384.17956.12.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.w1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.w1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 269515171
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.m1.a1', '6.n1.a1'], 'contains': ['24.q1.a1', '24.u1.a1', '24.bc1.a1', '24.bs1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6306, -1, 5840, -1, 9638, -1, 3860, -1], 'generators': [697885, 2366842, 6174490], 'label': '384.17956.12.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.x1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 269515172
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '12.y1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.i1.a1', '6.m1.a1'], 'contains': ['24.n1.a1', '24.p1.a1', '24.q1.a1', '24.v1.a1', '24.y1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4929, -1, 5146, -1, 5909, -1, 4097, -1], 'generators': [2366842, 575726, 6164698], 'label': '384.17956.12.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.y1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.y1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 269515173
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '12.z1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.i1.a1', '6.n1.a1'], 'contains': ['24.q1.a1', '24.z1.a1', '24.be1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6959, -1, 6235, -1, 7717, -1, 3087, -1], 'generators': [4265251, 2366842], 'label': '384.17956.12.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.z1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.z1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 269515174
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '12.ba1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 24, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.j1.a1', '6.m1.a1'], 'contains': ['24.q1.a1', '24.ba1.a1', '24.bb1.a1', '24.bt1.a1', '24.bt1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9340, -1, 7420, -1, 9327, -1, 502, -1], 'generators': [6166711, 1974553, 4642820], 'label': '384.17956.12.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.ba1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 269515175
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '12.bb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.m1.a1', '6.o1.a1'], 'contains': ['24.r1.a1', '24.t1.a1', '24.u1.a1', '24.v1.a1', '24.ba1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3428, -1, 4727, -1, 4160, -1, 5743, -1], 'generators': [5042485, 575726, 4605946], 'label': '384.17956.12.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bb1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 269515176
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '12.bc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.l1.a1', '6.o1.a1'], 'contains': ['24.u1.a1', '24.x1.a1', '24.bd1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5482, -1, 5321, -1, 6831, -1, 4924, -1], 'generators': [1974700, 4142903], 'label': '384.17956.12.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bc1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 269515177
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '384.20162', 'aut_weyl_index': 4, 'centralizer': '96.a1.a1', 'complements': ['192.f1.a1', '192.d1.a1', '192.d1.b1', '192.e1.a1', '192.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.d1.a1', '4.e1.a1', '4.g1.a1', '6.o1.a1', '8.h1.a1'], 'core': '2.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2831, 7838, 3725, 2499, 2108, 4399, 6945, 5591], 'generators': [5042485, 4605946, 6174490, 575726, 2122432, 4642820, 3333742], 'label': '384.17956.2.g1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.d1.a1', '4.e1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.g1.a1', 'projective_image': '96.226', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.g1.a1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 269515178
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '12.bd1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 24, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.l1.a1', '6.m1.a1'], 'contains': ['24.u1.a1', '24.y1.a1', '24.bb1.a1', '24.bx1.a1', '24.bx1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6131, -1, 8851, -1, 6398, -1, 1772, -1], 'generators': [6166711, 3035090, 4642820], 'label': '384.17956.12.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bd1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 269515179
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '12.be1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 48, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.d1.a1', '6.n1.a1', '6.o1.a1'], 'contains': ['24.b1.a1', '24.u1.a1', '24.be1.a1', '24.bw1.a1', '24.by1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8315, -1, 8523, -1, 5009, -1, 3235, -1], 'generators': [5734448, 4642820, 4605946], 'label': '384.17956.12.be1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.be1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.be1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 269515180
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '12.bf1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.51', 'aut_weyl_index': 48, 'centralizer': '12.bf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.k1.a1', '6.m1.a1'], 'contains': ['24.v1.a1', '24.bb1.a1', '24.bc1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7627, -1, 6695, -1, 8420, -1, 3990, -1], 'generators': [6166711, 575726], 'label': '384.17956.12.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bf1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 269515181
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '12.bg1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.51', 'aut_weyl_index': 48, 'centralizer': '24.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.i1.a1', '6.o1.a1'], 'contains': ['24.v1.a1', '24.bd1.a1', '24.be1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8468, -1, 7304, -1, 7507, -1, 3383, -1], 'generators': [1974700, 575726], 'label': '384.17956.12.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bg1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 269515182
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '12.bh1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 24, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.k1.a1', '6.l1.a1'], 'contains': ['24.x1.a1', '24.z1.a1', '24.bb1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5661, -1, 5583, -1, 6936, -1, 4358, -1], 'generators': [6166711, 4142903], 'label': '384.17956.12.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bh1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 269515183
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '12.bi1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.h1.a1', '6.o1.a1'], 'contains': ['24.x1.a1', '24.ba1.a1', '24.be1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8557, -1, 6526, -1, 7401, -1, 4271, -1], 'generators': [5042485, 4142903], 'label': '384.17956.12.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bi1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 269515184
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '12.bj1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '6.i1.a1', '6.l1.a1'], 'contains': ['24.y1.a1', '24.z1.a1', '24.bd1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6491, -1, 6355, -1, 7612, -1, 3000, -1], 'generators': [4265251, 4593842], 'label': '384.17956.12.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bj1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 269515185
    {'ambient': '384.17956', 'aut_centralizer_order': 8, 'aut_label': '12.bk1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '6.h1.a1', '6.m1.a1'], 'contains': ['24.y1.a1', '24.ba1.a1', '24.bc1.a1', '24.cb1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8128, -1, 6997, -1, 9811, -1, 3504, -1], 'generators': [697885, 4593842, 6174490], 'label': '384.17956.12.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bk1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 269515186
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '12.bl1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 48, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.g1.a1', '6.k1.a1', '6.n1.a1'], 'contains': ['24.b1.a1', '24.z1.a1', '24.bc1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7517, -1, 6167, -1, 7042, -1, 4184, -1], 'generators': [4265251, 4605946], 'label': '384.17956.12.bl1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bl1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 269515187
    {'ambient': '384.17956', 'aut_centralizer_order': 16, 'aut_label': '12.bm1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 48, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.g1.a1', '6.j1.a1', '6.o1.a1'], 'contains': ['24.b1.a1', '24.ba1.a1', '24.bd1.a1', '24.bz1.a1', '24.ca1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9933, -1, 7955, -1, 8056, -1, 2163, -1], 'generators': [5042485, 4642820, 6164698], 'label': '384.17956.12.bm1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bm1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 269515188
    {'ambient': '384.17956', 'aut_centralizer_order': 1, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.10494202', 'aut_weyl_index': 3, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.c1.a1', '6.d1.a1', '6.e1.a1', '6.f1.a1', '6.g1.a1', '6.h1.a1', '6.i1.a1', '6.j1.a1', '6.k1.a1', '6.l1.a1', '6.m1.a1', '6.n1.a1', '6.o1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6541, -1, 6313, -1, 7085, -1, 4110, -1], 'generators': [132667, 5042476, 575726, 6164698], 'label': '384.17956.3.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 269515189
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '12.bn1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 48, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1'], 'contains': ['24.bg1.a1', '24.bi1.a1', '24.bj1.b1', '24.bo1.a1', '24.bp1.a1', '24.bw1.a1', '24.bx1.b1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7327, -1, 9732, -1, 5262, -1, 859, -1], 'generators': [132667, 2166683, 3909614], 'label': '384.17956.12.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.bn1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269515190
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '12.bn1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 48, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1'], 'contains': ['24.bg1.b1', '24.bi1.a1', '24.bj1.a1', '24.bo1.b1', '24.bp1.b1', '24.bw1.a1', '24.bx1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7327, -1, 9956, -1, 5262, -1, 1981, -1], 'generators': [6166711, 2166683, 3909614], 'label': '384.17956.12.bn1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.bn1.b1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bn1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269515191
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '12.bo1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 48, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.d1.a1'], 'contains': ['24.bg1.a1', '24.bj1.a1', '24.bk1.a1', '24.bp1.a1', '24.bq1.a1', '24.bx1.a1', '24.by1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7112, -1, 9295, -1, 4340, -1, 2494, -1], 'generators': [132667, 2166683, 6164698], 'label': '384.17956.12.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.bo1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269515192
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '12.bo1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 48, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.b1', '6.d1.a1'], 'contains': ['24.bg1.b1', '24.bj1.b1', '24.bk1.a1', '24.bp1.b1', '24.bq1.b1', '24.bx1.b1', '24.by1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7112, -1, 9459, -1, 4340, -1, 1564, -1], 'generators': [4642835, 2166683, 6164698], 'label': '384.17956.12.bo1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.bo1.b1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bo1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269515193
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '12.bp1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 48, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1.a1'], 'contains': ['24.bl1.a1', '24.bn1.a1', '24.bo1.a1', '24.br1.b1', '24.bt1.b1', '24.bu1.a1', '24.bz1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9773, -1, 8204, -1, 9958, -1, 93, -1], 'generators': [132667, 5042476, 3909614], 'label': '384.17956.12.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '12.bp1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269515194
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '12.bp1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 48, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1.a1'], 'contains': ['24.bl1.b1', '24.bn1.b1', '24.bo1.b1', '24.br1.a1', '24.bt1.a1', '24.bu1.a1', '24.bz1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9773, -1, 8135, -1, 9958, -1, 267, -1], 'generators': [6166711, 5042476, 3909614], 'label': '384.17956.12.bp1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '12.bp1.b1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bp1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269515195
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '12.bq1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 48, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '6.j1.a1'], 'contains': ['24.bl1.a1', '24.bn1.a1', '24.bq1.a1', '24.br1.a1', '24.bt1.a1', '24.bv1.a1', '24.ca1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9683, -1, 7654, -1, 9506, -1, 354, -1], 'generators': [132667, 5042476, 6164698], 'label': '384.17956.12.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '12.bq1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269515196
    {'ambient': '384.17956', 'aut_centralizer_order': 4, 'aut_label': '12.bq1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 48, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.b1', '6.j1.a1'], 'contains': ['24.bl1.b1', '24.bn1.b1', '24.bq1.b1', '24.br1.b1', '24.bt1.b1', '24.bv1.a1', '24.ca1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9683, -1, 7723, -1, 9506, -1, 180, -1], 'generators': [4642835, 5042476, 6164698], 'label': '384.17956.12.bq1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '12.bq1.b1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bq1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 269515197
    {'ambient': '384.17956', 'aut_centralizer_order': 64, 'aut_label': '16.a1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 64, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '8.j1.a1', '8.k1.a1', '8.l1.a1', '8.m1.a1'], 'contains': ['48.d1.a1', '64.b1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4181, 4694, 4271, 3584, 2354, 4578, 6956, 3401], 'generators': [3333742, 6174490, 4605946, 2122432], 'label': '384.17956.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.b1', '8.b1.a1'], 'normal_contains': ['48.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '192.1472', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 269515198
    {'ambient': '384.17956', 'aut_centralizer_order': 48, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 192, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '8.c1.a1', '8.d1.a1', '8.e1.a1'], 'contains': ['32.a1.a1', '32.b1.a1', '32.b1.b1', '32.e1.a1', '32.j1.a1', '48.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [523, -1, 2067, -1, 795, -1, 8572, -1], 'generators': [2166683, 4642820, 2122432, 3333742], 'label': '384.17956.16.b1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.b1.a1', 'projective_image': '96.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}